Chapter 5 Notes page 174-219



Chapter 5 Notes page 174-219

Energy and Motion

5.1 Analyzing and Measuring Motion page 176

Distance, displacement, and position are some of the most fundamental quantities of mechanics. The definitions are precise and many other quantities depend on the correct definitions of these basic quantities.

Scalars and Vectors

Scalar quantities or Scalars: Quantities that describe magnitude (size or amount) but not direction. Ex: speed, distance and time.

Vector quantities or vectors: Quantities that do include direction as well as magnitude. Ex: velocity, displacement, and position.

• To distinguish between these quantities, symbols for vectors are written with arrows above them while symbols for scalars are not.

• Example the symbol for velocity is [pic] and the symbol for speed is[pic].

Defining Distance, Displacement, and Position

• Distance is NOT simply the magnitude of displacement.

• Distance is dependent on the path but displacement is not.

• Displacement depends only on the initial and final positions.

• For example, consider a runner who is racing on a oval track. If finish line is the same as the starting line, then the runners’ displacement for the race is zero although the distance that he/she ran might be 1.0 km.

• Displacement has not been fully reported unless both the magnitude and direction have been includes.

• Symbol for distance ∆d. Is this a scalar or vector quantity? Scalar

• The ∆ in the case of distance means the change in the location of an object when it moves from one point to another.

• Symbol for displacement ∆[pic]. Is this a scalar or vector quantity? Vector

• The ∆ in the case of displacement means the change in the position of an object when it is displaced.

• Position infers the existence of a frame of reference. Position cannot be expressed without a reference point and a definition of direction.

• An x-y coordinate system must be defined in order to describe a position.

• Symbol for position[pic]. Is this a scalar or vector quantity?

Vector

• [pic]See Figure 5.3 page 177 to see the relationship between

displacement vectors and position vectors.

• See example in page 177 Figure 5.4

Calculating Distance and displacement

• Even when working on one dimension, distance is not the same as the magnitude of the displacement.

• When an object goes back and forth along the same line, the entire path is included in distance.

• Once again, displacement depends only on the starting and ending points.

• Calculation of displacement in one dimension involves only addition and subtraction.

• The direction of the vectors will be indicated by compass directions (N,S,E or W) or by positive and negative signs (+ or -).

• The direction “west” is equivalent to the negative of “east”.

• So, the displacement has not been properly reported unless the sign (+ or -) has been defined and is included in the statement of the answer.

• Although a plus sign is not required on a positive number, it is often helpful to use plus signs when working with vectors in one dimension.

• Vectors in one dimension: up, down, right, left.

• Vectors in two dimensions: upward and westward, eastward and downward, etc

• See Model problem 1 page 178. (Make on overhead)

• When you subtract a vector, you point it in the opposite direction but keep the length the same.

• Do BLM 5-1 Interpreting Vectors

• Do Practice Problems 1 to 9 page 181

Speed and Velocity

• The relationship between speed and velocity is the same as the relationship between distance and displacement.

• You cannot assume that speed is the same as the magnitude of velocity.

• Speed is the distance travelled by an object during a given time interval divided by the time interval

• Velocity is the displacement of an object during a time interval divided by the time interval.

• Velocity depends only on the initial and final positions but speed depends on the path.

• The time interval has the same meaning for both speed and velocity.

• The relationship between time interval and time is similar to the difference between displacement and position.

• Time (t) and position are specific points.

• Time interval (∆t) and displacement are a difference between those two points.

• Reporting direction in compass directions can be very confusing. Just remember to point in the direction of the first symbol then rotate the number of degrees specified toward the second direction.

• See example on page 182-183

• See Model Problem 2 page 183

• Do practice Problems 11 to 22 page 184 – 185

• Do Find out Activity Measuring Velocity in One dimension page 186

Graphing Velocity

• Examine Figure 5.7 page 187and analyse how the motion of the sprinters matches the graphs below them.

• Uniform motion: motion with no change in velocity.

• Since velocity is the rate of change of position, the velocity is the slope of the position versus time graph.

• Slope = [pic][pic]

• Slope = [pic][pic]

• [pic][pic] = [pic]

• [pic][pic] = slope

• See example on page 188

• Don’t assume that the point (0,0 s, 0,0m) is a data point but, unless specifically stated in the data, the origin cannot be considered a data point.

• Line of best fit: leave an equal number of points above and below the line.

• When you calculate the slope of the line, do not use any of the actual data points because most of them do not lie directly on the line.

• For most accurate calculation, choose two points on the line that are near the opposite ends of the line.

• Calculate the slope from those points.

• See example page 189.

• Do Find out Activity Graphing Position-Time Data page 190.

• Do worksheets package

Defining Acceleration

Acceleration: A change in the velocity during a time interval. Is Acceleration a scalar or Vector quantity?

Vector

Calculation Acceleration

The direction of acceleration is not necessarily the same as velocity but is the direction of the change in velocity.

You can use the concept of force as a “push” to determine the direction of the acceleration. It is the direction that you would have to push on the object to cause the observed change in velocity.

See diagram page 191

When solving problems, the sign – positive or negative – of the answer will tell you the correct direction of the acceleration.

Look at Model problem 3 page 192

Do Practice Problems 23 to 31 page 192 193

Graphing Accelerated Motion

• The slope of a position versus time graph is the velocity. When the slope is changing, the velocity is changing.

• Acceleration is a change in velocity. Thus a curved position versus time graph is a clear indication of acceleration. See Figure 5.12 page 193.

• The slope of a velocity versus time graph is the acceleration.

• If the velocity versus time graph is a straight line, then the acceleration is constant. See Figure 5-13 A page 194.

• If the velocity versus time graph is a curve, then the acceleration is changing. See Figure 5-13 B and C page 194

• Motion with a constant velocity is called uniform motion,

• Motion with a constant acceleration is called uniformly accelerated motion or non-uniform motion.

• In the absence of air friction, an object falling under the influence of gravity is uniformly accelerated motion.

• Do Check Your Understanding questions 1to 9

5.2 Energy of Motion

The energy transformation involved to produce all motion is due to a force, whether provided by gravity or by applied force.

Energy of Motion = Kinetic Energy

Calculating Kinetic Energy

• Joule = (kg) ([pic] )( [pic]) = Kg ● [pic]

• See Model problem 4 page 198

• Do Practise problems 32 to 40 page 200

• Do BLM 5-5 Kinetic Energy

Work and Kinetic Energy

The relationship between kinetic energy and work is often studied using the first law of thermodynamics. It suggests that work done (joules) to make an object move from rest is equal to its kinetic energy (joule) once it is in motion.

Some work must always be done against friction. Thus some energy goes into heat.

Do Find out Activity Driving Safely page 201.

Do Check your Understanding questions 1 to 8 page 204.

5.3 Potential Energy

Potential energy is often described as the energy stored in a substance or object due to its position or condition.

An example of condition is the compression of a spring.

Form of Potential Energy

1. Elastic Potential Energy

An object is elastic if it always

returns to its original form.

•

Elastic potential energy: Energy stored in an elastic object when work is done to distort the shape of the object.

2. Chemical Potential Energy

Does gasoline contains potential energy?

Chemical potential energy: energy stored in the bonds of chemical compounds which is released when bonds in a molecule break or are rearranged.

Chemical potential energy is the difference in the potential energy of reactants and products. See Figure 5.19 page 206.

• Some chemical reactions release energy when they

Proceed (exothermic)

• Some chemical reactions require an input of energy in order to proceed. (endothermic)

• Nearly all chemical reactions that form compounds from their elements release energy when they proceed.

3. Nuclear Potential Energy

The energy stored in the bonds between protons and neutrons in the nuclei of atoms.

Fission : When the nucleus of an atom splits into smaller nuclei. See Figure 5.21

Chain reaction: the process continues

The nuclear potential energy that is released when the large nuclei fissioned is transformed into thermal energy.

This thermal energy in nuclear reactors converts water into the steam that drives an electric generator.

4. Graviational Potential Energy

Gravitational potential energy is stored as a result of an object’s position (height above surface). See Figure 5.22

Potential energy exists in many objects due to the potential effect of gravity on the object.

Potential energy is a property of a system –like the Earth and a mass above the Earth’s surface.

Explaining Gravity

Gravity is a property of anything that has mass.

Gravitational potential energy depends only how far an objects is lifted vertically.

Objects fall straight down (neglecting friction).

Acceleration due to gravity: the acceleration with which all objects near Earth’s surface would fall if there were no air friction; approximate value is 9.81 m/s2.

Calculating Gravitational Potential Energy

• Mass and weight are not the same.

• Masse affects the weight

• Mass never change.

• Weight is the force of gravity acting on a mass

Whether using ma or mg to calculate force, both multiply mass times acceleration

The direction of the motion must be parallel to the direction of the force.

If you move the object horizontally while lifting it, the horizontal motion does not contribute to the work done against gravity. Therefore, you do not include horizontal distance in your calculation. See Figure 5.23[pic]

Formula for gravitational potential energy

If : W = F∆d

So W= Fg ∆h

W = mg∆h

Eg = mg∆h

• See Model problem 5 page 210

• Do Practice Problems page 212

• See BLM 5-6

• Do BLM 5-7

• Do Investigation 5-B Gravitational Potential Energy and Work page 213

• Do Investigation 5-C page 215

• Do Check Your understanding page 216 questions 1to 9

• Do chapter at glance page 217 questions a to 0

• Do chapter review page 218 questions 1 to 20 and 21 to 30

Chapter test on __________________________

Chapter 6 Notes page 220-245

Energy Conversion and Efficiency

6.1 Efficiency of Energy Conversions

What form of energy nearly always accompanies energy transformations? See Figure 6.1. Heat is a by-product of most energy transformation.

Efficiency and the Second Law of Thermodynamics

All machines convert one form of energy into another form in order to accomplish a specific task.

Useful energy: Energy that performs a task.

During any process, some energy is always converted into a form that is not useful. This energy is often said to be “wasted”.

Do BLM 6-1 Analyzing Machines for Efficiency (Together with the class)

Calculating Efficiency

If for example, a system is 30 percent efficient (i.e., has a useful energy output of 30 percent), this means that 70 percent of the energy going into the system is wasted.

Simple systems

• Study Figure 6.3 Energy transformation in a pendulum

• Look at Model Problem 1 page 225-226

• Do Practice Problems page 227

• Do BLM 6-2 Calculating Efficiency

• Do Check Your Understanding page 231 questions 1 to 5 and 7

6.2 Energy Efficiency and the Environment

Because no system is 100 percent efficient all energy conversions result in an unavoidable waste of energy as heat (thermal energy).

This wasted energy is often referred to as “thermal pollution”.

Installing technology to capture the neat normally given off into the environment requires large capital expenditures, but is environmentally beneficial and often economically beneficial as well.

Efficiency of Some Common Technologies

1. Internal Combustion Engines

On average cars are only 20 percent efficient.

It’s mean that only 20 percent of the chemical potential energy stored in the gasoline is transformed into the mechanical kinetic energy.

Interior car heaters in vehicles provide an example of using “waste” heat for the benefit of the occupants.

While they do not convert the heat to another form of energy, car heaters do allow heat to from engine to be used beneficially, and lowers the temperature of heated air before it enters the environment.

The use of water to transfer the thermal energy from the engine to the heater is also significant. Water provides an excellent coolant due to its high heat capacity.

2. Electrical Devices

• Light bulb : 5 % efficient

• 5 % of the electrical energy use is converted into light energy

• Compact fluorescent bulbs:20% efficient

• See Figure 6.7

Generating Electrical Energy

Which electrical generating method –coal-burning, nuclear, or hydro-electric generation of electrical energy is more efficient because the energy-transformation “route” is shorter and more direct?

Coal-burning and nuclear reactors 30% efficient

Hydro-electric 90 % efficient

• Do Investigation 6-B Energy Transformations in

Electrical Energy Generation page 235

Drawing Conclusions about Efficiency

After the thermal energy has turned a turbine or moved a piston, the steam or hot gases still contain much of the thermal energy. This thermal energy is usually lost to the environment.

Efficiency of Energy Transformations in Living Plants

Photosynthesis: Process by which plants use light energy to produce food in the form of carbohydrates.

Photosynthesis is very inefficient (1 %) in terms of energy conversion, it is the only process that produces this specific conversion, and this conversion is necessary for nearly all life on Earth to exist.

In case of photosynthesis the total input energy is all the light energy that is converted into chemical potential energy.

Saving Energy

Cost effectiveness is probably the greatest challenge to innovative techniques and processes that conserve energy.

Cogeneration

Method of conserving energy by using “waste” heat from a thermoelectric-generating system to heat a building.

The system use 80 percent of the input energy for both electrical energy and space heating.

However, thermal energy cannot be transported over long distance.

• Do Check Your Understanding page 242 questions 1 to 6

• Do Chapter at a glance page 243

• Do BLM 6-6 (Word splash)

Chapter 6 Review page 244 -245 questions 1 to 12, 17 and 18 to 25

Scientific Theories of Heat (page 150)

Each early theory of heat was an important step in the development of scientific knowledge. Theories and models are based on the knowledge of the time. Each theory could explain the observation that “scientist” of the time had made. It was only when new information became available that a theory was modified or discarded.

Early Theories of Heat (page 150)

What was the theory of the

1. Greek philosopher Empedocles: All matter consisted of some combination of four elements: earth, air, fire, and water According to this theory, many objects contained fire. When these objects burned, the fire was released (Figure 4.12)

When: (492 –435 B.C.E.)

2. Phlogiston: Substances that could burn contained an invisible fluid. Scientist called this fluid phlogiston. It was believed that the phlogiston flowed out of an object when the object burned.

When: Early 1700s

3. Caloric: Caloric – or heat – was a massless fluid that was found in all substance. Caloric could not be created or destroyed, but could flow from one substance to another. The theory stated that caloric always flow from warmer objects to cooler objects. Unit of caloric – the calorie. 1 cal is the quantity of caloric that would increase the temperature of 1 g of water by 1° C.

When: Late 1700s

Modern Theories of Heat (page 151-153)Benjamin Thompson (Count Rumford’s) was the first person to reveal flaws in the caloric theory. He noticed that when a hole was bored in metal to make cannon, the tools, the metal, and the metal shavings became very hot. Since none of the objects had been hot before the boring process, what could be the source of the caloric, or heat?

1. Rumford Hypothesis: There is no substance such as caloric. Instead, he hypothesizes that some of the mechanical energy used to bore the holes was converted into heat. He was saying that heat is equivalent to energy.

When: 1798

2. Julius Robert Mayer : Found evidence supporting

the relationship between energy and heat. Mayer

was one of the first scientists to recognize that the

body uses oxygen to break down food and use it for

energy. He also reasoned that the same processes

that use oxygen to provide energy for the body must

also be providing heat. Therefore, heat is related to

energy.

When: 1840

3. James Prescott Joules : Receives the credit for

discovering the mechanical equivalent to heat.

When: 1818-1889

Energy and Work (page 153-155)

Work is always done by a force acting on an object.

• The work done on an object changes the position or condition of that object.

• More than one force can be acting on an object at the same time but the work done by different forces is reported separately.

• W = F • ∆d

Where W is the work in joules (J)

F is the force in newtons (N)

∆d is the distance in meters (m)

The GRASP (Given, Required, Analysis, Solution, Paraphrase) Method for solving numerical problems. (Page 153)

• Do BLM 4-4 Using GRASP to solve Problems

• See Model Problem 1 page 154

• Do Practice Problems 1 to 9 in textbook

• Do BLM 4-5 energy and Work Practice Problems

1. Graphical Methods for Determining Work (page 155-

158)

• See Figure 4.17. This graph shows a constant force.

• The area of the rectangle equals the length times the width.

A = l • W

• But on the graph the length is the Force and the width is the distance.

• Substitute F for length and ∆d for width in the formula for area.

A = F • ∆d so A = W

2. Graphs with Geometric Shapes

• See figure 4-18. This graph shows a changing force.

• The area under the curve determines the amount of work done by a force.

• The shape under the curve is a triangle. The area of a triangle is

A = ½ b • h

• On the graph the base is the distance and the height is the force.

• Substitute d for the base and F for the height in the formula.

A = ½ d • F so A = w

3. Graphs with Non-uniform Shapes

• See figure 4.19. This graph show that the force starts very small, but increases rapidly. Then it immediately begins to fall to zero.

• You can calculate the work done by calculating the work represented by each small square and then counting the squares.

• See calculations page 156

• See Model Problem 2

• Do Practice Problems 10 and 11 page 157 –158

• Do BLM 4-6 Graphical Methods for Determining work

Joule’s Method for Determining the Mechanical Equivalent of Heat

• See Figure 4.20 Joule’s experiment to determine the mechanical equivalent of heat.

• The unit of energy – the Joule

What Exactly is “Heat?”

The work of Mayer and Joule led to the law of conservation of energy. This law states that energy cannot be created or destroyed, but it can be converted from one form to another.

The Kinetic-Molecular Theory of Heat

• Because particles are undergoing random motion, they collide with each other and the walls of any container. These collisions are the fundamental step in the transfer of energy. See Figure 4.21

• Work and heat are closely related. When particles collide, transferring thermal energy (heat), the particles are doing microscopic work on each other.

• In a solid, the molecules do not move freely around and away from each other. The molecules vibrate in place. As the solid becomes warmer, the molecules vibrate faster. See Figure 4.22

Heat and Thermal Energy

Define the following term:

1. Kinetic energy : Energy of motion

2. Kinetic-molecular energy : Theory stating that the molecules of a gas are in constant random motion; the energy associated with this motion is known as thermal energy

3. Thermal energy : Energy related to the continual, random motion of atoms and molecules

4. Heat : Transfer of thermal energy from one object to another

5. Work : Transfer of mechanical energy from one object to another

• When describing the interactions of a system with its surroundings, work and heat are the two methods by which energy enters or leaves a system.

Specific Heat Capacity

• Specific Heat capacity: amount of energy (J) to increase the temperature of 1g of the substance by 1˚C.

• Symbol c

• Unit J/g˚C

• The specific heat capacity of a substance depends on the interactions of the molecules of the substance.

• Water molecule form relatively strong hydrogen bonds with each other. Therefore, the kinetic energy of individual molecules must be large in order to break away from adjacent molecules.

• For water c = 4.186 J/g˚C

Heat and Temperature

• While adding energy to a substance, some of the energy goes into breaking interactions and into rotational kinetic energy.

• These forms of energy do not contribute to temperature. It is only the translational – straight line – kinetic energy that contributes to temperature

• Temperature: measure of the average kinetic energy of the individual atoms or molecules in a substance.

• Complete the activity on page 162 Heat versus Temperature

The Laws of Thermodynamics

• Thermodynamics : field of physics that deals with forces and motion involving heat – transfer of thermal energy

• Or no process can be 100 percent efficient. Some energy will always remain in the form of thermal energy (friction).

• Or thermal energy always spontaneously flows from an object at a higher temperature to an object at a lower temperature

Check your Understanding page 163. Answer questions 3,4,5,7,8,9,10

-----------------------

Displacement

"[pic] = [pic]2 - [pic]1

Where [pic]"[pic] = [pic]2 - [pic]1

Where [pic]∆[pic] is displacement

[pic]2 is the final or ending position

[pic]1 is the initial or starting position

The SI unit for position and displacement in metres, m.

Speed

[pic][pic]ave =[pic][pic]

Where [pic]ave is average speed in metres per second,m/s.

[pic]is distance in meters, m

[pic] is the time interval in seconds, s.[pic]

Velocity

[pic][pic][pic] or[pic][pic]

where [pic]ave is average velocity in meters per second,m/s.

∆[pic] is the displacement in meters,m.

[pic]2 is the final position in metres, m.

[pic]1 is the initial position in metres,m.

∆t is the time interval in seconds,s.

t2 is the final time in seconds, s.

t1is the initial time in seconds,s.

Acceleration Unit Analysis

[pic][pic] or [pic][pic] [pic]

Where [pic] is average acceleration in [pic]

Meters par second squared, m/s2

∆[pic] is the change in velocity in meters per [pic] [pic]

second, m/s.[pic]

[pic] is the initial velocity in meters per second, m/s [pic] [pic]

[pic] is the final velocity in meters per second, m/s

t2 is the final time in seconds, s [pic][pic]

t1 is the initial time in seconds, s.

[pic][pic]

where Ek is the kinetic energy in Joules (J)

m is the mass of the object in kilograms (kg)

v is the speed in meters par second (m/s)

Weight

Fg = mg

Where Fg is used to represent weight and the units are newtons (N)

m is the mass in kilograms (kg)

g is the acceleration due to gravity in meters per

second squared (kg ●m/s2)

When all of the work done on an object give the object gravitational potential energy, the amount of work done is equal to the amount of gravitational potential energy gained by the object or

W = ∆Eg

Gravitational Potential Energy

Eg = mg∆h

Where Eg is the gravitational potential energy in joules (J)

m is mass in kilograms (kg)

g is the acceleration due to gravity in meters per second squared

(m/s2)

∆h is the height in meters (m)

Second Law of Thermodynamics

“No process can be 100 percent efficient. Some energy will always remain in the form of thermal energy.

[pic]Efficiency = useful output energy × 100%

total input energy

Efficiency is a ratio so it has no units.

The output and input energies must be in the same units so they will cancel.

First Law of Thermodynamics

Energy cannot be created or destroyed, but can be transformed from one form to another or transferred from one object to another.

Second Law of Thermodynamics

It is not possible for any process to remove thermal energy from an energy source and convert it entirely into work

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