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Mechanics III
Momentum and Impulse
Physics I Honors
What is Momentum?
It is a vector quantity that is the product of an
object’s mass and velocity.
  mv
What Are the Units?
m
  kg  
s
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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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Large Momentum Examples
– Huge ship moving at a small velocity
P = mv
–High velocity bullet
P = mv
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Momentum Examples
• 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?
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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.
 = mv
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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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Conservation
of 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
= mv/t
• So:
F  t = mv
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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.
F
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t
Maximize Momentum Change
Apply a large force for a short time.
– Examples:
• Boxing
• Karate
F
t
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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!
• 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
Before

v2

v1
m1
m2

v1 '
After
m1

v2 '
m2




m1v1  m2 v 2  m1v'1  m2 v'2
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Elastic Collisions
Conserve Energy and Momentum
Before Collision
After Collision
Case 1:
Equal masses
Case 2:
M>M
Case 3:
M<M
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Inelastic Collisions
• Momentum is conserved
• Kinetic energy is not conserved
v = 10
v=0
M
M
Before Collision
p = Mv
M
After Collision
p = 2Mv’
v’ = 5
M
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What about rebound?
p = p2 - p1 = -p1 - p1
p1
= -2p1
p2 = -p1
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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?
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