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Year 12 Physics Notes 2010 HSC
Space
9.2.1 The Earth has a gravitational field that exerts a force on objects both on it and around it
o Define weight as the force on an object due to a gravitational field
Weight is the force which acts on a mass within a gravitational field. Weight is proportional to the strength of the gravitational field. The SI unit for weight is the Newton (N).
Mass is an absolute measurement of how much matter is in a body or an object. Mass has the SI unit of kilogram (kg)
Mass and weight can be related by a simple equation: F = mg where
F = weight or the weight force, measured in N
m = the mass of the object, measured in kg and
g = gravitational acceleration on the object due to the presence of the gravitational field, measured in ms-2
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o Explain that a change in gravitational potential energy is related to work done
Gravitational Potential Energy, Ep, is the energy stored in a body due to its position in a gravitational field. This energy can be released (and converted into kinetic energy) when the body is allowed to fall.
When an object is lifted to a height above the ground, the force required to lift the object must be equal to (strictly speaking just greater than) the weight force of the object. Hence the work done on the object is equivalent to its gain in gravitational potential energy.
The work done, W, on an object when a force acting on the object causes it to move is given by:
W = F x s, where F is the force acting, and s is the distance the object is moved while the force is acting.
o Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field
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Gravitational potential energy is the work done to move an object from a very large distance away to a point in a gravitational field.
Why is gravitational potential energy negative?
This is because at a position very far away from Earth, an object would experience negligible gravitational attraction. If any such object was then given a small push towards Earth, it would begin to fall towards Earth, losing gravitational potential energy as it gains kinetic energy. Hence the more gravitational potential energy the object loses, the more negative the value of Ep (subtracting from zero results in a negative value)
Derived from above, where Gravitational potential energy is equal to work done
Ep = W = F x s
But we know F = mg
And S = h (As height is the distance moved)
Hence Ep = mgh
However, this equation is only accurate when the object is near the surface of the Earth. The equation assumes that the value of g is a constant and does not change with altitude, hence a universal definition of gravitational potential energy is required.
Derivation: Simultaneously solve
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Hence
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o Perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer-assisted technology and identify reason for possible variations from the value 9.8 ms-2
|Note: We will use the equation: |
| |
|[pic] |
| |
|Where T is the period and l is the length of the string. |
|[pic] |
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|Method: |
|Measure the length of the pendulum from the top of the string to the centre of the mass. |
|Move the mass so it makes an angle of about 5 degrees with the vertical. |
|Release the mass and record the time for 10 complete oscillations. |
|Change the length of the string and repeat the experiment. |
|Graph the results in the graph T2 vs l and determine the gradient of the line of best fit to determine the value of ‘g’ |
The reasons for possible variations from the value 9.8 ms-2 are;
o The simple pendulum motion might have transformed into a conical pendulum, and hence the result from using the formula for the period of a pendulum would have been inaccurate.
o Systematic errors (errors in the measuring devices, such as an inaccurate ruler, a slightly slow stopwatch, etc)
o Random errors (air resistance, reaction time, friction, parallax error, lateral motion of the pendulum)
o Gather secondary information to predict the value of acceleration due to gravity on other planets
The value of the gravitational acceleration, g, on the surface on any planet or other body can be found using its radius and its mass. Once g is known, the weight of any object can be calculated.
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In words, the gravitational acceleration of any planet is proportional to the mass of the planet and inversely proportional to the square of the distance from the centre of the planet.
The SI unit of g can be both ms-2 or Nkg-1
o Analyse information using the expression: F = mg to determine the weight force for a body on Earth and for the same body on other planets
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Since mass is the absolute quantity of matter in an object, it doesn’t change no matter where the object is. However, since weight is the force on an object due to a gravitational field, then as the gravitational field strength changes, the weight also changes.
In F = mg, both F and g are vector quantities, that is they have direction.
9.2.2 Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth
o Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components
Projectile motion is a motion that is under the influence of only one force – the weight force. The trajectory of a projectile is subject to its own inertia and to gravitational force, and the combination of these two forces result in the object following a parabolic path.
For projectile motion, there are two simple rules that govern it:
1. The horizontal motion and vertical motion are independent. They can be analyzed and calculated separately
2. The horizontal velocity is always constant (neglecting the air friction). The vertical motion has a constant acceleration (downward at 9.8 ms-2) and gravity is the only force acting on the object
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o Describe Galileo’s analysis of projectile motion
Galileo’s analysis of projectile motion resulted from the careful studying objects of rolling down an inclined plane. He came to the conclusion that:
• 2 dimensional – Horizontal and vertical components are completely independent from each other
• Horizontal component has constant velocity
• Vertical component has constant acceleration which is always acting downwards (due to gravity ( which he didn’t know of at the time)
• Path is parabola
• At any point or time the net displacement of velocity is the resultant of the horizontal and vertical component.
o Solve problems and analyze information to calculate the actual velocity of a projectile from its horizontal and vertical components using:
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Remember positives and negatives in equations
Convert to horizontal and vertical components first
List information
Vector addition is sometimes needed
Remember to add a DIRECTION and ANGLE and UNIT
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PRACTISE MASTER IT NOW
o Explain the concept of escape velocity in terms of the:
- gravitational constant
- mass and radius of the planet
Escape Velocity is the velocity at which an object is able to escape from the gravitational field of a planet.
If an object is to escape the gravitational field of a planet, its kinetic energy due to its velocity must exceed or at least equal its gravitational potential energy. Therefore;
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Note that escape velocity is not dependent on the mass of the escaping object, since m is cancelled out from both sides of the equation. As ‘G’ is also a constant, the only two variables are ‘r’, the radius of the planet and ‘M’, the mass of the planet itself.
|This has two consequences: |
|Different planets have different escape velocities |
|A massive body, such as a rocket, will have the same escape velocity as a small object like an atom |
o Outline Newton’s concept of escape velocity
Newton reasoned that, given the faster a projectile was fired the further it would go before it hit the ground, then there must be a firing speed which would cause it to orbit the Earth back to its starting point. He further reasoned that with greater speed, it will escape the Earth’s gravitational pull and never come back.
o Identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch
G force is a measure of acceleration force using the Earth’s gravitational acceleration as the unit.
As we stand, sit or walk we experience 1 g, due to the normal force that pushes upwards, as we feel our ‘normal’ weight.
A positive g force is one that is directed from the feet to the head (upwards), whereas a negative g force is in the other direction (downwards). If a person experiences the sensation of feeling more weight than normal, the g force is positive. Feeling less weight is due to negative g forces.
Enormous positive G force tends to train blood away from the head and brain, causing unconsciousness and death if it is prolonged
Enormous negative g force causes the blood to rush from the feet to the head and brain, which leads to excessive bleeding and brain damage.
As a rocket accelerates upwards the downward force (gravity +the reaction to the upward acceleration) on the astronaut increases
F = mg + ma
G-force is acceleration, so make a the subject.
Why G forces?
▪ We measure the forces astronauts experience as g-forces – multiples of the weight of the astronaut. The g-force scale makes it easier to communicate the force on astronauts
▪ Astronauts will have different masses so the total force acting on them will be different, but regardless of their mass they will be experiencing the same g-force.
▪ G-force = (rocket acceleration + 9.8)/(9.8)
o Discuss the effect of the Earth’s orbital motion and its rotational motion on the launch of a rocket
The Earth’s orbital motion and its rotational motion allows the launching of rockets to be more economical and efficient, as they reduce the amount of fuel required to achieve the same orbital velocity.
The Earth rotates on its axis from west to east at a speed of 465 ms-1 at the equator. At the same time it is orbiting the sun with a speed of 29.8kms-2. These high speeds can contribute to rocket launchings.
To launch a satellite that is to orbit the Earth, the rocket is usually launched in an eastward direction, the same direction as the Earth’s rotation. This is to take advantage of the rotational speed of the Earth so that the rocket can gain additional velocity during its lift-off without requiring fuel. Also, this type of launch is usually located at places near the equator, where the linear orbital speed of the Earth’s spin is the greatest.
If rockets are launched towards the east at the equator the rotational speed of the Earth ads 1700 kph (472ms-1) to their motion.
Also note that the Earth must be in the right position to take advantage of this orbital speed, so there are ‘launch windows’ during which a rocket much be launched. If it is launched outside these windows, the rocket will start its journey in the wrong direction or at the wrong time.
o Perform a first-hand investigation, gather information and analyze data to calculate initial and final velocity, maximum height reached, range and time of flight of a projectile for a range of situations using simulations, data loggers and computer analysis
Aim – To analyze an example of projectile motion and compared the calculated value for its horizontal displacement to the one measured experimentally
Equipment -
RAMP, ball bearing, foam cup, metre ruler
Method –
- Set up the experiment as shown:
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- Use a plumb bob and string to measure the height of the ramp (deltaY)
- Place the ball-bearing at the top of the ramp and allow it to roll down and along the horizontal section. Measure the time taken around 5 times and average the results.
- Calculate the horizontal velocity of the ball-bearing
- Using the height of the balcony and the horizontal velocity of the ball–bearing to calculate the horizontal range of the bearing from the edge of the bench. Mark this spot with chalk
- Place a foam cup in a direct line with the ramp and on the marked range.
- Release the ball-bearing from the top of the ramp, and see if it hits the target.
o Analyse the changing acceleration of a rocket during launch in terms of the:
Law of Conservation of Momentum
Forces experienced by astronauts
The law of conservation of momentum is also known as Newton’s third law. This law states that when one object exerts a force on another, it will itself receive an equal force but opposite in direction.
In the engine, the liquefied gases of hydrogen and oxygen combust and produce enormous amounts of energy. The gases push at the end of the rocket downwards with a very high velocity, and as these gases are pushed, the rocket receives an equal but opposite force, in accordance with Newton’s third law.
The upward acceleration of a rocket as it ascends increases gradually for three reasons;
1. As the rocket ascends, fuel is consumed, which results in a decreases in mass of the rocket.
2. The direction of the velocity changes from being vertical to horizontal as the rocket goes into orbit – thus its acceleration is no longer reduced by g
3. As the rocket ascends, it moves further and further away from the planet, this results in a decrease in the force of gravity. Consequently, the net upward force acting on the rocket increases, hence its acceleration increases.
The straight-line portion of the graph indicates that shortly after the engine is turned on, there will be acceleration. The curved portion shows the acceleration increases gradually over time. Note that for multistage rockets, the graph will be similar, except the acceleration drops to ‘-g’ at the end of each stage and rises in a similar way as before when a new stage is turned on.
To help astronauts withstand extremely large g forces during lift-offs, astronauts lie face up on a body contoured couch, as this provides maximum body support and stops blood draining from their heads.
o Analyze the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth
Objects traveling in Uniform circular motion have a constant orbital speed but are always changing direction. This means they have a changing orbital velocity. Since any change in velocity involves acceleration, the acceleration in circular motion is referred to as centripetal acceleration.
Centripetal acceleration always acts towards the centre of the circle and the magnitude of acceleration can be expressed as:
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Centripetal force is the force that provides centripetal acceleration and sustains circular motion – and its direction is also always towards the centre of the circle. Note that centripetal force cannot be applied; it is the resultant of other forces
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eg. A car is going around a bend on a flat surface
Forces acting: Gravity, friction between tires and road, driving force, air resistance, normal reaction force
Forces contributing to centripetal force – Component of friction force (towards centre of circle)
eg2. Conical pendulum
Forces acting: Gravity, air resistance, tension in the string, driving force
Forces contributing to centripetal force – TsinA (horizontal component of tension in the string)
Satellites orbiting the Earth are in a state of free fall. As a satellite orbits the Earth, it is pulled downwards by the Earth’s gravitational field. What keeps the satellite from falling is its linear orbital velocity. This results in its path being circular, as shown here.
The circular motion described by satellites can be said to have two components: one that is constant tangential speed, the other being free fall with constant acceleration of gravity.
Since the horizontal and vertical motions are independent, while the satellite is describing a circle, it can be considered to be in a state of free fall, just like an object undergoing projectile motion.
o Solve problems and analyze information to calculate the centripetal force acting on a satellite undergoing uniform circular motion about the earth using:
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DO QUESTIONS ON THIS
REMEMBER THE RIGHT UNITS
o Solve problems and analyze information using:
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o Compare qualitatively low Earth and geo-stationary orbits
Geostationary satellites are satellites that are situated above the Earth’s equator and orbit the Earth with a period of 24 hours, remaining directly above a fixed point on the equator.
Low Earth orbit satellites are satellites with smaller orbital radii than those of geostationary satellites; their orbital periods are greater than those of geostationary satellites. They orbit the Earth many times per day, and do not need to orbit above the equator.
| |Geostationary Satellites |Low Earth orbit satellites |
|Key Differences |Stay at one position directly above a fixed point on the equator |Move above the Earth so do not have a fixed |
| |Orbit with the Earth’s rotation, so their periods are the same as |position |
| |that of the Earth |Periods are much smaller that that of the Earth. |
| |Situated at a very high altitude, approximately 35900 km above the|May orbit the Earth many times a day |
| |Earth’s surface |Much lower orbital altitude |
| |Have a limited view of the Earth’s surface |Can be made to pass above any point on Earth |
| | |Able to view the Earth’s entire surface over |
| | |several orbits |
|Advantages |Easy to track since each satellite stays at one position at all |Able to provide scans of different areas of the |
| |times |Earth many times a day |
| |Do not experience orbital decay |Low altitudes enable a closer view of the surface |
| | |of the Earth |
| | |Low altitudes allow rapid information transmission|
| | |with little delay |
| | |Low altitudes mean the launchings of these |
| | |satellites are easier and cheaper, as less fuel |
| | |for the same satellite mass is required |
|Disadvantages |Delay in information transmissions must be considered |Much effort is required to track these satellites,|
| |Each satellite has a limited view of the Earth as it only stays at|as they move rapidly above the Earth |
| |one point above the Earth. Therefore many geostationary satellites|Atmospheric drag is quite significant and orbital |
| |are required to provide coverage of the entire surface of the |decay is inevitable |
| |Earth. Even then, polar regions may still not be properly covered |The orbital paths of the satellites have to be |
| |Their high altitude makes launching processes more difficult and |controlled carefully to avoid interferences |
| |expensive |between one satellite and another |
|Main uses |Information relay; information is sent up to one satellite and is |Geotopographic studies: including patterns of the |
| |bounced off to another place on the Earth |growth of crops and spreading of deserts |
| |Communication satellites, eg. Foxtel |Remote sensing |
| |Weather monitoring |Studying weather patterns |
o Define the term orbital velocity and quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler’s Law of Periods
Orbital Velocity is the speed at which a satellite has to travel in order to orbit a planet.
Orbital velocity can be found by equating centripetal force Fc with gravitational attraction force Fg
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Notice that orbital speed does not depend on the mass of the satellite.
Furthermore, from this equation we can see that the orbital speed of a satellite is inversely proportional to the square root of its distance from the centre of the planet – that is, the lower the orbit, the faster the satellite needs to go to stay in a stable orbit.
Orbital speed is also proportional to the mass of the planet – that is, when the mass of the planet increases, the orbital velocity increases.
Let T = period of the orbit, that is, the time to complete one revolution (in seconds)
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o Account for the orbital decay of satellites in low Earth orbit
Orbital Decay refers to the loss of altitude of a spacecraft caused by friction between it and the atmosphere at the orbit altitude
As a low Earth orbit satellite orbits the Earth, friction will be generated as the satellite is usually placed within the upper limits of the Earth’s atmosphere. This resistive force will slow down the satellites orbital velocity and causes the satellite to drop to a lower orbit. The lower altitude means the satellite is now in a yet denser part of the atmosphere. This leads to an even greater resistive force acting on the satellite. The satellite will then slow down further at a faster rate, and as this process continues eventually its orbital velocity will be too small to sustain its circular orbital motion.
o Discuss the issues associated with safe re-entry into the Earth’s atmosphere and landing on the Earth’s surface
Spacecraft or space shuttles on their return to Earth are purely under the influence of gravity, and only the atmosphere provides a frictional medium to slow them down. There are many issues associated with safe re-entry into the Earth’s atmosphere and landing on the Earth’s surface.
➢ For a spacecraft to return safely, it is important that the spacecraft enters the atmosphere within the optimum re-entry angle. (Discussed in dot point below). Modern spacecraft, such as the space shuttle, have wings and controls that give pilots some control over re-entry
➢ Returning spacecraft are subject to intense heat due to atmospheric friction and to g-forces due to deceleration
➢ The enormous heat build-up upon re-entry is of great concern, and many methods need to be used to reduce the heat:
- Blunt nose produces a shock wave of air in front of them, and this absorbs much of the frictional heat.
- Sacrificial skins (such as fiberglass) that absorb much of the heat energy as they vaporize
- External porous silicon complex tiles are employed to insulate against heat, while internal reflective aluminium plates are used to reflect the excessive heat back into space
- Air conditioners which keep the interior of the spacecraft at normal room temperature
➢ Having survived re-entry, astronauts have to survive landing. Early spacecraft used parachutes to slow the capsule, so it could soft land in the ocean and be retrieved by ships.
➢ A further problem on re-entry is ionization blackout. This is caused as heat build0up due to atmospheric friction ionizes air around the re-entry capsule and stops radio signals from entering or leaving the capsule.
o Identify that there is an optimum angle for re-entry into the Earth’s atmosphere and the consequences of failing to achieve this
For a spacecraft to return safely, it is important to ensure the spacecraft enters the atmosphere at a certain angle called the optimum re-entry angle.
If the re-entry angle is too big, then the upward resistive force (the friction between the spacecraft and the atmosphere) experienced by the spacecraft will be too large, so that it will be decelerated too rapidly. The g force experienced by the astronauts will be too large to tolerate, and the huge friction produces an enormous amount of heat too rapidly so that it will cause the spacecraft to melt or burn up.
If the re-entry angle is too small, then the spacecraft will not enter but will bounce off the atmosphere, and return to space. A spacecraft may not have sufficient fuel to re-align itself for a second attempt at a controlled re-entry – and burn up.
The re-entry angle varies depending on the shape of the craft and its re-entry speed. For the Apollo mission re-entry craft this angle was between 5.2 and 7.2 degrees.
o Identify data sources, gather, analyze and present information on the contribution of one of the following to the development of space exploration: Tsiolkowsky, Oberth, Goddard, Esnault-Pelterie, O’Neill or von Braun
Robert H. Goddard (1882-1945)
• As a young man he was inspired by science fiction tales from Jules Verne and others
• He measured the fuel values for various rocket fuels, such as liquid hydrogen and oxygen
• Launched the world’s first liquid-fuel-powered rocket
• Launched the world’s first liquid-fuelled supersonic rocket
• He published a pamphlet on rocketry which was mocked by the New York Times, commenting on Goddard’s lack of the “basic physics ladled out daily in our high schools”. He none the less continued to research and work on rockets.
• Goddard stated that multistage or step rockets were the answer to achieving high altitudes
• Developed pumps for liquid fuels, as well as rocket engines which have automatic cooling systems
• After the U.S entered WWII, Goddard tried to convince the military of the potential value of rockets, but the government saw no usefulness to the war effort in his research. Goddard instead went to the U.S Navy to work on jet-assisted takeoff rockets for aircraft.
9.2.3 The Solar System is held together by gravity
o Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it
A gravitational field in the region surrounding a massive object has an action at a distance force on other masses within the field. When two masses approach one another their gravitational fields interact creating a mutually attractive force between them. The forces are equal in magnitude, and opposite in direction, and can be related to Newton’s Third Law, where every action has an equal and opposite reaction.
Note that field lines do not start or stop in empty space. They end on a mass and extend back all the way to infinity. Also field lines never cross.
Furthermore the gravitational field lines are equidistant and in a radial 3D pattern.
o Define Newton’s Law of Universal Gravitation:
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Newton’s Law of Universal Gravitation states that the force between any two objects in the universe is proportional to the product of their masses divided by the distance between their centres squared. This can be mathematically expressed as F = G(m1m2/r2), where F is the force of attraction, G is the universal gravitational constant 6.67 x 10-11 Nm2kg-2 , m1m2 are the masses of the two objects, and r is the distance between their centres.
Thus the strength of the gravitational force around a massive object is proportional to the value of its mass and decreases in inverse proportion to the square of the distance from the centre of the object.
o Present information and use available evidence to discuss the factors affecting the strength of the gravitational force
There are many factors that affect the strength of a gravitational field and consequently the strength of the gravitational force acting on an object placed at that point. The law of universal gravitation states that the size of the attraction force is proportional to mass and inversely proportional to the square of distance; therefore the bigger the mass and the closer the distance is from the mass object, the larger the gravitational force.
Note that only very large bodies product noticeable gravitational fields, this is due to gravity’s weakness (the small value of G)
On earth there are also many reason’s affecting the strength of gravitational force. For example;
|Cause of variation in acceleration due to |Comments |Effect on ‘g’ |
|gravity | | |
|The Earth is flattened at the poles |This means that the distance of the surface |Increases the local value of g at the poles. |
| |from the centre of the Earth is less at the |Decreases the local value of g at the equator. |
| |poles and more near the equator. | |
|The Earth is rotating on its axis |A person standing at the equator already has |At the equator, the spin effect is greatest |
| |the speed of rotation equal to that of the |resulting in a lowering of the value of g. As you |
| |Earth. The effect of this is to reduce the |travel from the equator to the poles, the spin |
| |apparent value of acceleration due to gravity |effect on g shrinks to zero. |
| |slightly. This effect is stronger at lower | |
| |latitudes, reducing to zero at the poles. | |
|Increasing altitude above the Earth’s surface |The earth’s gravitational field is a radial |g decreases with increasing altitude |
| |field which decreases as you move further from | |
| |the surface | |
| |G is proportional to 1/r2 | |
|The Earth’s lithosphere varies in thickness |Thickness variations are a product of the |g increases with increasing thickness. |
| |source and history of the material. Oceanic | |
| |crust is thinner than continental crust. | |
| |Continental curst is thickest under mountain | |
| |ranges | |
|The Earth’s lithosphere varies in structure and|Density variations occur due to the presence of|g increases with increasing density |
|density |concentrated and large mineral deposits or | |
| |petroleum gas and related liquids trapped in | |
| |sedimentary rocks and structures | |
|Tidal effects – Gravitational pull of the moon |The gravitational attraction of the sun and |If distance to centre increases the ‘g’ decreases |
|and sun |moon distorts the shape of the earth, thus | |
| |changing the distance of the Earth’s centre | |
o Solve problems and analyze information using:
[pic][pic]
DO QUESTIONS FOR THIS!!@!
REMEMBER IT IS THE DISTANCE BETWEEN CENTRE OF MASSES
USE CORRECT UNITS AND DIRECTION
o Discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating the motion of satellites
Newton’s Law of Universal Gravitation is an important mathematical equation which allows scientists to calculate the force of gravity acting on a satellite towards the Earth. Since the gravitational force of attraction also serves as the centripetal force for the circular orbital motion of a satellite while the satellite is in orbit, we can equate Fg = Fc
By equating these two equations we can derive the orbital velocity of the satellite. This is important as it allows scientists to calculate the motion of satellites in space, and hence the velocity needed for a satellite to maintain a stable orbit at various altitudes.
The Russian scientists responsible for the planning of Sputnik 1 were able to use Newton’s law of universal gravitation to calculate how fast the spacecraft needed to be propelled by the rockets so that it would maintain a stable orbit. All other satellites which have been placed in orbit since Sputnik 1 have used the same calculations.
In our modern society satellites are relied upon for many uses, including pay TV and other communications, detailed weather observations, etc.
o Identify that a slingshot effect can be provided by planets for space probes
The slingshot effect is the principle of using a planets gravitational field and orbital speed to help a space probe gain extra speed by flying past the planet. A major advantage of the slingshot effect is that it produces a change in velocity with very little expenditure of fuel, and also reduces the time of its trip.
How it works
When a space probe is passing close to a planet, the probe accelerates due to the force of the planet’s gravitational field. However, when the space probe moves away from the planet, it decelerates for the same reason. Effectively, the incoming speed of the probe is about the same as its receding speed except the trajectory or pathway of the probe has now been changed. However, since a planet is not stationary but is orbiting around the Sun, as the probe is swung around the planet it will also have the speed of the planet added to its original speed; hence the probe speeds up with respect to the Sun.
A major advantage of the slingshot effect is that it produces a change in velocity with very little expenditure of fuel.
The extra velocity gained by the probe does not come for ‘free’. When the slingshot effect takes place, momentum will still have to be conserved. Hence the planet will lose momentum equal to that of which the probe has gained. However the speed lost by the planet will be insignificant compared to the speed gained by the probe.
Note there is a very narrow launching window which requires careful calculations and planning
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9.2.4 Current and emerging understanding about time and space has been dependent upon earlier models of transmission of light
o Outline the features of the aether model for the transmission of light
Aether was once proposed to be an undetectable (by touch, smell or vision), extremely thin, elastic material that surrounded all matter and at the same time was permeable to all matter on Earth.
Aether was thought to be the medium through which light propagates, as scientists thought it was logical that light, like all other waves, require a medium of propagation.
The aether model suggested that the aether had to be solid to transmit transverse waves, but at the same time sufficiently thin to let planets move through it unimpeded. It followed that having a high elasticity meant aether behaved like a solid when it was subjected to instantaneous and varying forces, like that of transverse waves. However, it could be distorted infinitely when it was under continuous uni-directional force, such as the motion of planets.
Properties of aether for the transmission of light
- Fills Space – light travels everywhere
- Be stationary in space – light travels in straight lines. If the aether was moving this movement would change the path of light traveling through it
- Be transparent – we cannot see it
- Permeate all matter – light travels everywhere
- Have an extremely low density – it cannot be detected
- Have great elasticity – transfer of energy over long distances requires the medium transmitting the wave to be highly elastic otherwise significant amounts of energy will be ‘lost’ to the particles of the medium.
o Gather and process information to interpret the results of the Michelson-Morley experiment
The Michelson-Morley experiment was based on the fact that aether was stationary in space. Because of this property of aether, aether winds would be created when the Earth is orbiting the sun and moving through space.
The results of the experiment:
When the entire apparatus was rotated 90 degrees, no change in the interference pattern was observed.
The null result of the experiment meant that the motion of the Earth through the aether (aether wind) could not be detected. Consequently, the existence of the aether could not be proven. Many scientists accepted the results as proof of non-existence of aether, however many other scientists were still unwilling to let go of the idea of an aether, and argued that the equipment was too insensitive or there were errors with the model.
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o Describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether
This is essentially what Michelson and Morley did (referring to the boat race analogy) They raced two light rays over two courses, one into the supposed aether wind and one across it, then swung the apparatus through 90 degrees to interpose the rays. They were looking for a difference between the rays as they finished their race, from which they could calculate the value of the aether wind.
Aim – To measure the speed of light relative to Earth from different directions
Equipment – Interferometer mounted on a large stone block floating on mercury so it could be rotated to repeat the experiment in different directions
Hypothesis - Interference patterns would indicate differences in the speed of light and give evidence for the existence of aether
Observations – No interference patterns observed
Results – Null result
Conclusion – None could be made
o Discuss the role of the Michelson-Morley experiments in making determinations about competing theories
- The Michelson-Morley experiment was one of those that split the aether believers two ways. Some maintained their belief and others rejected the idea of aether. However, there was still not alternate theory for light, so the problem of how light was transmitted still remained.
- Special relativity received a warm welcome by scientists mainly because of its consequences for light, but perhaps, because the Michelson-Morley results changed many scientists’ minds about the aether, and scientists were ready to give Einstein’s ideas some consideration
- The Michelson-Morley experiment has been able to help scientists of the twentieth century to reject the aether model and accept Einstein’s relativity. In this sense, it has been an important experiment in helping others to decide between competing theories, along with the comparative success of relativity experiments.
Hence the Michelson-Morley experiment played a significant role in making determinations about competing theories. It split up the aether believers into two groups, and arguable increased the open-mindedness of scientists. This further led to the scientific community heavily debating the aether model, and influenced scientists to readily make determinations about competing theories, and accept Einstein’s special theory of relativity
o Outline the nature of inertial frames of reference
A frame of reference is anything with respect to which we describe motion and take measurements. Eg. the frame of reference of a car is usually the ground. The frame of a person reading a book at their desk can be their desk (in which they are stationary), or the sun (in which they are orbiting with a speed of 30km/s
An inertial frame of reference is anything with respect to which we describe motion and take measurements, which are either stationary or moving with a constant velocity. It is a non-accelerated environment. (Including free fall frames)
For example if you are on a train with eye muffs and blindfolded, you will not know whether or not the train is moving a constant velocity or whether the train is stationary.
|Note that: |
|The principle of relativity only applies for non-accelerated steady motion. |
|When you are within an inertial frame of reference you cannot perform any mechanical experiment or observation that would reveal to you |
|whether you were moving with uniform velocity or standing still. |
A non-inertial frame of reference is one that is undergoing acceleration. Eg. A train slowing down or speeding up.
o Discuss the principle of relativity
The Principle of Relativity;
• All motion is relative. In physics this refers to the fact that constant velocity motion cannot be detected unless we have a frame of reference to compare it to.
• The principle of relativity applies only for non-accelerated steady motion. (Inertial frame of reference
• All inertial frames of reference are equal and no inertial frame of reference is truer than others
• The absence of aether also meant the velocity of light was constant, regardless of the relative motion of the source and observer
While the principle of relativity was accepted for most events, the aether theory meant that it did not hold for light. If the aether existed, then measurements of the speed of light made from an object moving with constant velocity would give different values, depending on which way the object was moving relative to the aether. This would enable the observer to determine that they were in an inertial frame of reference. This would violate the principle of relativity – constant motion cannot be detected without reference to a fixed position outside the frame of reference. Hence, Albert Einstein devised and put forward his special theory of relativity, which did not prove or disprove the existence of the aether – but simply made its existence unnecessary.
o Describe the significance of Einstein’s assumption of the constancy of the speed of light
• One of Einstein’s assumptions was that the speed of light was constant, regardless of the state of motion of an observer.
• This was significant in that it made the concept of aether unnecessary. Also it meant that we can no longer regard length and time as fundamental (unchanging) quantities.
• This led to the idea of the space-time continuum, where any event has 4 dimensions.
• A further consequence of Einstein’s work on light was his clarification of the principle of simultaneity in which he states that two events which are seen to be simultaneous in one frame of reference may not be seen to be simultaneous in a different frame of reference.
• The constancy of the speed of light also accounts for the null results of the Michelson-Morley experiment.
[pic]
[pic]
o Identify that if c is constant then space and time become relative
Einstein’s special theory of relativity proposes that the speed of light is constant, and that space and time change to accommodate this. That is, stationary observers and moving observers perceive space and time differently.
Because the speed of light is constant, it follows that many quantities, such as time, length and mass which were once thought to be absolute are now relative.
In other words, the measured length of an object and the time taken by an event depend entirely upon the velocity of the observer. Further to this, since neither space nor time are absolute, the theory of relativity has replaced them with the concept of a space-time continuum. Any event then has four dimensions (three space coordinates plus a time coordinate) that fully define its position within its frame of reference.
o Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard
In 1793 the French government decreed that the unit of length shall be 1x10-7 times the distance from the North Pole to the equator, passing through Paris. However, this meter standard was inaccurate, and has been changed since to keep pace with improvements in technology and science.
The current definition of the metre uses the constancy of the speed of light in a vacuum (299 792 458 ms-1) and the accuracy of the definition of one second (9 129 631 770 oscillations of the 133Cs atom).
One metre is defined as the length of the path traveled by light in a vacuum during the time interval of 1/299 792 458th of a second, and is highly accurate and consistent with the idea of space-time.
However, the present definition of the metre does not take into account time dilation, as well as how the speed of light is affected by the strength of the gravitational field through which it is traveling.
o Perform an investigation to help distinguish between non-inertial and inertial frames of reference
Method:
1. While walking in a straight line at a constant speed, through a tennis ball vertically above you and catch it again. Observe the motion of the ball relative to you, while a stationary observer also observes the motion of the ball.
2. Compare and contrast the motion of the ball as made by the two observers.
3. Next, while walking steadily as in step 1, throw a ball vertically above you. This time, while the ball is in the air, stop walking. Again, observe the relative motion of the ball with respect to you, and have a nearby stationary observer make their own observation.
4. Compare and contrast the ball’s motion as made by the two observers.
5. Discuss the results in the context of frames of reference.
o Analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and discuss the relationship between thought and reality.
Only the logic is valid in thought experiments. Thought experiments deviate a lot from reality because;
• Trains or spacecraft cannot travel at relativistic velocities
• Even if a train does travel this fast, it is then impossible for an observer outside the train to observe anything and make any accurate measurements
• In the time dilation thought experiment, it is impossible in reality to see a single light beam traveling up from the light source and then reflecting back from the mirror
• In the relative simultaneity though experiment, in order to observe any noticeable effects the train needs to be infinitely long, which cannot be achieved in reality. First it is simply impossible to construct such a train. Secondly, even if such a train is made, the observer will not be able to see the light flashes from the sources placed at both ends of the train. This is because the infinitely large distance will result in the light intensity dropping to zero before reaching the observer
Thought Experiment 1:
▪ Einstein wondered: “Suppose I am sitting in a train traveling at the speed of light. If I hold a mirror in front of me, will I see my reflection?”. There are two possibilities:
▪ No. If the traveling is traveling at the speed of light, light from his face would not reach the mirror in order to be reflected back. By not seeing his reflection he would know that the train was traveling at the speed of light without having to refer to an outside point. This violates the principle of relativity
▪ Yes. This means that light would travel at its normal speed relative to the train. This does not violate the principle of relativity. However, it also means that, relative to a stationary observer outside the train, light would be traveling at twice its usually speed!
▪ Einstein concluded that, if we accept the principle of relativity can never be violated, then:
- The aether model must be wrong
- He would see his reflection
- The speed of light is constant regardless of the motion of the observer
▪ On this basis, Einstein put forward hits theory of special relativity:
- All motion is relative – the principle of relativity holds in all situations
- The speed of light is constant regardless of the observer’s frame of reference
- The aether is not needed to explain light, and, in fact, does not exist
|Thought Experiment 2: |
| |
|A train carriage has light-operated doors. The light is in the middle of the carriage. When the light is switched on, it travels equal |
|distances to each door and opens them at the same time. At least, that’s how someone inside the train sees things happening. The train is at |
|rest relative to this observer, and the two events occur simultaneously. |
|However, a person outside the train sees the train moving. When the light is turned on it travels out towards each door, but at the same time,|
|the train moves forwards. So the light reaches the back door sooner than it reaches the front door because the back of the train has moved |
|closer to the light rays approaching it. Hence the back door opens first, and the two events do not occur simultaneously. |
|This thought experiment reveals relative simultaneity. Where two events that are simultaneous to one observer may not necessarily appear |
|simultaneous to another observer who is in a frame that is moving at a relativistic speed. |
Relativistic speeds are speeds that are more than about 10% of the speed of light.
o Explain qualitatively and quantitatively the consequence of special relativity in relation to:
- The relativity of simultaneity
- The equivalence between mass and energy
- Length contraction
- Time dilation
- Mass dilation
The relativity of simultaneity
Simultaneity refers to our idea that different things happen at the same time. Einstein’s relativity complicates this simple idea. At speeds approaching that of light, events that are simultaneous in one frame of reference may not be simultaneous in another frame of reference. This is known as relative simultaneity.
[Thought experiment 2]
The equivalence between mass and energy
The energy-mass equivalence is where energy and mass are equivalent and are interconvertible. Their relationship is quantitatively governed by the equation:
[pic]
If we apply a force to an object, then work is done on it. This energy would take the form of increased kinetic energy as the object speeds up. But since nothing can move faster than the speed of light, once an object already has sufficient kinetic energy it cannot speed up as we would normally expect. Instead it acquires extra mass.
Relativity results in a new definition of energy as follows:
E = Ek + mc2
Notice that when an object is stationary, it has no kinetic energy, and still has some energy due to its mass. This is called the rest energy.
Note that this equation challenges the law of conservation of energy and the law of conservation of mass, which state that their mass nor energy can be created nor destroyed. Einstein’s equation, which was derived by special relativity, caused a modification to create: The law of conservation of mass and energy: Matter and energy cannot be destroyed or created. They can only be transformed.
Length contraction
Length contraction is when the length of a moving object appears shorter compared to the length of the object when measured at rest.
Length contraction occurs according to the formula:
[pic]
Length contraction is only observed in the direction of the motion. If observers on Earth watch a spaceship zoom past, they will see the spaceship as shorter than its real length. Similarly the observer inside the moving spaceship will observe the diameter of the Earth as smaller than it really is. The faster an object travels, the shorter it appears to an observer.
Time Dilation
Time in Einstein’s special relativity loses its absolute nature and becomes relative.
Time dilation can be summarized as ‘a moving clock appears to run slower’.
Time dilation is the slowing down of events as observed from a reference frame in relative motion. The time taken for an event to occur within its own rest frame is called the proper time to. Measurements of this time, tv, made from any other inertial reference frame in relative motion to the first, are always grater. The degree of time dilation varies with velocity.
Thought Experiment 3
• A train is moving to the right at a constant velocity v that is close to the speed of light.
• A light source is placed on the floor of the train while a mirror is fixed onto the ceiling. A light beam is emitted at the light source.
• Observer A, who is inside the train, will see the light beam going straight up and down. Thus traveled 2d.
• On the other hand, Observer B, who is outside the train, will see the light beam traveling forward-upward and then forward-downward. So the light has covered a distance 2d’, with d’ being the hypotenuse. Since d’ > d (from pythag), then the time Observer B measures is always greater than the time Observer A measures.
Time dilation formula:
[pic]
Mass Dilation
Mass dilation is when the mass of a moving object appears greater compared to the object’s mass at rest.
The mass of an object within its own rest frame is called its rest mass mo. Measurements of this mass mv, made from any other inertial reference frame in relative motion to the first, are always greater. The degree of mass dilation varies with velocity. More simply state as: moving objects gain mass.
[pic]
Einstein believed very strongly that momentum must be conserved in all inertial frames of reference. In order to solve this dilemma he suggested that the mass of an object must increase, or dilate, at relativistic speed by a factor that compensates for the effect of time dilation on speed measurement.
At speeds approaching light speed, mass increase is exponential in the same way as time and length, approaching infinity at the speed of light. As mass increases so does the force needed to accelerate it. As mass approaches infinity, the force needed to accelerate it further approaches infinity. The consequence of this is that speeds beyond the speed of light are impossible.
o Discuss the implications of mass increase, time dilation and length contraction for space travel
Implications for space travel:
• Mass dilation: The increase in mass as the speed of a spacecraft approaches c means that it becomes more difficult to further accelerate the spacecraft once its velocity becomes relativistic. This factor limits the speed of the spacecraft, with the maximum speed being one that is slightly under the speed of light even in an ideal situation.
• Time dilation: As we have seen in the time dilation section, time in the moving frame appears to rune slower. Hence if a spacecraft can travel at a relativistic velocity, then its pilots’ time will run significantly slower. This means the extremely length space travel as observed by the people on Earth will be reduced considerable according to the pilots. This allows the pilots to make prolonged space travel within their life time.
• Length Dilation: When a spacecraft is moving through space, relative to the pilots on the spacecraft, the space in front of the spacecraft is moving towards them. This means that the distance of the journey will appear shorter to the pilots than that being measured by people on Earth. Consequently, it will take the pilots a shorter time to reach their destination.
Hence the implications of mass increase, time dilation and length contraction mean that if could go faster (which is currently restricted by energy cost and mass dilation), then there would not be as far to travel and it would take less time to get there (from the astronauts perspective).
o Analyse information to discuss the relationship between theory and the evidence supporting it, using Einstein’s predictions based on relativity that were made many years before evidence was available to support it
Relationship between theory and evidence:
▪ At the time they were put forward, Einstein’s ideas went strongly against established science developed by scientists like Newton
▪ While Einstein’s mathematics was strong supporting evidence for his ideas, he could not justify them through experiments. It was not until 1955, that technology had advanced sufficiently to provide the first practical evidence for time dilation
▪ Atomic clocks were synchronized and one flown around the world on a jet plane. Its clock ran slower than the clock left at the airport, as predicted by Einstein, hence time is dilated
▪ There are many modern ideas that are not supported by practical evidence. They are considered and not dismissed out of hand partly because scientists realize that developing technologies might provide the evidence they seek in the future.
▪ The supporting evidence for Einstein’s work so far in time from his theoretical proposal has certainly influenced the idea that ideas cannot be dismissed even if they have no experimental evidence
▪ In addition, the existence of a theory will provide a direction for further scientific study and scientific work – it will give direction to what scientists focus on, and therefore be valuable whether experimental evidence for it exists or not.
Further evidence: Muons are one type of subatomic particles, which have a very short half-life, about two micro-seconds. Although they travel at very high velocities (0.996c), at that speed it should take around 16 micro-seconds to travel through the atmosphere. However, muons have been detected at the surface of the Earth. This is explained as since muons are traveling at a relativistic velocity, their time will be dilated sufficiently for them to reach Earth, and hence provides strong evidence for the validity of special relativity.
o Solve problems and analyse information using:
[pic]
[pic]
PRACTISE NOW
REMEMBER TO USE THE RIGHT UNITS
REMEMBER TO READ THE QUESTION PROPERLY FOR % INCREASE
Motors and Generators
9.3.1 Motors use the effect of forces on current-carrying conductors in magnetic fields
o Identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field
|Prerequisite Knowledge: |
|A stationary charge produces an electric field |
|A moving charge with constant velocity produces an electric field as well as a magnetic field |
|A moving charge that is accelerating produces electromagnetic radiation |
|A stationary charge will experience a force in an external electric field. This is because the field produced by the stationary charge |
|interacts with the external field and results in a force |
|Similarly, a moving charge with constant velocity will experience a force in both an electric field and an external magnetic field. |
The motor effect occurs when a current-carrying conductor experiences a force in a magnetic field.
o Discuss the effect on the magnitude of the force on a current-carrying conductor of variations in:
- The strength of the magnetic field in which it is located
- The magnitude of the current in the conductor
- The length of the conductor in the external magnetic field
- The angle between the direction of the external magnetic field and the direction of the length of the conductor
1. As the strength of the magnetic field increases, the force increases
2. As the current in the wire increases, the force increases
3. If the length of the wire inside the magnetic field increases, the force increases
4. The size of the force is a maximum when the wire is placed perpendicular to the field lines. It reduces in magnitude and eventually becomes zero when the wire is rotated to a position where it is parallel to the magnetic field.
All the above can be shown through experiments using a current balance.
o Solve problems and analyse information about the force on current-carrying conductors in magnetic fields using F = BIlsinθ
Mathematically, the force on a current-carrying conductor which is being affected by various factors is given by the equation:
[pic] (or F=nBIlsinθ) where n = number of turns of wire
[pic] [pic](use θ1)
Do Questions Ofc
[pic]
Note that since force is a vector quantity, it must have both magnitude and direction. We can use the ‘right-hand palm rule- to determine the direction of the force acting on a current-carrying wire.
“When the fingers point to the direction of the magnetic field,
and the thumb points to the direction of the conventional current,
then the palm points towards the direction of the force”
o Describe qualitatively and quantitatively the force between long parallel current-carrying conductors:
[pic]
First remember that:
A current-carrying wire produces a magnetic field around it. The nature of the field forms planar concentric rings around the wire. The direction of the magnetic field can be determined by the right hand grip rule.
“When the thumb points in the direction of the conventional current, the fingers curl in the direction of the magnetic field”
Quantitative description
If two straight current-carrying wires are placed parallel to each other, one wire produces a magnetic field and the other wire experiences a force due to this magnetic field. The two fields will interact and produce a resultant magnetic field.
Qualitative description
[pic]
But remember force is a vector:
Two parallel wires that carry current in the same direction attract each other, whereas if they carry currents running opposite directions they will repel each other.
(Opposite to magnets)
Remember that l is common length and that
it is d not d2
o Solve problems using: F/l = k(I1I2)/d
[pic]
PRACTISE QUESTIONS – EVERY QUESTION IN TEXTBOOK/PAST PAPER/ SURFING
o Define torque as the turning moment of a force using t=Fd
Torque is the turning effect of a force. Quantitatively, it is the product of the distance from the pivot of turning to where the force is applied and the size of the force perpendicular to the distance.
In other words:
[pic]
Sometimes we need to resolve Fp to ensure that
we include the perpendicular force in the equation.
(In which case we will use trig)
eg. T=Fdsinθ
For example:
[pic][pic][pic]
Remember the direction, since torque is a vector. The SI unit for torque is Newton meter (Nm)
o Describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces
If a current is flowing through a coil and an external magnetic field is present then there will be forces acting on the coil. That is, in a current-carrying loop, each side of the coil which is perpendicular to the magnetic field will experience a force due to the motor effect. Together the forces create a turning moment.
[pic]
This is the basis of an electric motor, which is a device which converts electrical energy to useful mechanical energy
When the coil rotates to the position below, the two forces on both sides of the motor will be acting in opposite directions and hence cancel each other out. However, momentum pushes the coil past this point
[pic]
Here is a useful illustration of the motor:
[pic][pic]
[pic]
[pic]
Quantitative description of Torque:
[pic]
o Solve problems and analyse information about simple motors using:
t=nBIAcosθ
[pic]
This isn’t practiced much, make sure to use CORRECT ANGLE and correct units. PRACTISE
o Describe the need for a split ring commutator and explain how it works (not in syllabus)
Why do motors need a split ring commutator?
The coil in the motor will rotate correctly when it is parallel when inclined to the magnetic field. However, when the coil is at the vertical position, the torque acting on it is zero and there is no turning effect. Therefore with each rotation, the coil loses some of its momentum and inertia due to friction and will subsequently oscillate about the vertical plane and come to rest. Hence in order to make a DC motor spin continuously, a split ring commutator is needed.
What is a split ring commutator?
A split ring consists of two halves of a metal (usually copper) cylindrical ring electrically insulated from each other.
How does it work?
When the coil is parallel to the direction of the magnetic field, the commutator is horizontal as shown in the diagrams on the page above. When the coil reaches the vertical position, the halves of the commutator are not in contact with the brushes and the current flowing through the coil drops to zero. This however has no effect (as the current in the coil only stretches the coil anyway).
When the coil swings past the vertical position, each half of the commutator changes the brush it is contacting to one of opposite polarity. This effectively reverses the current direction in the coil. Consequently the direction of the force acting on the two sides of the coil will be reversed, allowing the coil to continue to turn in the same direction. After another half cycle the halves of the commutator will change their contacts again, reversing the direction and consequently reversing the direction of the force. This repeats and maintains the rotation in one direction.
[pic]
o Describe the main features of a DC electric motor and the role of each feature
The main features of a DC electric motor are: A magnetic field, a commutator, an armature and carbon brushes
A Magnetic Field
Since the motor effect states that, a current-carrying wire in a magnetic field will experience a force, for a functional motor a magnetic field is essential
Magnetic fields can be provided by either permanent magnets or electromagnets. Furthermore, the structure which remains stationary and provides the magnetic field is called the stator. The coil which usually rotates inside the field is called the rotor. (note that if the coil is the stationary one it is called the stator)
➢ Permanent magnets: Ferromagnetic metals which retain their magnetic property at all times. Magnetic field lines go from North Pole to South Pole.
➢ Electromagnet: An electromagnet consists of a coil of current-carrying wire called a solenoid wound around a soft iron core. Note that electromagnets are usually able to provide stronger magnetic fields than permanent magnets. Direction of magnetic field lines can be found by using the right-hand grip rule to find the North Pole.
Electromagnets have major advantages over permanent magnets in that their strengths are adjustable and can be switched on and off when desired.
Radial Magnetic Field
Since the torque acting on the coil varies as it rotates to different positions with respect to the magnetic field lines, the variation in the torque results in the varying speed of rotation of the motor. To fix this a radial magnetic field is introduced.
[pic]
The radial magnetic field ensures that the plane of the coil is parallel to the magnetic field at a greater range of positions, so that the angle between the magnetic field and the coil remains at zero for longer. Consequently with the torque maintained at the maximum for longer, the motor is more efficient.
Armature
Armature refers to the coil of wire that is placed inside the magnetic field. The coil is almost always wound around a soft iron core in order to maximize the performance of the motor
Note that in real DC motors, armatures have numerous loops to maximize the torque that is acting on them. Further more, there are usually three coils used instead of a single coil, with the coils aligned at 120 degrees to each other. This again maximizes the torque that can act on the coils
Split Ring Commutator
The purpose and role of the split ring commutator is explained in the previous dot-point.
Carbon Brushes
Carbon brushes are usually made of graphite, and are pressed firmly onto the split ring commutator by a spring system. Carbon brushes are responsible for conducting current into and out of the coil, and work with the split ring commutator to ensure the continuous spin of the motor.
|Note Carbon or graphite is used because: |
|Graphite is a lubricant; reduced friction enables the motor to run more efficiently |
|Graphite is a very good conductor of electricity |
|Graphite is able to withstand high temperatures generated by friction |
o Identify that the required magnetic fields in DC motors can be produced either by current-carrying coils or permanent magnets
Outline above.
o Identify data sources, gather and process information to qualitatively describe the application of the motor effect in:
- the galvanometer
- the loudspeaker
Galvanometer
A galvanometer is a very sensitive device that can measure small amounts of current. It works on the principle of the motor effect
A simple galvanometer consists of a fine coil with many turns wound around a soft iron core. The core is placed inside a radial magnetic field produced by permanent magnets with shaped pole pieces. It also has a torsional string attached to the axis of rotation of the coil. A pointer is attached to the coil and a scale is developed.
How it works:
When a current passes through the coil, the coil experiences a force inside the radial magnetic field (motor effect) and starts to rotate. However, as the coil rotates, it stretches the spring, which will then exert a torque that counteracts the initial torque created by the motor effect. Eventually the opposing torque is equivalent to the forward torque, and the degree of movement is indicated by the pointer on the scale. Since magnetic field strength and area of the coil are both constant, forward torque will only depend on and in fact be directly proportional to the size of the current. (t=nBIA, since a radial magnetic field is used)
|Note: Once again radial magnetic field ensures that the size of the forward torque is independent of the position of the coil and makes a |
|direct conversion from the angle of rotation to the size of the current possible. |
Loud Speaker
A loudspeaker also works on the basis of the motor effect: it converts electrical energy to sound energy
A simple loudspeaker consists of a coil of wire between the pole pieces of the magnets which form the core. A paper diaphragm is then attached to this coil-magnet unit.
When signals are fed into the coil inside the loudspeaker, the coil experiences a force as a result of the motor effect. When the current flow from A to B we can apply the right hand palm rule and see the force acting on the wire pushes the wire out. Similarly when current flows from B to A the force will pull the coil in. Since AC signals vary in direction very rapidly, the coil should move in and out very rapidly as well. Furthermore, since the coil is very tightly wound on the magnetic pole piece, they will vibrate, which causes the paper diaphragm to vibrate with it. This causes the air to vibrate which produces sound waves.
|The nature of the sound waves will depend on the characteristics of the AC signal inputs. The pitch is affected by the frequency (speed of |
|vibrations), and the loudness is dependent on the amplitude (strength of vibration). |
o Perform a first-hand investigation to demonstrate the motor effect
Aim: To investigate the direction of the force on a current carrying conductor in an external magnetic field
Method:
1. Pin a foil strip between 2 pieces of cardboard. Rest one card on the bench and support the other with a clamp and retort stand
2. Connect the wires to a power pack’s DC terminals, variable resistor and strip of foil
3. Position two strong magnets so that the strip is between the poles.
4. Briefly switch on the power pack and record any observations
5. Swap the poles of the magnets and briefly switch on the power pack, recording observations again.
9.3.2 The relative motion between a conductor and magnetic field is used to generate an electrical voltage
o Outline Michael Faraday’s discovery of the generation of an electric current by a moving magnet
Michael Faraday discovered the generation of electricity using a changing magnetic field, and proposed the theory of electromagnetic induction.
In 1819, Oersted had shown that an electric current produces a magnetic field. In 1821 he mapped the shape of this field, and in1831 Faraday was able to induce a current in a conductor when the conductor was subjected to a changing magnetic field.
When the primary coil was switched on the secondary coil recorded a momentary reading, and this occurred again when it was switched off. (this is because the current does not reach its maximum value immediately when switched on. When the current builds up, there is a brief period of increasing current, and since magnetic field strength is proportional to the current there is also a momentary period of increasing magnetic field strength. This increasing, therefore changing magnetic field, induces an EMF or current in the secondary coil.)
[pic]
Other experiments he did were:
Glass tube with a steel needle inserted inside.
Bar magnet moving towards a coil and being withdrew again.
o Define magnetic field strength B as magnetic flux density
Magnetic flux is defined as the number of magnetic field lines passing through an imaginary area.
Mathematically, if the magnetic field is perpendicular to the area than the magnetic field is equal to the product of the strength of the magnetic field and the size of the area.
[pic] is the magnetic flux in webers (Wb)
B is the magnetic field strength in Telsa (T)
A is the area in m2
However, if the magnetic field is not perpendicular to the area, than only the perpendicular component of the magnetic field is taken into consideration
[pic]
Note:
Since we can rearrange the formula to [pic], we can define magnetic field strength B in another way:
A magnetic field, B, can be defined as the amount of magnetic flux per unit area, or simply, the magnetic flux density
o Describe the concept of magnetic flux in terms of magnetic flux density and surface area
Done above (On this page)
o Describe generated potential difference as the rate of change of magnetic flux through a circuit
For a current to flow through a galvanometer in Faraday’s experiments there must be an electromotive force (EMF). (Since magnitude of current through the galvanometer depends on the resistance of the circuit and the magnitude of the EMF). Faraday noted that there had to be change occurring in the apparatus for an EMF to be created.
Faraday’s law states: The size of an induced EMF is directly proportional to the rate of change in magnetic flux
Mathematically:
[pic] the negative sign is explained later
where n is the number of turns and [pic] is the rate of change in flux
Consequently in order to induce an EMF, a charging magnetic flux is essential.
(Note that a changing magnetic field will result in a changing magnetic flux; however, there are other ways to create changes in magnetic flux)
|From the above equation we can determine that the following factors will affect the size of the induced EMF: |
|Size of the chance in the magnetic field |
|Speed of the relative motion between the magnetic field and the conductor |
|The number of turns of coil or conductors |
|The change in area that the magnetic field passes through |
o Account for Lenz’s Law in terms of conservation of energy and relate it to the production of back EMF in motors
Lenz’s Law
Whenever an EMF is being induced in a conductor as a result of changing magnetic flux, the direction of the induced EMF will be such that the current it produces will give rise to a magnetic field that always opposes the change and hence opposes the cause of induction.
Therefore the negative sign in Faraday’s law assigns the direction for the induced EMF, that is, it opposes the cause of induction
DO QUESTIONS
MASTER THIS CONFUSING CONCEPT
[pic] [pic][pic][pic]
Read few times + explain in own words
➢ Consider a wire moving through a magnetic field.
➢ As the wire moves it will experience a changing magnetic flux (as the wire moves it carves out a changing area; magnetic flux changes)
➢ Hence there will be an EMF induced and a current will flow (If we assume a complete external circuit)
➢ If the current DID NOT flow in the direction to oppose the cause of induction (that is the velocity of the wire stated above), then the wire would speed up rather than slow down
➢ This will create a greater changing magnetic flux and induce a greater EMF or current
➢ This induced current will further speed up the wire, inducing an even greater EMF or current. As the cycle continues eventually the wire would be moving at an infinitely high speed and there wo0uld be an infinitely large current flowing in the wire.
➢ Since no energy input is required energy is created!
➢ This cannot happen, since the law of conservation of energy states: Energy cannot be destroyed or created, it can only be transformed or transferred.
➢ Hence to obey the law of conservation of energy, the current must flow to oppose the cause.
➢ A result of the motion of the wire being opposed (due to Lenz’s law) is that it will slow down and eventually come to rest if there is no external force.
➢ To maintain a constant production of current force must be applied to maintain the motion of the wire, which satisfies the law of conservation of energy.
Note that even if EMF is induced, if there is no external circuit, there will only be a momentary flow of current that will then stop. This is because a migration of irons will cause one terminal of the wire to be negative and lack electrons, and other being positive. This build up of charge will resist further flow of electrons and momentarily later the electrostatic force will be in equilibrium with the induced EMF and the migration of the charges will stop.
However, when the two terminals are connected via a long wire outside the magnetic field, the circuit will be completed and a continuous flow of current will be established without electron deficiency at any terminals.
o Explain that, in electric motors, back EMF opposes the supply EMF
Back EMF is an electromagnetic force that opposes the main current flow in a circuit. When a coil of a motor rotates, a back emf is induced in the coil due to its motion in the external magnetic field
➢ When the coil of a DC motor is spinning inside a magnetic field, the coil is subject to a changing magnetic field caused by the relative motion between the coil and the field
➢ This changing magnetic flux will induce an EMF in the coil, and as a consequence of Lenz’s law, the induced EMF will cause the current to flow in such a way that it will oppose the cause of induction (the rotation of the coil)
➢ Hence the induced current will flow in the opposite direction to the input current, thus limiting the size of the input or forward current
➢ This will decrease the torque, slowing down the rotation of the motor.
➢ Since the induced EMF works against the input voltage (supply EMF), it is referred to as the back EMF
o Explain the production of eddy currents in terms of Lenz’s Law
Eddy Current is a circular current induced in a conductor that is stationary in a changing magnetic field, or that is moving through a magnetic field
Whenever there is a changing magnetic flux, EMF will be induced. The EMF will cause a current to flow in the wire provided there is an external circuit. However, in the case of a solid conductor, the EMF will cause loops of current to flow, and these circular currents are referred to as eddy currents (eddy = circle/loop)
In Terms of Lenz’s Law:
The induced eddy currents also follow Lenz’s law, that is, they circulate in such a way as to oppose the cause of induction
Note: Eddy currents are simply circulating currents
Inside the magnetic field the charged particles in the metal sheet experience a force upwards (by the right-hand push rule)
Outside the magnetic field, the charged particles are free to move and is able to flow downward in the metal to form a current loop known as an eddy current.
o Gather, analyse and present information to explain how induction Is used in cook tops in electric ranges
How an induction works
When an AC current flows through the coil, the changing current produces a changing magnetic field. This magnetic field passes through the ceramic cook top and the saucepan or any other metal containers. Within the saucepan’s base, eddy currents are generated. The circulation of eddy currents in the presence of the resistance in the saucepan generates heat. This heat can be used to heat the food content.
| |
|Advantages of cook top over others: |
|They are very efficient in converting electrical energy to heat energy. The source of |
|heat is in direct contact with the food being cooked |
|There is no open fire so it reduces the possibility of a fire hazard in the kitchen |
|The ceramic cook top is very easy to clean, improving hygiene maintenance |
|The cook top itself does not generate heat, so burns to individuals are less likely |
o Gather secondary information to identify how eddy currents have been utilized in electromagnetic braking
If a train wishes to stop, very powerful magnets are lowered down next to the metal wheels of the train. The rotating wheels in the presence of a magnetic field slow down very rapidly due to the production of eddy currents within the wheels that oppose the motion of the wheels as described above. (note that the braking effect reduces as the speed of the train decreases)
Hence, when the train reaches very low speeds, eddy current braking is no longer useful and at the point a mechanical brake is applied to stop the train completely.
|Advantages; |
|It is smooth- the braking force gradually becomes smaller to an unnoticeable force as the train slow down |
|There is no wear and tear as there is no physical contact between the braking system and the wheels. Consequently there is a low maintenance |
|effort and cost |
| |
|Disadvantages; |
|It only works for metal wheels and at higher speeds. |
How to explain:
CHEAT SHEET – THE FIVE MAGIC STEPS
|Eddy current breaking |AC induction motor |AC induction cook top |
|When a flat conductor cuts magnetic field lines|When alternating current in the field of coils |When alternating current in the coil under the |
|(OR the flux can cut the metal) |of t he stator produces a rotating magnetic |cook top produces a magnetic field, the field |
|( The conductor can be non-magnetic metal |field the expanding and contracting magnetic |lines cut the metal of the saucepan |
| |field lines cut the bars of the squirrel cage | |
| |rotor | |
|Eddy currents are generated in the conductor |Eddy currents are generated in the squirrel |Eddy currents are generated in the saucepan |
| |cage | |
|These eddy currents have their own magnetic |These eddy currents have their own magnetic |These eddy currents are VERY LARGE (because the|
|field |field |currents in the coil are very large) |
|The eddy current opposes the original magnetic |The eddy current magnetic field opposes the |These very large eddy currents generate heat |
|field (Lenz’s law) |original magnetic field (Lenz’s law) |energy (note the saucepan needs to be made of a|
| | |metal with significant resistance) |
|This results in the motion being opposed and it|This results in the squirrel cage rotor chasing|The heat energy in the saucepan transfers heat |
|will slow down |the rotating magnetic field of the stator |energy into the food |
Perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet
Aim: To investigate the generation of an electric current by moving a magnet in a coil or a coil near a magnet
Apparatus:
- Galvanometer
- 2 coils with different number of turns of wire
- 2 bar magnets of different strengths
- Connecting wires
Method:
1. Connect the coil with the fewest number of turns to the galvanometer. Push the N pole of a bar magnet into the coil. Describe what happens
2. Hold the magnet stationary near the coil. Describe what happens
3. Withdraw the N pole from the coil. Describe what happens
4. Repeat Steps 1-3 at different speeds. Describe what happens
5. Hold the magnet stationary and move the coil in different directions. Describe what happens
6. Rotate the coil so that first one end and then the other approach the magnet. Describe what happens
Conclusion:
[pic][pic]
o Plan, choose equipment or resources for, and perform a first-hand investigation to predict and verify the effect on a generated electric current when:
- The distance between the coil and magnet is varied
- The strength of the magnet is varied
- The relative motion between the coil and the magnet is varied
Aim: To predict and verify the effect on a generated electric current due to variations of distance between coil and magnet, strength of magnet and relative motion between coil and magnet
Hypothesis:
- As the distance increases the strength of the magnetic field decreases and thus less current is induced
- The stronger the magnet the greater the current induced
- The greater the relative motion the greater the current produced
Apparatus: Same as Above
Method: Same As Above
Conclusion: Same as Hypothesis
9.3.3 Generators are used to provide large scale power production
o Describe the main components of a generator
An electric generator is one that converts mechanical energy to electrical energy using the principle of electromagnetic induction
The main components of a generator are:
1. Magnetic field - A changing magnetic field (and hence flux) is created by a relative motion between the magnetic field and the coil. The magnets are usually the stator in simple generators, but in industrial motors they are often the rotor. This changing magnetic flux produces a changing emf across the ends of the wire that makes up the coil (In accordance with Faraday’s Law of Induction)
2. Armature – This refers to the coil of wire wound around a soft iron core. This can be the stator or rotor depending on the design of the generator, and multiple coil armatures are common for large scale electric generators
3. Commutator – The structure of commutators in generators is similar to that of motors. Dc generators have split ring commutators, whereas AC generators have slip ring commutators.
4. Carbon brushes – Carbon brushes in generators have the same structures, and are used for the same purpose as in electric motors.
o Compare the structure and function of a generator to an electric motor
A generator has a similar design as an electric motor; however, it functions in the opposite way compared to that of a motor. Just like a motor, there are DC and AC electric generators.
[pic] Both incorporate the use of a magnetic field, an armature, a commutator and carbon brushes. However, while a motor uses an input current to rotate the coil via the motor effect, a generator instead uses the turning of the coil to induce a current, and hence electricity.
Difference in function
The function of an electric motor is the reverse of the function of a generator. The function of a generate is to generate an emf by moving conductors through a magnetic field while the prime function of a motor is to produce a turning force by application of an external emf. A motor rotates when current is supplied while a generator supplies current when the rotor is made to rotate
An electric motor converts electrical energy into mechanical energy. A generator converts mechanical energy into electrical energy.
o Describe the differences between AC and DC generators
The major difference between a DC generator and an AC generator is the commutator used and the EMF induced
In a DC generator;
➢ The current is in one direction only (DC by definition)
The split ring commutator in a DC generator allows each half of the commutator to contact a difference brush every half rotation at the vertical positions. This ensures that as soon as the polarity of the half commutator reverses at the vertical positions, contact with the brush is also reversed. This is to ensure the brushes always maintain the same polarity, so that the direction of the output current can be maintained in one direction.
Ie. We can plot a graph of the EMF output of a DC generator against time
In an AC generator;
The purpose and functional principle of the slip ring commutator is to conduct electricity into and from the external circuit without tangling up the wires.
When the coil rotates, the polarity of two parts of the slip ring commutator reverses every half cycle at the vertical positions as in a DC generator (Due to the reverse in the current direction in the coil). Since there is no means by which they can change their contact with the brushes, the polarity of the brush will also change every half cycle, resulting in an alternating current. (The current direction varies constantly) [pic]
Note that the period and frequency of the EMF generated depends on the speed of rotation for both AC and DC output.
To work out the direction of the current, or the positive terminal, we use the right-hand push rule:
The thumb points to the direction of the movement of coil arm and movement of test positive charge
The palm points to the direction of force on test positive charge and direction of induced current.
The fingers point from N to S in the magnetic field.
Large scale AC generators are often Three-phase AC generators. The electricity produced by a three-phase AC generator is around 22 kV and is supplied to consumers by three separate active wires. The electricity is returned to the generator by a single wire to complete the circuit. Usually at a domestic level only one active wire is used (in industries all three may be used)
o Discuss the energy losses that occur as energy is fed through transmission lines from the generator to the consumer
Energy is lost as it is being fed through transmission lines from the generator to the consumer, mainly in the form of heat.
This is because as current flows through a conductor that has resistance, heat will be dissipated. Furthermore as resistance of a conductor is proportional to its length, wires over long distances will have a significant amount of resistance. Heat loss during transmission can be quantitatively described using the equation:
P=I2R
Furthermore, transformers used to change the voltage in the transmission process are less than 100% efficient. This can be explained by eddy currents in the soft iron core and resistance of wires, and results in unavoidable energy losses from generator to consumer
o Assess the effects of the development of AC generators on society and the environment
This is ASSESS which means you need to give a judgment of value, quality, outcomes, results or size. In this case value/outcome mostly.
Positive effects and impacts on society
1. Improvement to standards of living – AC generators allow people to have electricity at home. This makes people’s lives more comfortable and luxurious as they can use lights, heaters, air conditioners, etc.
2. Improved health of population – The health of the population has improved due to less pollution from power generation close to cities
3. Stimulated development of industry – The development of AC generators have allowed industries to efficiently produce goods and has hence stimulated the development of industry and progress of technology
Negative effects and impacts on society
1. Dependant on electricity– Easy access to cheap electricity has made society increasingly dependent on electricity. Disruption to electricity supply can now cause widespread inconvenience, loss of production/goods and even fuel an economic crisis.
2. Accidents – Injuries and deaths from electric shocks have become more common with the widespread use of AC power.
3. Unemployment – Many tasks that used to be done by humans have been replaced by electric tools and machines. This causes unemployment, adding a burden to society.
Positive effects and impacts on environment
1. Pollution away from cities – Pollution from coal burning is kept away from city areas thus reducing pollution in these areas
2. Can generate environmentally friendly power – Ability to generate power using environmentally friendly sources such as hydroelectricity and wind power reduces environmental pollution.
Negative effects and impacts on environment
1. Pollution – Pollution from burning fossil fuels is simply shifted away from cities
2. Fossil fuels – Depletion of energy sources such as fossil fuels. The burning of these also contributes to acid rain, which damages the environment
3. Power transmission lines – These lines cut through environmentally sensitive areas to transport electricity to cities, destroying large areas of natural habitats
4. Environmentally unfriendly power – Methods used to drive turbines can cause environmental damage. For example Nuclear power produces long lived radioisotopes and hydroelectricity causes thermal pollution
5. Global warming – Global warming is caused by burning fossil fuels in AC generators, and can damage the environment especially in the long term, threatening various habitats and animals.
Value/Judgment
The impact of the development of AC generators has had an overall positive impact on society with a marked increase in productivity and quality of life. The impact on the environment, however, has been strikingly negative with long term global warming as a consequence of the burning of fossil fuels.
o Plan, choose equipment or resources for, and perform a first-hand investigation to demonstrate the production of an alternating current
Aim – To observe the output voltage of an AC generator using a cathode ray oscilloscope
Equipment –
➢ Hand-cranked model generator
➢ Cathode Ray Oscilloscope (CRO)
➢ 2V light globe
➢ Connecting wires
Method –
1. Connect the AC generator to the CRO as shown in diagram
2. Turn the coil slowly and describe the trace on the CRO, noting the period, the peak voltage obtained and the shape of the trace.
3. Sketch the trace
4. Connect the light globe across the terminals of the generator. Comment on the easy of rotating the coil compared with when the global was not in use.
5. Increase the speed of rotation and record the new period, peak voltage and shape of trace.
6. Record and comment on results.
o Gather secondary information to discuss the advantages/disadvantages of AC and DC generators and relate these to their use
Remember the aim is to discuss whether the advantages and disadvantages of AC and DC generators influence their uses
Disadvantages of DC generators
• A DC generator requires a split ring commutator, which complicates the design of the generator. This results in higher costs for construction and effort for maintenance of the generator
• The gap present in the split ring commutator results in sparks being produced during the generation of electricity, posing problems at high speed rotations
• The output of DC generators loses more energy than that of AC generators during transmission (due to transformers)
Advantages of DC generators
• Some devices, such as battery rechargers and cathode ray tubes, rely solely on DC currents for their function. Although AC current can be converted to DC current using a rectifier, it will be more convenient and cost effective to produce DC directly using a DC generator
• For a given voltage, DC current is generally more powerful than AC, so that DC is preferred in heavy-duty tools. Under this circumstance, DC generators are superior
Disadvantages of AC generators
• Refer to advantages of DC generators
• In order to integrate electricity throughout the nation, the frequencies of AC generators in different regions must be synchronized, and this requires extra coordination.
• The output of AC generators is more dangerous than the equivalent DC generator output. This is because AC< with its conventional 50 Hz frequency, can most readily cause heart fibrillation
Advantages of AC generators
• Refer to the disadvantages of DC generator
• Three-phase AC currents are made possible, which makes current more reliable and can also power induction motors
• AC voltage is easily increased or decreased using transformers, allowing the use of appliances at voltages other than 240V in the home and for efficient long distance transmission of electricity.
The advantages of one generator are generally the disadvantages of the other. Discuss means to identify issues and provide points FOR and AGAINST
o Analyse secondary information on the competition between Westinghouse and Edison to supply electricity to cities
Edison was the first person to set up a business to supply electricity, and his system at the time was DC based. He initially installed light bulbs for homes, then street lights, and he also developed DC motors and other appliances that ran on DC.
Nikola Tesla was the first person to demonstrate the production of AC and its transmission system. In 1885, George Westinghouse bought the patent of the AC system from Tesla and opened up his own electric company to compete with Edison.
Westinghouse was the overall winner, as the AC system was more efficient for two reasons:
1. The split ring commutator in DC generators posed a problem with high speed rotation.
2. Most importantly, AC transmissions through the action of transformers were much more energy efficient. This allowed electricity to be transmitted over longer distances with only a small amount of energy loss.
In 1886, there was a competition for inventors to propose plans to build a power plant using the power of Niagara Falls to supply electricity to distance cities. Both Edison and Westinghouse participated. Westinghouse proved the high energy efficiency of his AC system through many demonstrations, and eventually won the competition.
o Gather and analyze information to identify how transmission lines are:
- insulated from supporting structures
- protected from lightning strikes
Protection from lightning
When transmission wires are struck by lightning there is the risk of the system being damaged, overloaded or shut down, as well as damage to infrastructure like transformers, power poles and wires.
To protect these wires from lightning an overhead wire is used. This wire runs over and parallel to transmission wires and is connected to the earth, so incase of a lightning strike, the lightning will hit the overhead wire and be diverted to the earth, leaving the transmission wires untouched.
Insulation of transmission wires from supporting towers
Since overhead transmission wires are usually bare, if they make contact with the supporting metal towers the tower will: 1) become live so anything that makes contact with the towers will experience an electric shock and 2) the wires will short circuit and disrupt electricity distribution.
Hence since neither of the above is desirable, the wires are insulated well away from metal towers. The wires are suspended by insulators that consist of stacks of disks made from ceramic or porcelain. These disk-shaped insulators increase the effectiveness by reducing the amount of dust/water build up on the insulators and minimizing the chance of a spark jumping across the gap.
Note: Transmission wires also are placed high above ground, both for safety reasons and because air is a great insulator, which prevents electricity from jumping to the ground or to the other wires.
9.3.4 Transformers allow generated voltage to be either increased or decreased before it is used
o Describe the purpose of transformers in electrical circuits (Diagram/s should be included)
Transformers are devices that increase or decrease the size of the AC voltage as it passes through them.
A transformer is a magnetic circuit with two multi-turn coils wound onto a common core.
It consists of a primary coil, where the AC voltage is fed in, and a secondary coil, as the output that will be connected to a load. Both coils are wound around a soft iron core.
[pic]
| |
|How it works: |
| |
|When AC power is fed into the primary coil, the changing current of the AC produces its own changing magnetic flux. |
|The magnetic flux is linked to the secondary coil via the soft iron core. |
|In the secondary coil, this changing magnetic flux will induce an EMF as the output. |
|Since the size of the magnetic flux depends on the number of turns in a primary coil, and the EMF induced depends on the number of turns of |
|the secondary coil, we can vary the number of coils to change the voltage. |
o Compare step-up and step-down transformers
Step-up transformers
For step-up transformers, the voltage output from the secondary coil is larger than the voltage input into the primary coil. The secondary coil has more turns than the primary coil
Step-down transformers
For step-down transformers, the voltage output from the secondary coil is smaller than the voltage input into the primary coil. The secondary coil has fewer turns than the primary coil.
o Solve problems and analyse information about transformers using:
Vp/Vs = np/ns
[pic]
o
o Explain why voltage transformations are related to conservation of energy
The Principle of Conservation of Energy stats that energy cannot be created nor destroyed, but that it can be transformed from one form to another
That means if a step-up transformer gives a greater voltage at output, there must be some kind of trade-off. The rate of supply of energy to the primary coil must be equal to the rate of supply of energy from the secondary coil. This is given by the equation P=VI, hence we can see if the output voltage is higher, the current will be lower in order to maintain the same amount of energy.
In this sense voltage transformations abide by and are related to the conservation of energy, in that if the output voltage changes then there must be a change elsewhere (in the current) to ensure that energy is not created or destroyed.
o Explain the role of transformers in electricity sub-stations
The voltage change during the transmission from the power plant to consumers can be described by:
1. Electricity is usually generated by a three-phase AC generator. Generally the voltage generated is as big as 23000V
2. For long distance transmissions, the electricity is fed into a step-up transformer that increases the voltage to 330000V (and correspondingly decreases the size of the current). (This is done to increase the efficiency of the transmission of the electricity)
3. After this electricity has been transmitted over a long distance, the voltage is stepped down at different regional sub-stations, mainly for safety reasons
4. Eventually the voltage is stepped down to 240V at local telegraph pole transformers for domestic uses
Hence the role of transformers is to increase the voltage of electricity from the power plants, which increases efficiency of the transmission over long distances, or decrease the voltage, which is done for safety reasons and to lower the voltage to a level suitable for domestic use.
o Discuss why some electrical appliances in the home that are connected to the mains domestic power supply use a transformer
Appliances in the home that are connected to the mains domestic power supply often function at voltages other than the standard domestic voltage of 240V.
Some appliances require step-up transformers: For instance, a TV requires thousands of volts for its operation in the cathode ray tube
Some appliances require step-down transformers: For instance, scanners, toys and computers require lower voltage for their correct operation as well as for safety reasons. Also, some electric ovens and cook tops need to step down the input voltage in order to increase the size of the current, which effectively increases the heating effect of such devices.
o Discuss the impact of the development of transformers on society
The impacts of the development of transformers on society include:
1. A shift from DC usage to AC usage: The revolutionary shift to Westinghouse’s AC system was mainly due to the invention of transformers, which allowed AC to be easily stepped up or down for efficient transmissions.
2. Increased efficiency in transmission of electricity: The power loss during transmission is reduced by the development of transformers. This allows electricity transmission to become more economical (electricity cheaper), and reduces our consumption of fossil fuels (environmentally friendly) ( Positive impacts
3. Allows distant location of power stations: Transformers led to efficient transmission, which means we can place power plants a long distance away from the site of electricity consumption. This decreases the level of pollution in metropolitan areas and allows generation of electricity to be concentrated at one place.
4. Allows development of appliances which run at different voltages: Only with the development of transformers were appliances such as TV’s and computers, which run at voltages other than 240V, made possible
o Identify data sources, gather and analyse secondary information to discuss the need for transformers in the transfer of electrical energy from a power station to its point of use (Diagram/s should be included)
As a current passes through conductors, heat energy is lost to the surroundings. The amount of energy lost can be described by P = I2R, hence P (the energy lost) depends on the current and the total resistance of the conductor.
However we also know, that increasing the size of the voltage decreases the size of the current without changing the power transmitted (P = VI). Hence by reducing the size of the current, there is less energy lost during transmission, making transmission much more efficient.
Hence transformers are important in the transfer of electrical energy from a power plant to its point of us, as it decreases the energy lost when the current passes through a conductor.
o Identify data sources, gather, analyse and use available evidence to discuss how difficulties of heating caused by eddy currents in transformers may be overcome
Transformers are not perfectly efficient. A portion of the input energy is lost, mainly in the form of heat, which is dissipated by both coils, and more extensively by the soft iron core.
The reason for heat dissipation is:
➢ Just like the secondary coil, the soft iron core is subject to the changing magnetic flux produced by the current in the primary coil. Hence being a solid conductor, there will be eddy currents generated in it.
➢ The circulation of eddy currents then generates heat – similar to how induction cook tops use eddy currents to heat food – which is then dissipated to the surroundings.
To minimize the heat dissipation by the soft iron core, the core is laminated.
Lamination means the core is constructed using stacks of thin iron sheets, each coated with insulation materials so it is electrically insulated from he neighbour iron sheets.
[pic]
Lamination increases the resistance of the core to the flow of eddy currents. This leads to a decrease in the heat dissipation by the core, and increases the overall energy efficiency of the transformer.
o Perform an investigation to model the structure of a transformer to demonstrate how secondary voltage is produced
Aim: To model a simply transformer which demonstrates how secondary voltage is produced
Method:
1. Wind a primary coil around a soft iron bar, carefully counting the number of turns
2. Wind a secondary coil around the top of the primary coil and also note the number of turns (this produces better linkage of magnetic flux)
3. Connect the primary coil to an AC power source from a power pack with known voltages
4. Measure the AC voltage outputs from the secondary coil using a cathode ray oscilloscope. (Warning: ensure the secondary coil has fewer turns than the primary coil)
5. Compare the measured values to the theoretically calculated values based on the turn ratios
9.3.5 Motors are used in industries and the home usually to convert electrical energy into more useful forms of energy
o Assess some of the energy transfer and transformations involving the conversion of electrical energy onto more useful forms in the home and industry
Remember Law of Conservation of Energy: Energy cannot be created or destroyed, it can only be transformed.
Note that none of the following energy conversions is perfectly efficient, it is inevitable that portions of the original energy are converted into undesirable energies (eg. Heat).
Electrical energy can be converted to:
|Form of energy |Example |
|Kinetic energy |Fans, drills, blenders |
|Light energy |Light bulbs, neon lights |
|Sound energy |Speakers |
|Chemical energy |Recharging batteries |
|Heat energy |Induction cook tops, furnaces |
Note Assess: Make a judgment of value
Energy Transfer: The same type of energy from one place to another
Energy Transformation: One type of energy changing to another form of energy
o Describe the main features of an AC electric motor
Slip ring commutators – This is responsible for conducting electricity from the power source without interfering with the rotation of the coil (unlike split ring commutators which reverse current direction every half cycle)
AC electric motors are similar to DC electric
motors in that there is also a magnetic field,
an armature and carbon brushes.
All these features have the
Same function as they do in
A DC motor.
Refer back to the features of a
DC motor if unsure.
o Perform an investigation to demonstrate the principle of an AC induction motor
Method:
1. Wrap a CD in aluminium foil
2. Pack the centre of the CD with blu-tack and thread a string through it so the CD is suspended evenly and spins smoothly.
3. Use glue (araldite or similar) to glue a dowel stick (or pencil) to the centre of a bar magnet
4. Insert the other end of the pencil or dowel stick into the chuck of an electric drill
5. With the CD suspended horizontally, position the drill so the magnet can rotate in a horizontal plane beneath the CD (but not touch it ) as shown below
6. Observe the motion of the aluminium disk as the magnet rotates in a horizontal plane and describe the results
Note: Know the eddy currents produced in the disk (and the direction) and explanation of why it happens
AC INDUCTION MOTOR
The AC induction motor consists of a stator and a rotor.
• Input current is fed into the stator and is responsible for creating magnetic fields
• The rotor is made up of parallel aluminium bars that have their ends embedded in a metal ring at each terminal, forming a “Squirrel cage”
AC current is fed into the multiple coiled stator to create magnetic fields. The current is fed in such a way so that a rotating magnetic field is created inside the stator. This will induce eddy currents within the squirrel cage motor. The eddy current will flow in a way that the rotor will rotate in the direction of the rotating magnetic field created by the stator.
NOTE: No current is fed into the rotor; current is induced inside the rotor which then interacts with the external magnetic field of the stator to result in rotation.
[pic]
[pic]
READ AND UNDERSTAND – BE ABLE TO EXPLAIN
Ideas to Implementation
9.4.1 Increased understandings of cathode rays led to the development of television
o Identify that charged plates produce an electric field
An electric field is a region in which charged particles experience a force. Charged plates produce an electric field
Note that an electric field is a vector quantity; hence it has both magnitude and direction.
Direction = the direction of the force a positive charge would experience
Magnitude = Size of the force acting per unit of charge
o Discuss qualitatively the electric field strength due to a point charge, positive and negative charges and oppositely charged parallel plates
The strength of an electric field at any point is defined as the size of the force acting per unit of charge.
[pic]
Radial electric field lines going INTO (for negative) or OUT OF (for positive) a point charge
Note that density of the field lines represents the strength of the electric field.
Electric field between positive and negative charge
Note that the parallel field lines represent a UNIFORM ELECTRIC FIELD
o Describe quantitatively the electric field due to oppositely charged parallel plates
The strength of the electric field between a pair of parallel electric plates is proportional to the size of the applied voltage and inversely proportional to the distance separating the plates.
This is governed by the equation:
[pic]
o Solve problems and analyse information using E=V/d
[pic]
Use correct units, d in metres, V in Volts and E in N/C.
o Identify that moving charged particles in a magnetic field experience a force
A charge experiences a force inside an electric field.
A charge that moves at a constant velocity also experiences a force inside a magnetic field
o Describe quantitatively the force acting on a charge moving through a magnetic field F = qvBsinθ
The magnitude of the force acting on a charged particle as it moves through a magnetic field is given by:
[pic]
“Queen Victoria Building”’
Direction
Direction can be found using right-hand palm rule:
Thumb points to direction in which the positive charge is moving
Fingers point to the direction of the external magnetic field
Palm pushes in the direction of the force.
o Solve problems and analyse information using: F = qvBsinθ and F = qE
Use equation above and:
The force acting on a charge when it is in an electric field
[pic]
Direction
For positive charges, the forces act in the direction of the electric field
For negative charges, the forces act in the opposite direction to the electric field
o Explain why the apparent inconsistent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves
A little over 100 years ago there was a vigorous debate revolving the nature of cathode rays as to whether they were charged particles or electromagnetic waves. The main reasons behind this debate were the apparent inconsistent behaviour of the cathode rays:
Heinrich Hertz strongly believed cathode rays were waves. He mistakenly ‘proved’ that cathode rays could not be deflected by electric plates because there was a small amount of gas in his CRT. The electric plates also did not function properly due to it being placed outside the glass tube, and not being able to influence the cathode ray which was within the tube. In addition, the fact that cathode rays could cast shadows and be diffracted as well as cause fluorescence provided evidence for the wave nature of cathode rays.
However, other scientists strongly supported the particle nature of cathode rays. Experiments showed cathode rays were able to charge objects negatively through interaction. Other experiments with paddle wheels showed cathode rays carried and were able to transfer momentum. These suggested cathode rays were particles
o Outline Thomson’s experiment to measure the charge to mass ratio of an electron
Note: You should be able to confidently reproduce the content of this experiment and its implications, including sketching the diagrams.
Aim:
To measure the charge to mass (q/m) ratio of cathode rays
Procedure:
Thomson assumed that cathode rays were negatively charged particles and were emitted from the cathode. The experiment involves 2 parts;
Part 1: Finding an expression for the velocity of the cathode ray
- A beam of cathode ray is emitted at the cathode and is made to accelerate towards the multi-anode collimators. This ensures the cathode ray is fine and well defined.
- Electric field is turned on by switching on the voltage supply to the electric plates. The deflects the cathode ray to 2.
- The magnetic field is turned on by supplying a current to the coil. The current is directed so it deflects the cathode ray to 3.
- The strength of the electric and magnetic fields are adjusted to be equal and cancel out, so that the beam ends up traveling to 1.
- Since the strengths of magnetic field and electric field are equal:
[pic]
[pic]
Part 2: Finding the charge to mass ratio of the cathode ray
- The electric field is then turned off. The cathode ray is deflected by the magnetic field only, and thus curves down in an arc of a circle.
- Since the magnetic force provides the electron with the centripetal force:
[pic]
[pic]
The strength of the electric field (E) and magnetic field (B) can be determined (by measuring the size of the applied voltage and current) and the radius r of the arc described by the cathode ray can be measured. Thus the charge to mass ratio can be calculated.
Conclusion from the experiment and implications
- The experiment proved cathode rays were indeed (negatively charged) particles. The fact that the charge to mass ratio of cathode rays could be measured indicated that cathode rays had measurable mass, which in turn provided definitive evidence for the particle nature of cathode rays. This effectively ended the debate over the nature of cathode rays
- Showed that the particles had a large (negative charge) with very little mass
- Contributed to the discovery of electrons and the development of the models of atoms
- Allowed the mass of electrons to be calculated
o Explain that cathode ray tubes allowed the manipulation of a stream of charged particles
Cathode ray tube consists of an evacuated glass tube (almost all gas removed) and two metal electrodes, one at each end of the glass tube. The two electrodes are connected to a power source. The electrode connected to the negative terminal is named the cathode, while the electrode connected to the positive terminal is called the anode.
Cathode ray tubes allow the manipulation of a stream of charged particles. This is because a charged particle will be deflected by an electric field. Since the charged particles in the cathode ray move at a constant velocity, they can also be deflected by a magnetic field. Hence the streams of charged particles can be manipulated inside a cathode ray tube by different electric and magnetic fields.
Note that an induction coil is used to step-up the DC voltage to a high level (a transformer cannot be used). High voltages are required to pull electrons off the cathode and have enough kinetic energy to make their way from the cathode to the anode.
Low pressures are needed to ensure minimal collisions between the air molecules inside the tube and the electrons
o Perform an investigation to demonstrate and identify properties of cathode rays using discharge tubes:
- containing a Maltese cross
- containing electric plates
- with a fluorescent display screen
- containing a glass wheel
- analyse the information gathered to determine the sign of the charge on cathode rays
Cathode rays are emitted at the cathode and travel in straight lines
This is shown by using a CRT containing a Maltese cross. The cathode rays illuminate the Maltese cross and cast a clearly defined shadow of it at the other end of the tube.
Cathode rays can cause fluorescence
This is shown by a CRT containing a background fluorescent material; as the cathode ray passes from the cathode to the anode it causes the material to fluoresce and leave a clear trace of itself. Cathode rays are also able to cause the wall of the glass tube to glow
Cathode rays can be deflected by magnetic fields
When a pair of bar magnets is placed next to the CRT the cathode rays are deflected as predicted by the right hand palm rule.
Cathode rays can be deflected by electric fields
Similarly when a pair of electric plates is used, the cathode rays are deflected in the opposite direction to that of the electric field
Cathode rays carry and are able to transfer momentum
This can be shown using a CRT containing a paddle wheel. As the cathode rays strike the paddle wheel, some of their momentum is transferred to the paddle, which makes the paddle wheel roll in the same direction as the cathode rays are traveling.
Cathode rays are identical regardless of the type of material used as the cathode
Cathode rays can also facilitate some chemical reactions and expose photographic films.
The sign of the charge on cathode rays can be determined by using electric plates or bar magnets
o Outline the role of:
- electrodes in the electron gun
- the deflection plates or coils
- the fluorescent screen
in the cathode ray tube of conventional TV displays and oscilloscopes
A standard CRO consists of
• An electron gun, which emits a beam of cathode rays
• A deflection system, which consists of two sets of parallel electric plates
• A display screen that has on its inner surface materials that will fluoresce when struck by the cathode rays. The screen usually contains a grid that makes displays easier to read and measure
Electron Gun
A beam of electrons is emitted at the cathode and is accelerated towards the multiple anodes, and then travels into the deflection part of the tube as a fine, well-defined beam.
A small, separate voltage supply generates a current in the cathode to heat it. The heated cathode releases many free electrons which can be accelerated with little effort (Thermionic emission). There is also another electrode between the cathode and anode called the grid. Making the grid positive or negative controls the number of electrons reaching the anodes and hence striking the display screen per unit time. This controls brightness of display.
[pic]
Deflection system
The deflection system helps manipulate the cathode ray so that useful information can be displayed on the screen. The system consists of:
• Y-plates – These plates are horizontal and result in the vertical deflections of the cathode ray. The pattern and range of deflection is directly related to the type and strength of input signal, as the voltage supply to these plates are a copy of the external signal input.
• X-plates – These plates are vertical and thus result for the horizontal deflections of the cathode ray. The plates are controlled by inbuilt circuitry that supplies a time-based voltage. By adjusting the pattern of the time-based voltage, one can make the left to right deflection run at different speeds – really slowly as a dot or so fast that the dot appears to be a line.
Display Screen
The screen contains many pixels made from fluorescent materials, or phosphors. When a fine beam of the cathode ray hits the pixel it fluoresces, which allows the information to be displayed. A CRO displays a signal as a voltage-time graph, and with the help of the grid on the screen the amplitude and period of the wave can be determined.
Television
A television uses the same principle as a CRO but with a number of differences:
Electron gun
The electron gun used in a TV is similar to that used in a CRO. A black and white TV has only one electron gun, whereas a colour TV has three electron guns. There is also a grid in each electron gun to control the brightness of the display. All these functions are controlled by amplified electric signals captured by an antenna.
Deflection system
Unlike a CRO, the TV utilizes magnetic fields that are created by current coils. Magnetic fields ensure more efficient and larger deflections
Display screen
Again, the screen consists of pixels. For a black and white TV, the phosphor will glow from the maximum intensity beam (white) to zero beam intensity (black). For a colour TV, each pixel has three sub-pixels of phosphor. A shadow mask is used to ensure the beam from each colour gun only hits the corresponding spot in each pixel.
Also, unlike a CRO, where a beam of cathode rays scans across the screen to trace out a single dot or line, the electron guns of a TV scan a series of horizontal lines across the entire screen 50 times a second. The odd lines are scanned first then the even lines (this is called raster).
o Perform an investigation and gather first-hand information to observe the occurrence of different striation patterns for different pressures in discharge tubes
Procedure
Place five or six discharge tubes that are held vertically and parallel to each other by a stand. Each tube contains a different preset air pressure and is sealed permanently
The anodes of these discharge tubes are connected together to form one common outlet whereas the cathodes are separated. Hence the positive terminal of the power source can remain attached to the anode, while attaching the negative terminal to each individual cathode selectively operates that particular discharge tube.
Observations
‘High’ pressure tube (5 kPa)
Purple streamers appear between the cathode and anode. With a slightly lower pressure tube, the streamers change to a gentle pink glow that usually fills the entire tube.
‘Medium’ pressure tube (0.1 kPa)
The pink glow starts to break down into alternating bright regions and dark regions. The cause of the glows and dark spaces is generally due to the electrons (cathode rays) carrying different energies. When they collide with gas molecules in the tube, they may At even lower pressure, the dark spaces elongate and the glow is usually faint
‘Low’ pressure tube (0.02-0.04 kPa)
With an extremely low air pressure, the glows in the tube completely disappear, that is the dark spaces fill the entire tube (dark space is defined as the Crooke’s dark space). The only visible glow in this case is the green fluorescence on the glass wall at the anode region.
9.4.2 The reconceptualisation of the model of light led to an understanding of the photoelectric effect and black body radiation
o Identify the relationships between photon energy, frequency, speed of light and wavelength: c=fλ
Electromagnetic radiation (EMR) consists of changing magnetic and electric fields that propagate perpendicularly to each other.
EMR is a wave which can propagate through a vacuum and travels at a constant speed of light. Since we know that the velocity of a wave can be determined by: v=fλ, and we know that all EMR travels at the speed of light. Hence we can substitute v with c:
c=fλ
A stationary charge produces its own electric field. A charge moving at a constant velocity produces a magnetic field. An accelerating or oscillating charge produces EMR. The reverse is also true: EMR can cause charges to accelerate or oscillate
Planck’s hypothesis relates photon energy to frequency by the equation below, E=hf
o Solve problems and analyse information using: E=hf and c=fλ
[pic][pic]
Remember units and that the two can be used together in calculations
o Outline qualitatively Hertz’s experiments in measuring the speed of radio waves and how they relate to light waves
Evaluating how major advances in scientific understanding and technology have changed the direction or nature of scientific thinking
Hertz’s discovery was the first of its kind to identify the nature of a form of EMR (other than light) that was predicted by Maxwell’s equations. Once Hertz had identified radio waves, which behaved as Maxwell’s equations predicted, the search was on for yet other unidentified forms of EMR. By measuring the speed of radio waves, Hertz’s discovery verified the existence of what is known as the electromagnetic spectrum. Many uses of the other forms of electromagnetism could then be developed. Thus Hertz’s discovery was a profound step in this area of scientific research and endeavor.
Hertz was able to determine the speed of the EMR he produced by measuring its frequency and wavelength. The frequency of the EMR must be identical to the frequency of the oscillation of the electric current, which could be predetermined. The wavelength was determined by taking measurements from the interference pattern generated by allowing the newly produced wave to take two slightly different pathways and recombining them at the receiving coil.
How they relate
Not only did the newly produced EMR have the same speed as light, Hertz showed that this radiation had all other properties of light. (Reflection, refraction, interference and polarization). Hence he verified Maxwell’s earlier predictions of the whole spectrum of EMR
o Describe Hertz’s observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate
Aim: Hertz aimed to produce EMR other than visible light and determine its properties to see whether they agreed with Maxwell’s early theoretical predictions
Procedure:
1. Production of EMR – The current that was fed into the primary loop from the induction coil oscillated back and forth. This oscillation of charges (accelerating electrons) in the primary loop generated EMR, which was emitted at the gap.
2. Transmission of EMR – The EMR was focused by the parabolic plates and traveled to the receiving coil
3. Reception of EMR – The EMR (radio wave) was again focused at the receiving coil. The EMR caused electrons in the receiving coil to oscillate, thus regenerating the electric signal that was used in the primary loop, although much weaker.
An induction coil is used as a high voltage is used to allow electrons to jump across the gap. The spark in the receiving coil is fainter than the spark in the primary coil.
o Identify Planck’s hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised
Black body is an object that can absorb and/or emit energy perfectly
Eg. A piece of tungsten metal is a perfect black body. The Earth itself is almost a perfect black body. A star is a non-perfect black body.
When a black body is heated to some temperature in a vacuum, it starts to emit radiation perfectly, known as black body radiation. If the data is measured experimentally and plotted as intensity against wavelength, this produces a black body radiation curve.
When mathematics was applied to the black body radiation curve, they found inconsistencies. Max Planck proposed a hypothesis, known as Planck’s hypothesis
The radiation emitted from a black body is not continuous as waves – it is emitted as packets of energy called quanta (photons)
Planck’s hypothesis led to the idea that energy is quantized.
o Explain the particle model of light in terms of photons with particular energy and frequency
Light can be reflected, refracted, deflected, interfered and polarized, which undoubtedly proves light is a transverse wave.
However, based on the quantum hypothesis proposed by Planck, the energy of light is quantized and comes as packets; this suggests light is composed of particles. Each light particle, or photon, posses an amount of energy related to the frequency of the light wave, as describe by the equation E=hf.
This leads to the wave-particle duality of light.
Note that both the particle and wave model of light are correct, and work conjointly with each other to describe all the behaviors of light
o Identify Einstein’s contribution to quantum theory and its relation to black body radiation
In 1905 Einstein combined Planck’s hypothesis that the energy of radiation was quantized and the particle model of light to explain the photoelectric effect, as follows:
1. Light behaves like particles called photons, each carries a discrete package of energy. (related by E=hf). The collisions between photons and electrons lead to the photoelectric effect.
2. Only photons with energy above the work function (W) of a metal can cause the photoelectric effect. The work function is the minimum energy required to free electrons from the metal surface. The minimum frequency the light must have to cause the photoelectric effect in a metal is called the threshold frequency. The kinetic energy of the photoelectrons released is determined by: Ek = hf-w
3. A photon can either transfer all of its energy to an electron or none.
Graphically
Plotting the maximum kinetic energies of photoelectrons emitted against the frequencies of the illuminating EMR for one particular metal surface will result in the graph as shown
• The slope of the graph is equal to Planck’s constant h.
• The x-int of the graph is equal to the threshold frequency. If a metal with a larger work function is used this point shifts to the right
• The absolute value of the y-int is equal to the work function. If a metal with a larger work function is used then the y-int shifts downwards.
o Identify data sources, gather, process and analyse information and use available evidence to assess Einstein’s contribution to quantum theory and its relation to black body radiation
Einstein used Planck’s hypothesis and used it to successfully explain the photoelectric effect, providing convincing evidence to back up Planck’s radical hypothesis.
Einstein used the equation Ek = hf-w to explain some properties of the photoelectric effect. Including that once photoelectrons are emitted, what determines their kinetic energy is the frequency of the incident EMR and the value of the work function. The all or none principle and the role of intensity of photons was also determined.
Later on Millikan performed an experiment to verify Einstein’s equation for the photoelectric effect. He was able to determine a more precise value for h. This strengthened the connection between the photoelectric effect, the black body radiation curve and Planck’s hypothesis, which form the heart of quantum physics. Hence Einstein has had a significantly positive contribution to quantum theory, with the help of others such as Planck and Millikan.
o Identify data sources, gather, process and present information to summarise the use of the photoelectric effect in photocells
Photocells are electronic devices with resistances that alter the presence of light
A photocell consists of a low-pressure glass bulb, in which is embedded an anode and a large cathode coated with a photoelectric material. The gap between the cathode and anode means that the resistance it develops is infinite and no current flows. When a light shines on the light sensitive cathode, electrons are emitted as a result of photoelectric effect. These free electrons conduct electricity from the cathode to the anode, which consequently lowers the resistance of the photocell. As a result, a current starts to flow in the circuit. The current triggers another functional system such as an alarm.
Uses of photocells include:
Alarm systems in the house – if thieves turn on the lights the alarm sounds
Automatic doors – infrared light from the sensor is reflected from the approaching objects and triggers the photocell
Door alarms for shops – which beep when customers come into the shop
o Process information to discuss Einstein and Planck’s differing views about whether science research is removed from social and political forces
Einstein
Einstein was a politically active man, openly criticized German militarism during World War I. During WWII, he convinced the US president to set up the project of making nuclear bombs. His rationale was his fear that the Germans were developing nuclear technology and might build nuclear bombs first. Hence Einstein’s science research made him inseparable from social and political forces. His physics research (such as E=mc2) led to the creation of a deadly weapon, and also served as the basis for the development of nuclear power stations.
Planck
Planck’s famous quantum theory made him the authority in German physics. He was not as politically active as Einstein and focused on his physics research even during the war. However, Planck did go to Adolf Hitler in an attempt to stop his racial policies. It could be argued that he simply did this to preserve the development of German physics OR for moral reasons, but either way his science research is influenced by social and political forces.
o Perform an investigation to demonstrate the production and reception of radio waves
Radio waves are produced by sparks. Sparks from an induction coil produce radio waves which can be received by any AM radio. (An oscillating current in the induction coil means accelerating electrons, which produces EMR). The static noise can be heard in time with the sparking.
Risk: Extreme care needs to be taken with the induction coil due to the high voltage and X-rays produced.
Note it is rather difficult to measure the speed or determine the properties of these radio waves experimentally in school labs.
A second AM radio tuned off a station by about 500 Hz from the other radio and with the volume turned down can help you hear the other one. (it will act as an oscillator and with a bit of fiddling produce a ‘tone’)
9.4.3 Limitations of past technologies and increased research into the structure of the atom resulted in the invention of transistors
o Identify that some electrons in solids are shared between atoms and move freely
Metallic bonds are bonds in which metal atoms are joined together to form a lattice structure. There is a ‘sea of delocalized valence electrons’ surrounding the metal ions. The valence electrons of all metal atoms are freed and are shared among other metal atoms.
Note that these delocalized electrons give metals their unique physical properties, such as high thermal and electrical conductance
o Describe the difference between conductors, insulators and semiconductors in terms of band structures and relative electrical resistance
The energy band is the range of energy electrons possess in a lattice. There are two types of energy bands:
1. Valence band: The energy levels of the valence electrons of individual atoms. It has a higher energy than energy bands formed by the electrons found in the inner shells
2. Conduction band: When valence electrons gain energy, they might move up to even higher energy levels that were previously empty. These electrons make up the conduction band. In the conduction band, these electrons are free to move and therefore are able to conduct electricity
Except for conductors, electrons in the conduction bad usually have higher energy than those in the valence band. The energy gap that electrons have to overcome to move from the valence band to the conduction band is referred to as the forbidden energy gap.
Semiconductor
• Band structure – 4 valence electrons of each semiconductor atom form 4 covalent bonds with the neighbouring atoms. Therefore the valence band is full. By the nature of a semiconductor, the valence electrons only need to gain a small amount of energy if they are going to move into the conduction band; hence the conduction band is separated from the valence band by a very small forbidden energy gap. At room temperature, a minority of electrons in the balance band can overcome the small forbidden energy gap. Hence at room temperature, the conduction band of the semiconductor is partially filled.
[pic]
• Electrical resistance – The small number of electrons in the conduction band means at room temperature the conductivity of a semiconductor is moderate (and so is its electrical resistance). As the temperature of a semiconductor increases, its conductivity increases and its resistance decreases. This is because as temperature increases the electrons in the valence band gain more thermal energy. This allows more electrons in the valence band to overcome the forbidden energy gap and move into the conduction band. More electrons in the conduction band results in higher conductivity for the semiconductor.
Conductors
• Band structure – The valence electrons for metal atoms are all delocalized and shared. These electrons have gained high energy and are free to move, and hence these electrons are all in the conduction band. Since all the valence electrons of a conductor are in the conduction band, the valence band of a conductor is said to merge with the conduction band. The forbidden energy gap is non-existent.
[pic]
• Electrical resistance – A conductor has a very good electric conductivity, or low electric resistance. This is because there are as many electrons found in the conduction band as there are in the valence band, and hence the amount of electrons in the conduction band is very high. As the temperature of a conductor increases, its conductivity decreases and its resistance increases. This is because at higher temperatures the lattice will possess more thermal energy and vibrate more vigorously. These vibrations lead to more collisions between conducting electrons and lattice and therefore impede the motion of these electrons. This results in a decrease in conductance or an increase in resistance of the conductor.
Insulators
• Band structure – In an insulator all the valence electrons are used to form covalent bonds to hold its atoms together within the lattice. Thus the valence band is full, and the valence electrons are locked in position and can not move. The valence band is separated from the conduction band via a very large forbidden energy gap. At room temperature virtually no electrons can gain enough energy to jump across the large forbidden energy gap. Therefore the conduction band is virtually empty.
• Electrical resistance – Since the conduction band of an insulator is empty, its conductivity at room temperature is almost zero, and its resistance is infinite. Remember that IF enough energy is applied to an insulator, by applying a very high voltage or heating it to a very high temperature, the electrons in the valence band will eventually gain enough energy to overcome the forbidden energy gap to occupy the conduction band. In these cases the insulator will start to conduct; however, during such processes its structure might have already been damaged
[pic]
o Identify absences of electrons in a nearly full band as holes, and recognize that both electrons and holes help to carry current
Electron-hole pair conduction
When one electron ‘jumps’ across the forbidden energy gap to occupy the conduction band, there will be an electron efficiency in the valence shell.
The missing of one electron constitutes a positive hole. Although positive holes do not migrate, when an electron jumps into a positive hole, there will be another positive hole left at the positions where the electron was before.
Hence when a voltage is applied across a semiconductor, conduction can occur in the conduction band by the movement of free electrons, as well as in the valence band by the movement of positive holes in the opposite direction due to the movement of electrons into and out of these holes.
o Compare qualitatively the relative number of free electrons that can drift from atom to atom in conductors, semiconductors and insulators
Conductors
The valence electrons for metal atoms are all delocalized and shared. Hence there is a very high number of electrons that can drift from atom to atom.
Semiconductors
Since all 4 valence electrons of a semiconductor atom form 4 covalent bonds with neighbouring atoms, all the electrons are locked into position. When this occurs no free electrons drift from atom to atom. However, due to the nature of a semiconductor the valence electrons only need to gain a small amount of energy to move into the conduction band. If this occurs in addition to applying a voltage, then a small amount of free electrons will drift from atom to atom towards the positive terminal. This is due to electron-hole pair conduction.
Insulators
In an insulator all the valence electrons are used to form covalent bonds to hold its atoms together. Hence all the electrons are locked in position and cannot drift from atom to atom.
o Identify differences in p- and n- type semiconductors in terms of the relative number of negative charge carriers and positive holes
|Semiconductors can be broadly classified into two categories: |
|Intrinsic semiconductors – Pure semiconductors. These semiconductors conduct electricity by electron-hole pair conduction, and have moderate |
|conductivity at room temperature |
|Extrinsic semiconductors – Semiconductors that have other types of impurities added. These impurities increase their conductivity by modifying|
|their electrical properties |
Extrinsic semiconductors can be further classified into two types:
• P-type semiconductors – A p-type semiconductor is created when a pure semiconductor such as silicon is doped with any group III elements, for instance boron. Since group III elements have 3 valence electrons, there will be regions of the silicon lattice where there is an electron deficiency, and hence a positive hole. The presence of positive holes allows p-type semiconductors to have much higher conductivity compared to intrinsic semiconductors
• N-type semiconductors – A N-type semiconductor is created when a pure semiconductor is doped with any group V elements. All group V atoms have 5 valence electrons, and hence each group V element will have one spare electron that is not required for bonding. These electrons are free to move and have sufficiently high energy to occupy the conduction band. N-type semiconductors contain free electrons (which are negative). The presence of free electrons increases the conductivity of n-type semiconductors.
P-type has more positive holes and less negative charge carriers
N-type has less positive holes and more positive charge carriers
o Describe how ‘doping’ a semiconductor can change its electrical properties
Doping
Doping is the process of adding substances (impurities) to semiconductors in order to change their electrical properties. The amount of impurities added is very small, about 0.001%
If a semiconductor is added with an impurity from group III, positive holes will be created due to an electron deficiency. This improves its electrical conductivity, as electrons can easily migrate from the negative to the positive terminal by jumping in to and out of positive holes.
If a semiconductor is added with an impurity from group V, there will be ‘spare’ electrons that are not required for bonding and allowed to occupy the conduction band. This also improves electrical conductivity, as the extra numbers of free electrons are free to move in the presence of an applied voltage.
o Other important notes
Drift velocity
Even when there is no potential difference, electrons are moving randomly in all directions at very high speeds. However, due to their randomness there is no net current.
When a voltage is applied across a conductor, superimposed on top of the random motions of the electrons is that all electrons start to ‘drift’ uniformly in one direction. This is known as drift velocity, and can be given by the equation:
[pic] , where v is drift velocity, I is current, n is electron density, e is charge of electron and A is cross sectional area of the conductor.
When a p-type semiconductor is joined with a n-type semiconductor
P-type conductors have positive holes and positive holes and therefore lack electrons, while n-type semiconductors have excessive free electrons. When a p-type semiconductor and a n-type semiconductor join together, electrons from the n-type migrate into the p-type at the junction to fill up positive holes in this area.
Hence the p-type will now possess more electrons than its protons and display a negative charge, whereas the n-type will display a positive charge due to the loss of electrons. This creates a potential difference across the junction, which is also known as the depletion zone.
o Gather, process and present secondary information to discuss how short comings in available communication technology lead to an increased knowledge of the properties of materials with particular reference to the invention of the transistor
The need for the transistor
During WWII, the use of thermionic devices (vacuum tubes) became important in communications and in other developing technologies such as radar. Light and reliable transceivers that could be powered by batteries rather than mains power for portability were needed. Reliable communication between pilots of aircraft and control towers was needed. Radar also became increasingly important to detect approaching bombers.
Diodes
A diode is an electronic device which only allows electric current to flow in one direction. It can be constructed when a p-type semiconductor is joined with an n-type semiconductor.
A diode can be forward biased when the p-type part is connected to the positive terminal, or reverse biased when the p-type part is connected to the negative terminal.
Note that by combining p-type and n-type semiconductors in different ways, many other useful solid state devices are created.
Transistors
A transistor can be created by either sandwiching a thin layer of p-type semiconductor in between two pieces of n-type semiconductor, or vise versa. A transistor has three connecting leads: collector, base and emitter.
Function of transistors
The three leads of the transistor allow it to be connected across two circuits. One circuit goes through the emitter and the base, while the other goes through the emitter and the collector.
The flow of charge carriers through the emitter and the base alters the electric property of the middle piece semiconductor; this will affect the conductivity of the transistor between the emitter and collect, thereby affecting the flow of charges in the circuit
Hence a small current flowing through the base can module the flow of – usually – a larger current in the main circuit that goes through the collector. Hence a small current can either produce a much larger copy of itself in the main circuit (as an amplifier) or stop the current flow (as an electronic switch)
o Describe differences between solid state and thermionic devices and discuss why solid state devices replaced thermionic devices
Thermionic devices
Thermionic device is one which consists of a vacuum tube with two or more electrodes embedded in it. Emission of electrons is from the cathode with the aid of the thermionic effect.
Why solid state devices replaced thermionic devices
This occurred due to their advantages over thermionic devices:
• Miniature size – Solid state devices are considerably smaller than thermionic devices. The trend of miniaturization of electronic devices, such as mobile phones, means the tiny solid state devices are much preferred
• Durable and long lasting – Solid state devices are touch and can withstand a reasonable amount of physical impact, while thermionic devices are extremely fragile as they are made from glass bulbs
• More rapid operational speed – Solid state devices operate at a much faster rate than thermionic devices
• More energy efficient – Thermionic devices require very high voltages for their operation, whereas solid state devices can function at voltages less than 1V. In addition, the large amount of heat dissipated during the operation of thermionic devices means that there is a considerable amount of energy wasted
• Cheap to produce – Solid state devices are much cheaper to make than the thermionic devices
o Identify that the use of germanium in early transistors is related to lack of ability to produce other materials of suitable purity
Early solid state devices were mostly made from the semiconductor germanium. This was because the semiconductors used to make solid state devices must be extremely pure. However, at this early time there was only the technology for extracting and purifying germanium. There was no technology for preparing silicon with a sufficiently high purity.
Today silicon is used as it has many superior properties compared to germanium:
• More economical – Silicon can be extracted from sand, which allows it to be obtained at a much lower price and consequently reduces the price of solid state devices
• Functions well under high temperature – Heat is produced while electronic devices are operating, which elevates the temperature of such devices. Under these high temperatures silicon will still maintain its semi conductivity, while germanium tends to become a better conductor.
• The ability to form an oxide layer – Silicon is able to form an impervious silicon dioxide layer when it is treated by heat in the presence of high oxygen content. This is an essential property for the production of microchips which is not present in germanium.
o Identify data sources, gather, process and present information to summarise the effect of light on semiconductors in solar cells
What advance in physics
By utilizing the photoelectric effect to transform light energy into electrical energy, photovoltaic cells can be created.
What technologies arose
Solar cell technology, or photovoltaics, is widespread in remote communities and in smaller, mobile applications such as boats where connection to the mains power grid is not possible or practical. Satellites and space stations also use solar panels as a source of electricity for their long-term missions.
Photoelectric effect
Is the phenomenon that a metal surface emits electrons when struck by EMR with a frequency above a certain value.
Solar cell
A solar cell consists of a joined p-type and n-type semiconductor, sandwiched in between two metal contacts that are responsible for conducting electricity into and out of such a device. When sunlight reaches the p-n junction, electrons are freed from the semiconductor at the junction as a result of the photoelectric effect. These electrons have now gained high enough energy so that they occupy the conduction band. Since these electrons are free to move, they can be easily accelerated by the electric field existing naturally at the p-n junction towards the n-type semiconductor. After being accelerated through the n-type semiconductor, the electrons are collected by the front metal grids to enter the external circuit to do work.
[pic]
o Identify data sources, gather, process, analyse information and use available evidence to assess the impact of the invention of transistors on society with particular reference to their use in microchips and microprocessors
Integrated circuit
This is an assembly of electronic devices and their connections, fabricated in a single unit (a single chip), which is designed to carry out specific tasks as they would if they were made individually and connected by wires.
Microprocessors
A microprocessor is a type of microchip that contains enough complicated electronic devices and their connections to perform arithmetic, logic and control operations.
The invention of transistors has allowed many devices to be integrated onto one chip, and the eventual invention of microchips and microprocessors.
Advantages
As the number of semiconductor devices on a single chip increases, the devices are placed closer together. Hence the transmission signals between devices become more efficient due to the smaller operating distant between the devices. The power dissipation is also reduced due to both the small size of the devices and small distance of separation between them (small distance results in less resistance to electric signals and therefore less heat loss). Low heat dissipation means the devices become more power efficient, and the requirement for heat removal is also reduced.
Note that cost doest NOT increase as there is less cost per unit for each transistor (they are smaller)
Evaluation
The invention and development of integrated circuits has formed the basis for the development of many forms of useful electronic devices, such as medical diagnosis, biotechnology, telecommunications, etc
Further development of microprocessors enables computers to be made. Computers are essential in our day-to-day lives and are used in business and industries and by scientific research. This is improved the standards of living for society.
The developments of microprocessors also lead to the development of industrial robots. This has proved beneficial for society in areas where heavy labour is involved or dangerous situations are anticipated.
o Perform an investigation to model the behaviour of semiconductors, including the creation of a hole or positive charge on the atom that has lost the electron and the movement of electrons and holes in opposite directions when an electric field is applied across the semiconductor
Creation of positive holes and movement of positive holes and electrons in the presence of an external electric field:
A draughts board can be used, leave a space in one of the squares. As the playing pieces are moved into the hole, and the pieces behind are moved too, it is observed that pieces (representing electrons) move in one direction, but the space (representing the positive hole) moves in the opposite direction.
9.4.4 Investigations into the electrical properties of particular metals at different temperatures led to the identification of superconductivity and the exploration of possible applications
o Outline the methods used by the Braggs to determine crystal structure
Sir William Henry Bragg and his son, Sir William Lawrence Bragg hypothesized that X-rays are penetrative enough to reach different planes of the lattice and thus be scattered and reflected by these planes. These scattered or reflected X-rays would result in an interference pattern that could be detected and analysed to give information about the internal structure of the lattice.
Theta is the angle between the X-ray beam and the crystal surface to give constructive interference.
How to determine distance (d)
• Beam B travels 2CD longer than beam A
• CD = dsinθ, where d is the distance between atoms
• The angle θ is adjusted so that there is constructive intereference. That is, the beams A and B are in phase when arriving at the detector (by letting the difference be whole number multiples of their wavelengths)
• This gives us the equation [pic]
• ‘d’ can be determined since all other factors are known.
o Identify that metals possess a crystal lattice structure
Metal has a structure that can be represented as a sea of delocalized electrons surrounding a lattice of metal ions.
o Describe conduction in metals as a free movement of electrons unimpeded by the lattice
Generally, metals are excellent conductors of electricity due to the presence of the large number of delocalized electrons. These electrons are free to move and so are able to conduct electricity. These electrons are unimpeded by the lattice. Note: Conductivity is high and resistance is low in metals (the two are always inversely related).
o Identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations
Factors affecting resistivity of metal conductor: (Anything that impedes the movement of delocalized electrons would reduce the conductivity of the metal, and so increase its resistance.
• Temperature – As the temperature increases, the energy of the lattice increases. This leads to an increase in bivration of particles inside the lattice. This vibration will cause more collision between the electrons and the lattice, impeding their movement. Thus the increase in temperature will decrease its conductivity or increase its resistance.
• Impurities – Adding impurities impedes the electron movement, and hence decreases the conductivity or increases the resistance.
• Length – The longer the conductor, the longer the electrons need to travel and the higher the change for collision. This increases resistance
• Cross-sectional area – The larger the cross-sectional aera, the easier it is for electrons to pass through the conductor without collisions. This educes the resistance
• Electron density – Electron densities refer to how many free electrons per unit volume of the conductor are able to carry out conduction. Some metals naturally have more electron density than other metals, and hence these metals (silver) have lower resistance.
o Describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance
Superconductivity – is the phenomenon exhibited by certain metals where they will have no resistance to the flow of electricity when their temperature is cooled below a certain value (their critical temperature)
As the temperature of a metal decreases, its resistance also decreases. There will be a point where the resistance of the metal suddenly drops to zero.
Note that only some metals exhibit superconductivity.
o Process information to identify some of the metals, metal alloys and compounds that have been identified as exhibiting the property of superconductivity and their critical temperatures
Type 1 – Metal and metal alloys – (Critical temperature)
Aluminium – 1.2K
Mercury – 4.2K
Niobium-aluminium-germanium alloy – 21K
Advantages
• These metal and metal alloy superconductors are generally more workable, as they are malleable and ductile
• They are generally tough and can withstand physical impact
Disadvantages
• Have very low critical temperatures, which are technically very hard to reach and maintain
Type 2 – Oxides and ceramics – (Critical temperature)
YBa2Cu3O7 – 90K
HBaCaCuO – up to 130K
Advantages
• Liquid nitrogen can be used to reach critical temperature, and this is much cheaper than the liquid helium which is used by type 1 superconductors
Disadvantages
• More brittle, fragile, shatter more easily and are generally less workable than metal or metal alloy superconductors
• Chemically less stable and tend to decompose in extreme conditions.
• More difficult to produce
o Discuss the BCS theory
The BCS theory explains why some materials lose their resistance completely when they are cooled below certain temperatures while others do not. Bardeen, Cooper and Schrieffer developed the BCS theory which is as follows;
Phonons are packets of sound waves produced by the crystal lattice as it vibrates. Phonons are quanta of sound energy and are emitted and absorbed by the vibrating atoms at the lattice points in the solid. Phonons possess discrete energy (E=hf). However the speed of the phonon varies depending on the type of phonon.
Cooper pairs
1. When an electron passes through a gap in the crystal lattice there is an inward distortion of the lattice. This creates an area of grater positive charge density around itself.
2. Another electron (With the opposite spin and equal momentum in the opposite direction) is attracted to this area, and the two electrons interact by exchange of a virtual phonon. This exchange is an attractive force, and as a result, the electrostatic repulsion between the two electrons is momentarily overcome and the two become a Cooper pair.
3. Since electrons that are paired have opposite spin and opposite momentum, the result is that a cooper pair has no net spin and zero net momentum.
4. Because the net momentum is zero, then according to de Broglie equation[pic], the wavelength they have is infinite. As a consequence, these electron pairs are not scattered by normal mechanisms in the crystal lattice and can move through the lattice unimpeded.
Current persists forever
In a superconductor which is cooled below its critical temperature, an applied electric field will displace all Cooper pairs producing a net current flow, and they are able to move through the lattice with no resistance to their motion. When the electric field disappears, however, scattering (due to collision with vibrating lattice or impurities) is not possible because it is energetically unfavourable. The current therefore persists forever, as long as the temperature remains below the critical temperature.
o Perform an investigation to demonstrate magnetic levitation
The phenomenon that a superconductor is able to totally exclue external magnetic fields, therefore its internal magnetic field is always zero, is known as the Meissner effect. The Meissner effect allows a superconductor to be able to levitate a small piece of magnet placed on top of it.
Method
1. A piece of superconductor is cooled by immersing it in liquid nitrogen
2. Use a pair of forceps to pick up a small piece of permanent magnet and carefully place it above the superconductor.
3. Describe observations
Note: Liquid nitrogen has a temperature of -196C. Hence wearing safety goggles and rubber gloves is mandatory for this demonstration.
o Analyse information to explain why a magnet is able to hover above a superconducting material that has reached the temperature at which it is superconducting
• The superconducting material is cooled below its critical temperature
• When an external magnetic field attempts to enter a superconductor, it induces a perfect eddy current to circulate the superconductor.
• The current is ‘perfect’ as a result of zero resistance to the flow of electricity in the superconductor. This ‘perfect’ current flows in a such a direction that the magnetic field it produces is just as strong, but in the opposite direction to the external magnetic field.
• This leads to a total cancellation of this external magnetic field and allows none of it to penetrate through the superconductor
• The perfect flow of induced current in the superconductor will allow it to set up magnetic poles that are strong enough to repel the small magnet forcefully enough to overcome its weight force.
o Gather and process information to describe how superconductors and the effects of magnetic fields have been applied to develop a maglev train
Maglev trains
Levitation
To levitate the train, the magnets are set up between the train and the track such that they are made to have the same pole so that they can repel. The repulsion is made strong enough to overcome the weight of the train and thus the train hovers. Only the electromagnets on the trains are made from superconductors, due to current costs.
Propulsion
A group of magnets are used, both on the side of the train and the side of the track. When the train moves forwards, the north poles will be pulled back by the south poles on the track. Every time the train gets past one set of magnets, the polarity of the magnets on either the train or the track will reverse. This accelerates the train faster. As a train speeds up, the frequency of polarity change will increase. Hence we can alter the frequency at which the magnetic poles change to limit the speed of the train
Advantages
1. No physical contact ( minimizes frictional drag ( improves maximum speed
2. No mechanical energy is lost ( Train is extremely energy efficient
3. Hovering ( Smooth to run ( Less wear/tear ( Less effort for maintanence
Disadvantages
1. Very expensive to run, mainly due to the need for coolants to maintain low temperatures and confine the low temperatures
2. High running costs ( high costs for tickets ( discourages production of maglev train
o Process information to discuss possible applications of superconductivity and the effects of those applications on computers, generators and motors and transmission of electricity through power grids
Superconductors are mainly used due to the following properties;
1. Efficient conduction – Energy is lost as heat when a current flows through a conductor. (P=I2R). However, since superconductors have zero resistance, then no heat loss will occur
2. Powerful magnets – A very strong magnetic field requires a very large current, which inevitably results in a significant amount of energy losses as heat. However, if an electromagnet with zero resistance is used, no heat loss will occur as the current flows. Hence this makes the whole process more energy efficient and allows the magnetic field to be stronger.
Also, once a current is established, due to the lack of resistance in the conductor, the flow of current will not diminish even if the power source is removed.
Supercomputers
The fact that superconductors have effectively zero resistance and therefore effectively zero heat production when electricity flows through them means that the devices made from superconductors can be integrated closer than those made from ordinary semiconductors. This makes the integrated circuits made from superconductors far more powerful. Closer packing means less delay in signals and faster circuits.
Motors and generators
When superconductors are used in motors, the low resistance to the flow of electricity means that with given amount of voltage, the net current flow in the motors will be bigger, which means the motors are more powerful. Furthermore no heat loss means the devices are more energy efficient
Transmission of electricity through power grids
Once transmission wires are made from superconductors, the resistance of the transmission wires is effectively reduced to zero. This minimises the heat lost, which means all of the energy produced at the generator can be transferred to households, making the process almost 100% efficient. Minimal energy losses enable the whole process to become more environmentally friendly. Also it enables power stations to be built further away from large cities, which reduces pollution near metropolitan areas. A major disadvantage is that it is very difficult to cool the wires, as they are open to the environment. Also, super conducting wires only transmit DC, which makes it hard to operate on our current AC system.
o Discuss the advantages of using superconductors and identify limitations to their use
Advantages
- Increases energy efficiency of many operations
- Provides applications and services otherwise not possible (Maglev train)
- Very strong magnetic fields can be produced, which are very useful in MRI machines which detect disease
- Superconductive films may result in the miniaturization and increase speed of computer chips
Limitations
- Their low operating temperature of superconductors is extremely hard and expensive to reach. Even once it is established, it is difficult to insulate from the surroundings.
- Also there is a huge cost and inconvenience.
- The materials of which they are made, are often brittle and hard to manufacture
In the near future, there is a possibility that superconductors that can operate at room temperature will be developed. This will remove the need of coolants and maintenance of low temperatures, and will allow perfectly energy efficient devices, as well as super powerful computers, to be easily economically produced.
Ideas to Implementation
9.7.1 Our understanding of celestial objects depends upon observations made from Earth or from space near the Earth
o Discuss Galileo’s use of the telescope to identify features of the Moon
Galileo did not invent the telescope, but was the first person to construct one so that it could produce a sufficiently clear image to observe features on the Moon. He noticed that there existed mountains and craters on the Moon. He used the angle of the sun to estimate the heights of lunar mountains, and showed that the craters were deep with high sides around them.
o Discuss why some wavebands can be more easily detected from space
The atmosphere is composed mainly of nitrogen and oxygen gas. The atmosphere is transparent to visible land and most radio waves, as there is little interaction with the molecules in the atmosphere.
- However, blue light, having a shorter wavelength in the visible spectrum, is scattered by fine particles and larger molecules in the atmosphere.
- Further to the scattering effect is distortion, caused by the refraction of light as it passes through air of slightly different densities due to temperature variations. (ie. Twinkling of stars)
- For other wavebands, the atmosphere acts as a shield, absorbing nearly all gamma and X-rays.
- A majority of UV wavelengths are absorbed by ozone gas molecules.
- Infrared radiation is partially absorbed by carbon dioxide and water vapour molecules.
For the above reasons some wavebands are more easily detected from space, where there are no atmospheric influences.
o Define the terms ‘resolution’ and ‘sensitivity’ of telescopes
Resolution of a telescope- is its ability to make distinct images of objects, which are close to each other in angular separation. (ie. Two stars with a small angular separation may appear as one. A larger telescope may make the two stars become distinctly separate)
Sensitivity – This is a measurement of the light gathering ability of a telescope. This is directly proportional to the surface area used to collect the incoming light, either the objective lens for a refracting telescope or a primary mirror for a reflective telescope.
o Discuss the problems associated with ground-based astronomy in terms of resolution and absorption of radiation and atmospheric distortion
Ground-based astronomy has a number of limitations imposed by the effects of the atmosphere on observations. Wavebands such as gamma rays, X-rays, UV and infrared are all extremely useful to astronomers, yet the detection of these are limited by atmospheric distortion. (See above) Ground-based telescopes also suffer from ‘seeing’, which is the result of warmer air pockets with a lower refractive index in surrounding cooler air.
To reduce the limitations of ground-based astronomy, the telescope can be placed as high as possible. This reduces pollution, water vapour haze and also results in a lower distance needed to be penetrated by radiation through the atmosphere.
o Outline methods by which the resolution and/or sensitivity of ground-based systems can be improved, including adaptive optics, interferometry and active optics
The resolving power of a standard ground-based telescope is about one arc second. This can be improved by;
Adaptive optics
This uses a brighter light source from either a nearby star or a laser beam. The way in which the atmosphere affects this bright light source is analysed in real time by a wave front sensor. Corrections to the distortion are fed into the telescope’s rapidly adaptable mirror so that the observed image has the distortion caused by the atmosphere largely eliminated.
Active optics
This employs a wavefront sensor to detect distortion in the collected light. However, active optics uses a slower feedback system that corrects deformities in the primary mirror of the telescope. These deformities can be caused by physical movement of the telescope to different positions and differences in temperature.
Interferometry
This is applied to radio astronomy. This is where two or more radio telescopes are linked by computers, which combine the incoming signals from the separate telescopes to produce an interference pattern. This is than analysed further and is converted into an image with a resolution approaching those of the largest optical telescopes.
o Identify data sources, plan, choose equipment or resources for, and perform, an investigation to demonstrate why it is desirable for telescopes to have a large diameter objective lens or mirror in terms of both sensitivity and resolution
An observer can compare the clarity of detail of objects in the far distanced viewed through two binoculars of difference sizes. This provides a qualitative comparison of resolution.
9.7.2 Careful measurement of a celestial object’s position in the sky (astrometry) may be used to determine its position
o Define the terms parallax, parsec and light-year
Light-year
The distance traveled through space by electromagnetic waves during one Earth year. In metres 1 l.y. = 9.4605x1015m (Or 0.3066 parsecs)
Parsec (pc)
One parsec, or parallax-second, is the distance that corresponds to an annual parallax of 1 second of arc
Parallax
The apparent shift in position of a close object against a distant background due to a change in position of the observer
Annual parallax
Half the angle through which a nearby star appears to shift against the backdrop of distance stars, over a particular six-month period
Note: Arcminute = 1/60th of a degree. Arcsecond = 1/60th of a arcminute
o Explain how trigonometric parallax can be used to determine the distance to stars
Trigonometric parallax
This is a method of using trigonometry to solve the triangle formed by parallax to determined distance
By determining the annual parallax, we can use the formula d=1/p to determine the distance to a star.
o Discuss the limitations of trigonometric parallax measurements
Limits in the resolution of telescopes due to seeing (The blurring effect of the Earth’s atmosphere) make parallax angle measurements of less than 0.01 arcsecs not possible with errors of less than 10%. This places an effective limit of 100 parsecs on the distance measuring capability of trigonometric parallax from ground-based observers.
Other factors such as refraction of starlight by the atmosphere, may cause errors in the position of the star that must be corrected. Since trigonometric parallax is used by astronomers to calibrate other distance measuring techniques, this is quite a severe limitation.
o Solve problems and analyse information to calculate the distance to a star given its trigonometric parallax using: d=1/p
A simple formula can be applied to calculate the distance to a star once its parallax angle is measured [pic]
[pic]
NOTE: P’’ = X’’ on calculator, when in degrees
o Gather and process information to determine the relative limits to trigonometric parallax distance determinations using recent ground-based and space-based telescopes
Ground-based observations are limited to distances of around 40 parsecs due to atmospheric distortion, while the Hipparcos satellite was capable of determining distances of around 1000 parsecs.
9.7.3 Spectroscopy is a vital tool for astronomers and provides a wealth of information
o Account for the production of emission and absorption spectra and compare these with a continuous black body spectrum
o Define absolute and apparent magnitude
Apparent magnitude (m)
The apparent magnitude of an object is how bright it appears from earth using the magnitude scale.
Note that brighter objects have a lower (possibly negative) apparent magnitude, while cooler objects have a higher apparent magnitude. The sun has an apparent magnitude of
-27 while the faintest object detected by the Hubble space telescope is +30
Absolute magnitude (M)
The absolute magnitude of an object is how bright it would appear to be if placed at a distance of 10 parsecs using the same magnitude scale as that used for apparent magnitude.
In this case the absolute magnitude of the Sun is +4.8
Also, a magnitude 1 star is 100 times brighter than a magnitude 6 star, since the scale is logarithmic. Ie. For a star which has a magnitude of about 10 lower than the Sun, its luminosity is 100x100=10000 greater.
o Explain how the concept of magnitude can be used to determined the distance to a celestial object
Only the closest stars can have their parallax angle determined and thus their distance measured directly. However, if a star’s absolute magnitude can be found and its apparent magnitude measured, the distance to a celestial object can be calculated.
The difference between a stars apparent magnitude (m) and its absolute magnitude (M) is known as the star’s distance modulus:
[pic]
Using the distance modulus, the distance to a star can be calculated using a technique called spectroscopic parallax.
Spectroscopic parallax
A method of using the HR diagram and the distance modulus formula to determined the approximate distance of a star
Note: Absolute magnitude is BIG M (absolute = big)
o Solve problems and analyse information using: M=m – 5log(d/10)
and Ia/Ib = 100(mb-ma)/5
A star closer than 10 pc will have a negative distance modulus, while a star further away than 10 pc will have a positive distance modulus. Hence using this distance modulus and the definition used to determined the magnitude scale, the equation:
Can be used to calculate the distance to the star. The distance given will be in parsecs (unit = pc) Note it is log10 not loge
Note: Magnitude is apparent magnitude
DO QUESTIONS OF COURSE
o Describe binary stars in terms of the means of their detection: visual, eclipsing, spectroscopic and astrometric
Binary stars are cases where stars are so close together that they have a common centre of gravity and revolve around one another. Several methods are used by astronomers in identifying binary stars that to the naked eye appear as a single star.
Visual binaries
Visual binary stars can be resolved by a suitably large telescope. Successive observations over time show that the two stars do indeed revolve around each other. Visual binaries can also be seen with the resolving power of binoculars or a small telescope (eg. Alpha Centauri)
Eclipsing binaries
Eclipsing binaries revolve about each other in a plane that brings one star in front of the other when viewed from Earth. This eclipsing may result in a detectable dimming of the overall brightness of the light being observed from both stars
For example, if two identical stars are orbiting in a plane
The light curves of most eclipsing binaries require careful analysis, taking in factors such as the size of each star, their spectral types as well as the plane of the star’s orbits.
Spectroscopic binaries
There are many examples where a binary star system cannot be identified by resolving the image of the two stars and that the binary stars do not orbit in a plane that causes eclipsing of either star.
In these cases, further analysis of the star’s spectrum reveals the slight Doppler shifting of the spectral lines as one star recedes from the observer and the other approaches. The simultaneous blue shifting and red shifting cause the spectral lines to split into two and then recombine when the star’s motion is side-on, or translational, to the observer.
[pic]
Astrometric binaries
The exact position of a star in the night sky can be measured very accurately. Stars are not fixed in their positions – most exhibit some degree of proper motion as they move through space.
Astrometric binary star systems are detected by observing a star’s very slight ‘wobble’ in its position along its path of proper motion. The only force known that could cause a star to deviate in such a way is gravity from a nearby, invisible companion star (or planets) that much be orbiting the visible star. The mass and separating distance of the companion star (or planet) can be calculated from the motion of the visible star.
[pic]
Note: Other than the mass of the companion star, little else about its nature can be found out as its spectrum is not detectable from Earth.
o Perform an investigation to model the light curves of eclipsing binaries using computer simulation
o Explain the importance of binary stars in determining stellar masses
Astronomers are particularly interested in binary star systems as they are the only way in which the mass of stars can be measured.
• The mass of a star not only determines its position on the main sequence of a Hertzsprung-Russell (HR) diagram but also its luminosity. A more massive star will be larger and hotter, and therefore more luminous. (Mass-luminosity relationship) The luminosity of a star gives its absolute magnitude, M.
• It is a very useful tool in being able to find the distance to the star using spectroscopic parallax.
Once the period and separation of a binary system is determined, we can mathematically find the mass of the two stars.
o Solve problems and analyse information by applying: m1+m2 = 4π2r3/GT2
[pic]
Note: this equation can be modified and used with NON-SI units of:
Solar masses (for m1 + m2) (6x1030kg = 1 solar mass)
Astronomical units (For separation distance r)
And Earth years (For time T)
This leaves us with a simplified equation of: [pic]
BE VERY CAREFUL WITH UNITS
o Classify variable stars as either intrinsic or extrinsic and periodic or non-periodic
Variable stars are ones that appear to vary in brightness. This may be due to the changing luminosity of the star itself, or it may be due to an external factor such as a companion star passing in between the observer and the star, causing an apparent dimming of the star.
Intrinsic variable stars – Intrinsic variables vary in luminosity, that is, the light output of the star changes. This results in the change of brightness of the star
Extrinsic variable stars – Extrinsic variables appear to change in brightness; however, their luminosity is not changing, but an external factor changes the light reaching the Earth
Types of extrinsic variable stars
A star may be an extrinsic variable if it is in an eclipsing binary system. (However it is also possible that the stars in a binary system are intrinsic variables). Also, sunspots in a star are not dispersed symmetrically around a star. As the star rotates, an observer may notice a slight variation in its luminosity, which classifies stars as extrinsic variables. (Rotating variable)
Types of intrinsic variables stars
Many stars have been identified as being pulsating variables. These stars are periodically expanding and contracting, which changes their size, spectral type and luminosity. These stars appear to be otherwise stable, and are a type of intrinsic variable star. (The regular variation in brightness is due to a disequilibrium that exists between the two forces that act upon a star to determine its size, the forces being gravitational force and radiation pressure)
Occasionally, a star is observed to brighten by millions of times. Current theories suggest that this is a supernova, which occurs to a white dwarf in a binary system while ‘accreting’ matter from its nearby companion star, until a cataclysmic explosion occurs. The less common type 2 supernova events are the result of the collapsing core of very massive stars at the end of their life cycle.
Other types of intrinsically variable stars are known as ‘eruptive’. One event is believed to be due to the way in which a white dwarf companion to a red giant is able to ‘blow off’ matter it has accumulated without destroying itself, repeating the action every 100000 years or so. The observation is that the star system suddenly brightens and returns to normal over a number of days or weeks
Non periodic
The cataclysmic and eruptive type of variable stars that do not repeat their brightness variation are considered non-periodic. Includes supernova, nova, flare stares.
Periodic
Stars which can vary in brightness on a regular, repeating basis are called periodic, as is a sine or cosine curve.
[pic]
o Explain the importance of the period-luminosity relationship for determining the distance of Cepheids
Cepheid variables are very luminous yellow giant stars.
In the early 1900s Henrietta Leavitt found that there was a good correlation between the periods of the 47 Cepheids observed and their luminosities. These Cepheids all have approximately the same distance from Earth, making it possible to correlate the period with the luminosity of the Cepheids.
These were cross-referenced with a number of Cepheids of known distance. The Cepheids could now be used as ‘standard candles’, stars which astronomers can use as distance measuring tools.
The time magnitude in the diagram is a log scale
Cepheid variables also exhibit light output curves characterized by a more rapid brightening phase and a more gradual dimming phase. The shape of the curve is indicative of a Cepheid, and is due to the mechanisms within the star that cause the pulsating.
[pic]
By identifying a Cepheid variable and relating it to its position on a period-luminosity relationship graph, the distance to the star can be calculated.
The use of Cepheid variables has allowed astronomers to estimate the size of the known universe. An early recalibration of the period-luminosity relationship caused a near doubling in the estimated size of the Universe. More recently, observations of the red shift of distance galaxies has allowed a more accurate measurement of the Hubble constant, H, and therefore a more accurate estimation of the age of the Universe itself. The use of Cepheid variables as standard candles, or distance measuring stars has helped this estimation.
[pic]
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