Chapter 6
Momentum
Momentum and Collisions
• This chapter is concerned with inertia and
motion.
• Momentum helps us understand collisions.
• Momentum = mass X velocity
• p = mv
• Momemtum is a vector
Sample Questions
• Which has more momentum, a 1-ton car
moving at 100 km/hr or a 2-ton truck
moving at 50 km/hr?
• Car
• Truck
p = mv = (1 ton)(100km/hr)
p = (2 ton)(50 km/hr)
• Large Momentum Examples:
Huge ship moving at a small velocity
P = mv
High velocity bullet
P = mv
Impulse
• Newton’s Second Law can read
SF = ma
= m(Dv/Dt)
= (Dmv)/(Dt)
= (Dp/ Dt)
Rearranging,
Impulse = Dp = FDt
Sample Question
• Does a moving object have impulse?
Impulse is not a property of the object, but
something that it can give or get from an
interaction.
Notice that it is not motion that gives us an
impulse (v) but a change in motion (Dv).
Sample Question
• Does a moving object have momentum?
Yes, but recall that motion is relative, so the
momentum depends on having velocity with
respect to the standard of rest.
When Force is Limited
• Apply a force for a long time.
 Examples:
 Follow
through on a golf swing.
 Pushing a car.
F
Dt
Make it Bounce
p1
p2 = -p1
Dp = p2 - p1 = -p1 - p1
= -2p1
Minimize the Force
• To minimize force …
Increase Dt
catching
a ball
Bungee jumping
Dt
F
Maximize Momentum Change
Apply a force for a short time.
Examples:
 Boxing
 Karate
F
Dt
• If SF = 0, then impulse = Dp = zero, or
Momentum is conserved
Demonstrations
• Rocket balloon
• Cannon
• Rocket Scooter
When can Momentum be Conserved?
Internal
forces cannot cause a
change in momentum of the
system.
For
conservation of momentum,
the external forces must be zero.
COLLISIONS
• Collisions involve forces internal to
colliding bodies.
• Inelastic collisions - conserve momentum
• Totally inelastic collisions - conserve
momentum and objects stick together
• Elastic collisions - conserve energy and
momentum
v = 10
v=0
M
M
v’ = 5
M
Mv = 2Mv’
v’ = ½ v
M
Before Collision
p = Mv
v’
After Collision
p = 2Mv’
Collisions
Air Track Link
Conserve Energy and Momentum
Before Collision
Case 1:
Equal masses
Case 2:
M>M
Case 3:
M<M