Forces and Motion - Weebly



Forces

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Forces

Force ( F ) - A push or pull upon an object resulting from the objects interaction with another object.

▪ Units: Newtons ( N ) = kg • m/s2

Two Types of Forces

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|Contact |Field |

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|Forces in which two interacting objects are physically in contact with each |Forces in which the two interacting objects are able to exert a push or pull|

|other. |despite physical separation. |

| | |

|Frictional – exerted by a surface |Gravitational – sun and planets (attraction between masses) |

|Tensional – string, rope, wire |Electromagnetic – magnets, protons & electrons |

|Normal - support |Strong Nuclear – protons & neutrons |

|Air Resistance |Weak Nuclear – decay of particles |

|Applied – person pushing | |

|Spring - exerted by a stretched or compressed spring | |

Field Forces

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1. Which forces are strong only over a relatively short range of distance?

Weak and Strong Nuclear Forces

2. Which forces are strong over a relatively long range of distance?

Gravitational and Electromagnetic Forces

3. Which is the strongest force?

Strong Nuclear

4. Which is the weakest force?

Gravitational

Everyday Forces

Weight

o Mass ( m ) – the amount of matter that makes up an object

• Units – kilogram (kg)

o Weight (Fgrav) - The magnitude of the force of gravity acting upon an object.

• Units – Newton (N)

• Weight is not an inherent property of an object.

Find the super hero’s weight in each of the following locations.

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Determine some factors that effect weight.

• Mass

o Celestial Body

o Object

• Location

o Acceleration due to gravity

o Altitude

1. Frieda Beemee weighs 490 newtons on Earth. Determine her mass.

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2. Frieda then decides she would like to take a vacation to Planet X. If acceleration due to gravity on Planet X is 4.2 m/s2, determine her weight.

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3. A 70.-kilogram astronaut has a weight of 560 newtons on the surface of planet Alpha. What is the acceleration due to gravity on planet Alpha?

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Normal Force

o Normal Force (Fnorm) – A supportive force exerted by one object on another in a direction perpendicular to the surface of contact.

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|Which vector best represents the direction of the normal force acting on the box? |

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|C |

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|Make a statement regarding the normal force from the above image? |

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|The magnitude (amount) and direction of the normal force does not necessarily have to be equal and opposite to the force of gravity. |

1. A 6.0 kg mass is at rest on a surface. Draw the gravitational force and the normal force for the mass below.

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2. A 15.6 kg block is at rest on a table top. Determine the magnitude of the normal force.

Since the block is at rest, the Fgrav must equal the Fnorm.

Fnorm = - Fgrav = -mg

= -(15.6 kg)(-9.81 m/s2)

= +153 N = 153 N up

Friction

o Friction (Ffric) – The force that opposes the motion between two surfaces that are in contact.

o Static Friction - The force that opposes the start of the motion.

o Kinetic Friction - The force between surfaces in relative motion. (less than static)

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Coefficient of Friction ( µ ) – measures how easily one surface slides over another

Make a conclusion concerning the relationship between μ and the amount of friction.

As μ increases, the amount of friction increases.

What are some factors that affect friction?

Mass, gravity, roughness of surface, normal force

A child is pushing a 20.0 kg block of granite at constant speed across a concrete sidewalk with an applied force of 100. N. Determine the coefficient of friction between the granite block and the concrete sidewalk.

Drawing Free Body Diagrams

Free Body Diagram – Diagram used to show the relative magnitude and direction of all

forces acting upon an object in a given situation.

Steps to Drawing Free Body Diagrams

1. Depict and identify which forces are present for that object in the given situation.

2. Determine the direction in which each force is acting.

3. Draw a box (or simple picture) and add arrows for each existing force in the appropriate direction

i. The size of the arrow in a free-body diagram is reflective of the magnitude of the force.

ii. The direction of the arrow reveals the direction in which the force acts.

4. Label each force arrow according to its type.

Apply the method described above to construct free-body diagrams for the situations described below.

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|A book is at rest on a table top. Diagram the |A girl is suspended motionless from a bar which |A rightward force is applied to a book in order to|

|forces acting on the book. |hangs from the ceiling by two ropes. Diagram the |move it across a desk with a rightward |

| |forces acting on the girl. |acceleration. (Neglect air resistance.) |

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|[pic] | |[pic] |

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Balanced and Unbalanced Forces

▪ Normal ( FN ) – Supportive force

▪ Gravitational Force (FG ) - Downward force

When all of the forces acting upon an object balance each other, the object will be at equilibrium; it will not accelerate.

Can an object be moving and be at equilibrium? How?

Yes, because it would be accelerating if any of the forces were unbalanced.

What exactly does the phrase “unbalanced force” mean?

An individual force acting on an object which is not balanced by another force of equal magnitude and opposite direction.

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Determining the Net Force

Net Force - the unbalanced force that exists whenever all vertical forces (up and down) do not cancel each other and/or all horizontal forces (left and right) do not cancel each other.

• The sum of all of the forces

Free-body diagrams for three situations are shown below. Determine each situations net force.

| |[pic] |[pic] |

|[pic] | | |

| | Fnet = [pic] | Fnet = [pic] |

|Fnet = [pic] | | |

Earlier we learned that a net force (an unbalanced force) causes acceleration. Combine your prior understanding of acceleration with your newly acquired knowledge that a net force causes an acceleration to determine whether or not a net force exists in the following situations.

|Motion |Net Force: Yes or No |

| |Yes |

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| |No |

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| |Yes |

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| |No |

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| |Yes |

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| |Yes |

|[pic] | |

Newton’s Laws of Motion

In this course so far, we have discussed a variety of ways by which motion can be described (words, graphs, diagrams, numbers, etc.) This unit, Newton's Laws of Motion, will discuss the ways in which motion can be explained.

o First Law of Motion - An object at rest tends to stay at rest and an object in motion tends to

stay in motion (with the same speed and direction) unless acted upon

by an unbalanced force.

Also known as The Law of Inertia

o Inertia – The natural tendency of objects to resist changes to their velocity.

▪ Change in velocity = acceleration

• Galileo developed the concept of inertia. (objects eventually stopped due to friction)

Describe what happens during each demonstration.

|The Car and the Wall |The Motorcyclist |The Truck and Ladder |

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Can you think of any other examples of Newton’s First Law?

o Head goes back as a car ( or rollercoaster )accelerates very fast from rest.

o Trying to walk with a full cup of coffee or juice.

o Hitting windshield in car

o Seatbelt provides the unbalanced force which brings you from a state of motion to a state of rest.

|Thought Experiment |

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|If a book resting on a desk was pushed into motion. Would it continued to move forever if nothing were to obstruct its path? Why? |

|No, friction would cause it to slow down to a stop. |

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|What if you pushed the book in outer space? |

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|It would continue to move forever unless it came into contact with another force. |

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|After the book is pushed (in outer space) would you require another force to keep it moving? |

|No, forces are not needed to keep an object in motion; rather only to accelerate an object. |

|For 2,000 yrs prior to Newton people believed that forces were needed to keep objects in motion, and the natural tendency of an object was to come to |

|rest. |

|Newton declared that an object does not cone to rest because of an absence in force; rather it is the presence of a force which brings an object to a |

|halt. |

Which object would be the hardest to move if a person applied the same amount of force on each? Refrigerator

|[pic] | |[pic] |

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| |[pic] | |

Why?

Because it is the most massive

Construct a statement regarding the relationship between inertia and mass.

Inertia is a quantity which is solely dependent upon mass.

Newton’s Second Law of Motion

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced.

Second Law of Motion – A mass experiences an acceleration in the presence of an unbalanced force. This acceleration is proportional to the force and inversely proportional to the mass.

Finding Acceleration

1. An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

Fnorm = 80 N up m = 8 kg Fnet = 40 N right a = 5 m/s2 right

2. An applied force of 20 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the coefficient of friction (µ) between the object and the surface, the mass, and the acceleration of the object. (Neglect air resistance.)

Fnorm = 100 N up m = 10kg Fnet = 10 N right μ = .1 a = 1m/s2 right

Finding Forces

To gain a feel for how this method is applied, try the following practice problems. The problems progress from easy to more difficult.

1. Free-body diagrams for four situations are shown below. The net force is known for each situation. However, the magnitudes of several of the individual forces are not known. Analyze each situation individually to determine the magnitude of the unknown forces.

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A = 50 N left B = 200 N up C = 1100N up D = 20 N right E = 300 N down F=H G = 50N right

2. A rightward force is applied to a 6-kg object to move it across a rough surface at constant velocity. The object encounters 15 N of frictional force. Use the diagram to determine the gravitational force, normal force, net force, and applied force. (Neglect air resistance.)

Fnet = 0 N Fapp = 15 N right Fgrav = 60 N down Fnorm = 60 N up

3. A rightward force is applied to a 10-kg object to move it across a rough surface at constant velocity. The coefficient of friction, µ, between the object and the surface is 0.2. Use the diagram to determine the gravitational force, normal force, applied force, frictional force, and net force. (Neglect air resistance.)

Fnet = 0 N Fgrav = 100 N down Fnorm = 100 N up Ffric = 20 N left Fapp = 20 N right

4. A rightward force is applied to a 5-kg object to move it across a rough surface with a rightward acceleration of 2 m/s2. The coefficient of friction, µ, between the object and the surface is 0.1. Use the diagram to determine the gravitational force, normal force, applied force, frictional force, and net force. (Neglect air resistance.)

Fnet = 10 N right Fgrav = 50 N down Fnorm = 50 N up Ffric = 5 N left Fapp = 15 N right

5. A rightward force of 25 N is applied to a 4-kg object to move it across a rough surface with a rightward acceleration of 2.5 m/s2. Use the diagram to determine the gravitational force, normal force, frictional force, net force, and the coefficient of friction between the object and the surface. (Neglect air resistance.)

Fnet = 10 N right Fgrav = 40 N down Fnorm = 40 N up Ffric = 15 N left μ = .4

Falling with Air Resistance

Air Resistance - the result of collisions of the object's leading surface with air molecules.

➢ Factors Effecting Air Resistance:

1. Speed

2. Cross – sectional area

Terminal Velocity

Terminal Velocity - maximum velocity reached by a body falling through the atmosphere under the attraction of gravity

|Activity |

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|Two students are given spring scales. They hook their spring scales together and are instructed to pull at different amounts. Describe what happens. |

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|Two people are unable to pull at different amounts. |

o Third Law of Motion – For every action, there is an opposite and equal reaction.

*Not on reference tables

Examples

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Other Examples

o Bounce ball against the wall

o Rocket

o Sitting in Chair

o Earth exerts force on moon, moon exerts force on us.

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Why was the boy flung backwards when he released the water from the nozzle?

In order for the water to move to the right, it had to exert an equal and opposite force in the opposite direction (left). Therefore, this force was probably stronger than the boy’s weight, thus causing him to be flung backwards (left).

Identifying Action and Reaction Force Pairs

Consider the following interaction between a baseball bat and a baseball.

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Action: Reaction:

The baseball forces the bat to the right. The bat forces the ball to the left.

Consider the following three examples. The action force is stated; determine the reaction force.

|Example #1 |Example #2 |Example #3 |

|[pic] |[pic] |[pic] |

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|Action: |Action: |Action: |

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|Athlete pushes bar upwards. |Bowling ball pushes pin rightward. |Compressed air pushes balloon wall outwards. |

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|Reaction: |Reaction: |Reaction: |

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|Bar pushes athlete down. |Pin pushed bowling ball left. |Balloon wall pushes compressed air inwards. |

Identify at least five pairs of action-reaction forces in the following diagram.

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1. The strong man’s feet push forwards on the ground; the ground pushes backwards on his feet.

2. Strong man pulls backwards on the rope; rope pulls forward on strong man.

3. The left end of the second rope pulls rightward on the monkey; the monkey pulls leftward on the second rope.

4. The right end of the ropes pulls leftward on the monkey; monkey pulls rightward on the right end of the second rope.

5. The tree pulls rightward on the right end of the second rope; the right end of the second rope pulls leftward on the tree.

Gravitational Forces and Inclined Planes

Label the following forces on the diagram below:

▪ Gravitational Force

▪ Normal Force

▪ Frictional Force

Finding Component Vectors

Perpendicular Parallel

*Not on reference tables *Not on reference tables

Alwasys At rest

*Not on reference tables *Not on reference tables

A trunk weighing 562 N is resting on a plane inclined at 30.0° from the horizon. Find the components of the weight parallel and perpendicular to the plane.

Since we know the weight of the trunk to be 562 N, we can resolve its vector into components.

If the angle of the incline increases and the object remains at rest, the normal force __decreases_ and the frictional force __increases___.

A 5.4 kg bag of groceries is in equilibrium on an incline of 15°. Find the magnitude of the normal force on the bag.

Fgrav = mg

= (5.4 kg) (9.81 m/s2)

= 53 N

Fnorm = Fgrav cos θ

= 53 N (cos 15°)

= 51 N

Finding Acceleration Down an Incline

A block weighing 46 N is resting on a frictionless plane inclined at 20.° from the horizon.

Explain the motion of the block in terms of forces.

The block is accelerating because it is not in equilibrium (an unbalanced force exists).

Determine the magnitude and direction of the acceleration of the trunk.

1. Fnet = Fg para = Fgrav sin θ

= 46 N (sin 20°)

= 16 N

Riding in the Elevator: Weight and Normal Force

Elevator Video

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|Going Up: | |Coming Down: | |

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|Readings on Scale: | |Readings on Scale: | |

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|Increases | |Decreases | |

Under what conditions do the scale readings change?

When the elevator is accelerating

Under what conditions do the scale readings read the “true” weight of the person?

When the elevator is stopped or moving at constant speed

In the following scenarios a 40. kg girl rides an elevator. Determine the following:

|A |B |C |

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| |[pic] |[pic] |

|D |E |F |

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|[pic] |[pic] | |

|G |H |

|[pic] |[pic] |

1. Astronauts on the space shuttle appear to be weightless, yet they are under the influence of Earth's gravitational field. Using the information from this lesson, formulate a hypothesis as to why they appear weightless.

gspace = 8.7 m/s2

Astronauts appear weightless because they are in a state of constant freefall.

2. Compare this type of “weightlessness” with that of the astronauts who traveled to the Moon.

Shuttle - If there is no upward force present then you do not have sensation of weight.

Outer Space – If there is no (or very little) force due to gravity present (Fg gets small quickly as you leave the planet) then you are weightless because you have no downward pull.

3. Some pilots, in aerobatic maneuvers, can withstand an acceleration of 8 g's (eight times that of normal gravity). How much would the pilot weigh?

8 times heavier

8g = (9.81 m/s2) (8) = 78.5 m/s2

If pilot was 70.kg, then he’d weigh 5500N

Fg = mg = (70. kg) (78.5 m/s2) = 5500 N

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Fapp

Fg = mg

= (6.0 kg)(-9.81 m/s2 )

= - 59 N = 59 N down

Fnorm = - Fg = + 59 N = 59 N up

All objects pull up on Earth with a force equal to the force that the Earth pulls down on that object.

Motion:

Scale reads 500. N

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Motion:

Scale reads 1000. N

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Gravitational Force

390 N

up

390 N

down

0 N

0 m/s2

390 N

down

390 N

down

80 N up

470 N

up

250 N

up

140 N down

390 N

down

390 N

up

0 N

0 m/s2

390 N

down

400 N up

790 N

up

390 N

down

390 N down

0 N

9.81 m/s2

down

10. m/s2

up

2.0 m/s2

up

3.5 m/s2

down

390 N down

500 N up

110 N up

2.8 m/s2 up

390 N down

1000. N up

610 N up

15 m/s2 up

Galileo – working on projectiles – posed a ? – shoot something so fast it fell at rate of Earth’s curve – would it land? NO!

Today we can test it – satellites

Shoot at different speeds to obtain different orbiting heights

Ffric

Fgrav

Draw the forces present.

Fnorm

Strong Nuclear

Weak Nuclear

Electromagnetic

Gravitational

DEMONSTRATION – Roll one empty jar and another jar filled with sand down an incline. Ask students which jar would be harder to stop.

Frictional Force

Normal Force

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Givens

Fgrav = 46 N

¸ = 20°

g = 9.81 m/s2

Unknowns

Fnet = ?

m = ?

a = ?

Givens

m = 5.4 kg

¸ uation.DSMT4 [pic]

Givens

Fgrav = 46 N

θ = 20°

g = 9.81 m/s2

Unknowns

Fnet = ?

m = ?

a = ?

Givens

m = 5.4 kg

θ = 15°

g = 9.81 m/s2

Unknowns

Fgrav = ?

Fnorm = ?

Draw a diagram.

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Fnorm balances out with Fg perp

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Do objects have to physically touch in order for a force to occur?

Keep protons and neutrons together in the nucleus of an atom. Overcomes the electromagnetic repulsion between protons.

Long ago, people believed the earth didn’t spin. They believed evidence of this was when a bird left a tree to grab a worm, the earth wouldn’t spin underneath it.

• Aristotle believed that moving objects had a natural tendency to come to a stop.

• Galileo believed that moving objects had a natural tendency to remain moving.

F = - F

Fnorm = 59 N up

[pic]

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Fg perp = Fgrav cos θ

= 562 N (cos 30.0)

= 487 N

a = -9.81 m/s2

Video mentions that the scale measures the upward force. Ask students what the upward force is? Normal Force

Since she is freely falling at same rate as floor, it does not support her

4

1

3

2

Add/sub

= mg

=ma

Copy

over

1

2

3

4

Copy over

= mg

subtract

=F/m

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Scale: 1cm = 29.5 N

590N down

0N

96N down

840N down

normal

Fg para = Fgrav sin θ

= 562 N (sin 30.0°)

= 281 N

Astronauts have difficulty with the concept of being weightless, but still having inertia – lighter objects rebound from walls easier.

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normal

heavier

heavier

lighter

weightless

Vomit Comet

The free-body diagram above depicts four forces acting upon the object. Objects do not always have four forces acting upon them. There will be cases in which the number of forces depicted by a free-body diagram will be one, two, or three.

There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram.

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