Notes Chapter 8 Momentum
Objectives:
• Define momentum. (8.1)
• Define impulse and describe how it affects momentum.
(8.2)
• Explain why an impulse is greater when an object
bounces than when the same object comes to a sudden
stop. (8.3)
• State the law of conservation of momentum. (8.4)
• Distinguish between an elastic collision and an inelastic
collision. (8.5)
• Given an example of how the vector nature of
momentum affects the law of conservation of
momentum. (8.6)
8.1 Momentum
• Inertia in motion.
• A measure of how difficult it is to change the
motion of an object in motion.
• A moving object can have a large momentum of it
has a large mass, speed, or both.
• A vector quantity.
m om entum m ass velocity
p  mv
Question
1. Can you think of a case where a roller skate
and a truck will have the same momentum?
8.2 Impulse Changes Momentum
• For an object, momentum
changes when velocity changes,
an acceleration occurs.
• What causes
acceleration?....Force
• The change in momentum
depends on the force that acts
and the length of time it acts.
impulse Ft
The greater the impulse exerted on an object, the greater will be the change
in momentum.
impulse Ft  (mv)  mvf  mvi
• Increasing momentum
– Maximum change in
momentum can be
achieved if maximum
force is applied for as long
as it can be applied.
– In baseball and golf, swing
really hard and follow
through.
– Average force
• Decreasing momentum
– If you increase the contact time—time which
your momentum is decreased—the force is
decreased.
• The product of force and time remains the same.
• Double the time, force is decreased to half.
• Opposite is true if contact time is decreased. Force
increases.
Questions
1. When a dish falls, will the impulse be less if it
lands on a carpet than if it lands on a hard
floor? Explain.
2. The boxer in Figure 8.6 is able to make the
impact time five times longer by “riding”
with the punch. How many times will the
force of impact be reduced?
8.3 Bouncing
• Impulses are greater when a bounce occurs.
– Book example of flower pot on head.
• The impulse required to stop and then to
“throw it back again” is greater than the
impulse required to simply bring the object
to a stop.
8.4 Conservation of Momentum
• Momentum of system cannot change unless
acted on by an external force.
• Law of conservation of momentum states that,
in the absence of an external force, the
momentum of a system remains unchanged.
• If all forces acting on the system are internal, the
net momentum of the system remains the same.
• Recall that momentum is a vector quantity—has
both magnitude and direction.
• In the case of the cannon firing a cannonball, the
action and reaction force are internal.
• The forward momentum (mv) of the cannon ball
is the same as the backwards momentum of the
cannon (-mv).
– Cannon and cannonball both start at rest, i.e. zero
momentum.
– Though both have a momentum after firing, the net
momentum is ZERO, i.e. they cancel out.
Questions
1. Newton’s second law states that if no net force
is exerted on a system, no acceleration occurs.
Does it follow that no change in momentum
occurs?
2. Newton’s third second law states that the force
a cannon exerts on a cannonball is equal and
opposite to the force the cannonball exerts on
the cannon. Does it follow that the impulse the
cannon exerts on the cannonball is equal and
opposite to the impulse the cannonball exerts
on the cannon?
8.5 Collisions
• Whenever objects collide in the absence of
external forces, the net momentum of the
objects before the collision equals the net
momentum of both objects after the
collision.
net m om entum
before collision  net m om entum
after collision
pbefore  pafter
m1v1 before  m2v2 before  m1v1 after  m2v2 after
m1v1  m2v2  m v  m v
'
1 1
'
2 2
• Elastic collision – collision in which colliding
objects rebound w/o lasting deformation or
heat generation.
Car Rear Ends Truck
Truck Rear Ends Car
Car and Truck in Head-on
Collision
• Inelastic collision – a collision in which
colliding objects become tangled or coupled
together and/or generate heat during a
collision.
m1v1  m2v2  (m1  m2 )v'
Car Rear Ends Truck
Truck Rear Ends Car
Car and Truck in Head-on
Collision
• Final note on collisions:
– Perfectly elastic collision are NOT common in the
everyday world.
• Some heat is generated
• This has implications when we cover energy.
– Energy is conserved in a perfectly elastic collision
– Not so in inelastic collisions because heat is lost from the
system. (More on this later.)
– At the atomic level, charged particles (ions) exhibit
perfectly elastic collisions.
8.6 Momentum Vectors
• The vector sum of the momenta is the same
before and after a collision.
Example Problem 1
• A car of mass 1100 kg moves at 24 m/s. What
braking force is needed to bring the car to a
halt in 20 s?
Example Problem 2
• An 80. kg astronaut carrying a 20. kg tool kit is
initially drifting toward a stationary rocket ship
at a speed of 2.0 m/s. If she throws the toolkit
toward the ship with a speed of 6.0 m/s, what
is her final velocity (speed and direction)?
Example Problem 3
Example Problem 4
• Data just before a perfectly elastic collision if
provided in the illustration above. If the
velocity of the truck after the collusion is
10. m/s, what is the velocity of the car after
the collision?