Motion

Unit 1: MotionChapter 4: Conservation Laws

4.1 Newton’s Third Law and Momentum

4.2 Energy and the Conservation of Energy

4.3 Collisions

4.1 Investigation: Conservation of Energy

Key Question: What happens when equal and

opposite forces are exerted on a pair of Energy Cars?

Objectives: Explain the meaning of action–reaction forces. Apply knowledge of Newton’s first and second laws

to explain the resulting force when objects experience equal and opposite forces.

Use different numbers of marbles in each Energy Car to see how motion is affected.

Newton’s Third Law Newton’s Third Law (action-

reaction) applies when a force is placed on any object, such as a book on a table.

The second law says the acceleration of an object is directly proportional to force and inversely proportional to the mass (a = F ÷ m).

Newton’s Third Law Forces always come in pairs. Since the action and reaction forces are

equal in strength, Newton accelerates more because his mass is smaller.

The Third Law: Action/Reaction Newton’s Third Law

states that every action force creates a reaction force that is equal in strength and opposite in direction.

There can never be a single force, alone, without its action-reaction partner.

Action and reaction When sorting out

action and reaction forces it is helpful to examine or draw diagrams.

Here the action force is on the ________________, and the reaction force is on the _______________.

Action and reaction forces don’t cancelThe forces do not cancel because they act on different objects.

A woman with a weight of 500 newtons is sitting on a chair. Describe one action-reaction pair of forces in this situation.

Action and reaction

1. Looking for: You are asked for a pair of action and reaction forces.

2. Given: You are given Fw = 500 N.3. Relationships: Action-reaction forces are equal

and opposite, and act on different objects.4. Solution: The downward contact force the

woman exerts on the chair is an action. This action force happens to equal her weight, which is 500 N. The reaction force is the chair acting on the woman with an upward force of 500 N. Fw = -500 N

Fc = 500 N

MomentumMomentum is the mass of a object times its

velocity.The units for momentum are

kilogram•meters per second (kg·m/s).

Momentum

Stopping a fast-moving object is harder than stopping a slow-moving one.

Momentum Newton’s third law tells us that any time two

objects hit each other, they exert equal and opposite forces on each other.

The effect of the force is not always the same.

Calculating momentumMomentum is

calculated with velocity instead of speed because the direction of momentum is always important.

ImpulseThe change in momentum is often referred to

as impulse.We can use this relationship to solve equations

using changes in mass or velocity.

ImpulseThe tennis ball’s

momentum changes after it is hit by the racquet with a force of 80 N for 0.1 seconds.

Both the change of momentum and the impulse are +8 N·s.

A net force of 100 N is applied for 5 seconds to a 10-kg car that is initially at rest. What is the speed of the car at the end of the 5 s?

Force and momentum

1. Looking for: … the speed.2. Given: … the net force (100N), the time the force acts

(5s), and the mass of the car (10 kg).3. Relationships: Use: impulse (Δp) = force (F) × time (t)

momentum = mass (m) × velocity (v)4. Solution: Δp = 100 N × 5 s = 500 kg·m/s

Velocity is momentum divided by mass, orv = (500 kg·m/s) ÷ 10 kg = 50 m/s

Momentum and the third law If we combine Newton’s third law with the

relationship between force and momentum, the result is a powerful new tool for understanding motion.

If you stand on a skateboard and throw a 5 kg ball, with a velocity of 4 m/s, you apply a force to the ball.

That force changes the momentum of the ball. If the ball gains +20 kg·m/s of forward momentum,

you must gain –20 kg·m/s of backward momentum assuming there is no friction.

MomentumThe result of throwing

a 5-kg ball at a speed of 4 m/sec is that person and the skateboard with a total mass of 40 kg move backward at a speed of -0.5 m/sec (if you ignore friction).

We use positive and negative numbers to show opposite directions.

Law of momentum conservationThe law says the

total momentum in a system of interacting objects cannot change as long as all forces act only between the objects in the system.

An astronaut floating in space throws a 2-kilogram hammer to the left at 15 m/s. If the astronaut’s mass is 60 kilograms, how fast does the astronaut move to the right after throwing the hammer?

Using the momentum relationship

1. Looking for: …the velocity of the astronaut after throwing the hammer.

2. Given: … the mass of the hammer (2 kg) and the velocity of the hammer (15 m/s) and the mass of the astronaut (60 kg).

3. Relationships: The total momentum before the hammer is thrown must be the same as the total momentum after it is thrown.

momentum (p) = mass (m) × velocity (v)

A negative sign indicates the velocity is to the left.

Using the momentum relationship4. Solution: Both the astronaut and hammer were initially at

rest, so the initial momentum was zero. Use subscripts a and h to distinguish between the astronaut and the hammer.

momentum after + momentum before = 0mava + mhvh = 0

— Substitute the known quantities:(60 kg)(va) + (2 kg)(–15 m/s) = 0

— Solve:(60 kg)(va) = +30 kg·m/s

va = +0.5 m/s— The astronaut moves to the right at a velocity of 0.5 m/s.

Unit 1: MotionChapter 4: Conservation Laws

4.1 Newton’s Third Law and Momentum

4.2 Energy and the Conservation of Energy

4.3 Collisions

4.2 Investigation: Conservation of Energy

Key Question: How can you predict the

maximum velocity of a pendulum?

Objectives: Describe the relationship between potential energy and kinetic

energy in a system. Apply the law of conservation of energy to predict the maximum

velocity of a pendulum when it is released from different heights. Use the time required for a swinging bob to break the photogate’s

beam to calculate the velocity of the pendulum at different heights. Compare the measured and predicted velocities.

What is energy? Energy measures the ability for things to change

themselves or to cause change in other things. — A gust of wind has energy because it can move

objects in its path.— A piece of wood in a fireplace has energy

because it can produce heat and light.— You have energy because you can change the

motion of your own body.— Batteries have energy because they can be

used in a radio to make sound.— Gasoline has energy because it can be burned

in an engine to move a car.— A ball at the top of a hill has energy because it

can roll down the hill and move objects in its path.

Units of energy

Pushing a 1-kilogram object with a force of one newton for a distance of one meter uses one joule of energy.

A joule (J) is the S.I. unit of measurement for energy.

Joules One joule is a small amount of energy.

An ordinary 100 watt electric light bulb uses 100 joules of energy every second!

Work In science, work is a

form of energy you either use or get when a force is applied over a distance.

You do 1 joule of work if you push with a force of 1 newton for a distance of 1 meter.

Work When thinking about work, remember that

work is done by forces that cause movement.

If nothing moves (distance is zero), then no work is done.

Work

W = F x dDistance (m)

Force (N)

Work (joules)

Potential energy Systems or objects with

potential energy are able to exert forces (exchange energy) as they change.

Potential energy is energy due to position.

Potential energyA stretched spring has potential energy. If released, the spring will use this

energy to move itself and anything attached to it back to its original length.

Potential Energy

EP = mgh

height object raised (m)

gravity (9.8 m/sec2)

PE (joules)

mass of object (g)

Kinetic energy Energy of motion is called

kinetic energy. A skateboard and rider

have kinetic energy because they can hit other objects and cause change.

The amount of kinetic energy is equal to the amount of work the moving board and rider do as they come to a stop.

Kinetic Energy

EK = ½ mv2

mass of object (kg)

velocity (m/sec)

KE (joules)

Kinetic EnergyKinetic energy increases as the square of the speed.A car going twice as fast has four times the kinetic

energy and needs four times the stopping distance.

A 2-kg rock is at the edge of a cliff 20 m. above a lake. It becomes loose and falls toward the water below. Calculate its potential and kinetic energy when it is on the cliff edge and when it is halfway down. Its speed is 14 m/s halfway down.

Potential and kinetic energy

1. Looking for: … the potential energy (Ep) and kinetic energy (Ek) at two locations.

2. Given: … the mass (2 kg), the height at cliff edge (20 m), and the speed halfway down (14 m/s). You can assume the initial speed is 0 m/s because the rock starts from rest.

3. Relationships: Use: Ep = mgh and Ek = ½mv2

Potential and kinetic energy4. Solution:

— Potential energy at the top: Ep= (2 kg)(9.8 N/kg)(20 m) = 392 J

— Potential energy halfway down: Ep= (2 kg)(9.8 N/kg)(10 m) = 196 J

— Kinetic energy at the top:Ek= (½)(2 kg)(0 m/s)2 = 0 J

— Kinetic energy halfway down: Ek= (½)(2 kg)(14 m/s)2 = 196 J

Conservation of EnergyThe law of conservation of

energy states that energy can never be created or destroyed, just converted from one form into another.

If gravity is the only force acting on the ball, it returns to your hand with exactly the same speed and kinetic energy it started with, except that it returns to your hand from the opposite direction.

Conservation of EnergyThe law of energy conservation says the total energy

before the change equals the total energy after it.

The law of energy conservation says the total energy before the change equals the total energy after it.

A 2-kg car moving with a speed of 2 m/s starts up a hill. How high does the car roll before it stops?

Potential and kinetic energy

1. Looking for: … the height.2. Given: …the car’s mass (2 kg), and initial speed (2

m/s)

3. Relationships: The law of conservation of energy states that the sum of the kinetic and potential energy is constant. The ball keeps going uphill until all of its kinetic energy has been turned into potential energy.

Potential and kinetic energy

4. Solution: — Find the kinetic energy at the start:

EK = (½)(2 kg)(2 m/s)2 = 4 J— Use the potential energy to find the height:

EP = 4 J = mgh— Therefore:

h = (4 J) ÷ (2 kg)(9.8 N/kg) = 0.2 m— The car rolls to a height of 0.2 m above where it

started.

Using and conserving energyWhen you “use” energy by turning on a light,

you are really converting energy from one form (electricity) to other forms (light and heat).

In the “physics” sense, the energy is not “used up” but converted into other forms of energy.

The total amount of energy stays constant.

Unit 1: MotionChapter 4: Conservation Laws

4.1 Newton’s Third Law and Momentum

4.2 Energy and the Conservation of Energy

4.3 Collisions

4.2 Investigation: Collisions

Key Question: Why do things bounce back when they collide?

Objectives: Explore collisions and explain how they obey the

law of conservation of momentum. Describe how Newton’s laws explain collisions.

CollisionsThere are two main

types of collisions, elastic and inelastic.

When an elastic collision occurs, objects bounce off each other with no loss in the total kinetic energy of the system.

Collisions In an inelastic

collision, objects change shape or stick together, and the total kinetic energy of the system decreases. An egg hitting the floor is

one example of an inelastic collision.

Collisions When two billiard balls collide, it looks like they bounce without a loss of kinetic energy.

But the sound of the collision tells you a small amount of kinetic energy is being changed into sound energy.

MomentumAs long as there are no outside forces (such as

friction), momentum is conserved in both elastic and inelastic collisions.

Conservation of momentum makes it possible to determine the motion of objects before or after colliding.

Momentum Using momentum to analyze collision problems takes

practice.

1. Draw a diagram.

2. Decide whether the collision is elastic or inelastic.

3. Let variables represent the masses and velocities of the objects before and after the collision.

4. Use momentum conservation to write an equation stating that the total momentum before the collision equals the total after. Then solve it.

An 8,000-kg train car moves to the right at 10 m/s. It collides with a 2,000-kg parked train car. The cars get stuck together and roll along the track. How fast do they move after the collision?

Momentum and collisions

1. Looking for: … the velocity of the train cars after the collision.

2. Given: … both masses (m1= 8,000 kg; m2= 2000 kg) and the initial velocity of the moving car (10 m/s). You know the collision is inelastic because the cars are stuck together.

Momentum and collisions3. Relationships: Apply the law of conservation of

momentum. Because the two cars are stuck together, consider them to be a single larger train car after the collision (m3). The final mass is the sum of the two individual masses: initial momentum of car1 + initial momentum of car2 = final momentum of combined cars.m1v1 + m2v2 = (m1+ m2)v3

4. Solution: — (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s) = (8,000 kg + 2,000

kg)v3

— v3 = 8 m/s. — The train cars move together to the right at 8 m/s.

Forces in collisionsCollisions create forces because the

colliding objects’ motion changes. Since most collisions take place

quickly, the forces change rapidly and are hard to measure directly.

The total change in momentum is equal to the force multiplied by the time during which the force acts.

Solving impulse problems Impulse can be used to solve many practical

problems.

A 1 kg clay ball hits the floor with a velocity of –5 m/s and comes to a stop in 0.1 second. What force did the floor exert on it?

Impulse

1. Looking for: …upward force exerted by floor.2. Given: …ball’s mass (1 kg) final velocity (-5 m/s) and

final time (0.1 s)3. Relationships:.Use: Ft = mv2 − mv1 ,then solve for F

4. Solution: F = (1 kg)(0 m/s) – (1 kg) (-5 m/s) = 50 N (0.1s)

Car crash safety Air bags work together with seat

belts to make cars safer. An air bag inflates when the force

applied to the front of a car reaches a specific level.

Automakers use crash test dummies to study the effects of collisions on passengers.

Crash test dummies contain electronic sensors to measure the forces exerted at various places on the body.

Forensic Engineering

We usually think of engineering as a science focused on designing and constructing things—like bridges, computers, automobiles, or sneakers.

However, there is one branch of engineering that focuses on how things fail, collapse, or crash.