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Mechanics IIIMomentum and Impulse

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What is Momentum?What is Momentum?It is a vector quantity that is the product of an

object’s mass and velocity.

mvWhat Are the Units?

s

mkg

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What Is Momentum?

Two identical cars at different speeds…have different amounts of momentum.

Two different cars are the same speed…have different amounts of momentum.

Momentum relates to the size of the car and how fast it is moving.

That is to say, momentum is related to the car’s mass and its velocity…

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P = mv

Large Momentum Examples– Huge ship moving at a small velocity

P = mv

–High velocity bullet

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• A large truck has more momentum than a car moving at the same speed because it has a greater mass.

• Which is more difficult to slow down? The car or the large truck?

Momentum Examples

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Here Are Some Thoughts…• Hitting a baseball or a golf ball

requires a short period of time.• Stopping a train, a ship, or a car

takes a while.

• Obviously, the train or the ship have more momentum than the baseball.

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How does the object change momentum?

• Because momentum is mass x velocity, – and the mass of the object does not change, – any change in momentum means the velocity

changes.

= mv

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The force that causes a change in momentum in time t, is called an impulse.

• The act of hitting a baseball or a golf ball over a period of time or stopping a train or ship or car is the impulse that changes the momentum of the ball.

• Force x time is the impulse.• Impulse causes a change in momentum. • It is a vector quantity whose direction is that of the

force.

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i.e.

• P = mv

• Δp = mΔv = m(vf – vi)

• Ft = mΔv

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Concept check

• What is the change in momentum of a 2 kg ball going from 3m/s to 6m/s in the same direction?

• What Impulse will cause this change?

• What force will cause this change if applies for 10 ms.?

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Conservationof Momentum

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Newton’s Second Law

• Newton’s Second Law can now be restated as the change in momentum per unit time! !

• A force is required to change momentum…• …the speed relates to how long (time) the force

must be applied!F = ma

= mv/t• So:

F t = mv

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Impulse

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When Force is Limited• Apply a force for a long time.

– Examples: • Follow through on a golf swing.

• Pushing a car.

Ft

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Maximize Momentum Change

Apply a large force for a short time.– Examples:

• Boxing

• Karate

Ft

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Relation of Force and Impulse

• If forces come in equal and opposite pairs, what about Impulse?

• If Impulses are equal what is the difference caused by a bigger mass?

• Hint a 600 lb sumo wrestler and 90 lb nerd collide with equal Impulse. What difference would you observe?????

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Conservation of Momentum

(and energy?)

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The Law of Conservation of Momentum!

• Momentum cannot be created or destroyed.• The amount of momentum in the universe is

constant.• This means that the total momentum in the system

doesn’t change.

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Momentum Is Conserved!

• In a closed system, the amount of momentum before an event, such as a collision or explosion, is equal to the amount of momentum after the event, unless the system is acted upon by an outside force.

PA + PB = PA' + PB

'

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Newton’s Third Law and Momentum!Newton’s Third Law and Momentum!

• When two objects collide Newton’s Third Law applies.

• Impulses are equal in magnitude but opposite in direction.

• New momentums are equal to old momentums.• Internal forces cannot cause a change in

momentum. • Momentum is conserved in all collisions that

occur in a closed, isolated system.

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Momentum and Collisions Elastic Collisions

– objects rebound

– Momentum is conserved

– Kinetic energy is conserved

Inelastic Collisions – object stick together an usually become distorted and

generate heat

– Momentum is conserved

– Kinetic energy is not conserved

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Collisions

m1 m2

Before

'v1

m1

'v2

m2

After

22112211'vm 'vm vm vm

1v

2v

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Elastic Collisions

Conserve Energy and Momentum

Case 1:

Case 2:

Equal masses

M > M

Case 3: M < M

Before Collision

After Collision

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Inelastic Collisions

• Momentum is conserved• Kinetic energy is not conserved

Before Collision

p = Mv

After Collisionp = 2Mv’

v = 10 v = 0

M M

M M

v’ = 5

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What about rebound?

p1

p2 = -p1

p = p2 - p1 = -p1 - p1

= -2p1

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quiz

• 1. What is the impulse momentum theorem?

• 2. A baseball of mass 0.14 kg is moving at +35 m/s.

• a. Find the momentum of the baseball• b. Find the velocity at which a

bowling ball, mass 7.26 kg, would have the same momentum as the baseball.

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More quizzical

• Explain the difference between elastic and inelastic collisions.

• Explain the law of conservation of momentum

• Explain the law of conservation of energy

• What is their significance in studying collision?

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A problem?

• A 80kg student going east at 5m/s, collides with a 60kg student going west at 10m/s. After the collision , the heavier student rebounds at 3m/s. What is the speed and direction of the lighter student after the crash?