Download Momentum

Physics Chapter 6
Impulse and Momentum
Momentum
• Momentum depends on…
– Mass
– Velocity
– Momentum = Mass x Velocity
• The property of momentum…
– Variable: p
– Unit: kg  m
s
– Scalar or Vector?
– Equation: p = mv
Example #1
Which has more momentum, a 1-ton car
moving at 100 km/h or a 2-ton truck
moving at 50 km/h?
Example #2
How fast would a 18 kg kid on a tricycle
have to go in order to have the same
momentum as a 55 kg car traveling at 25
m/s?
Impulse
• Momentum can change. Most often, the
mass of an object remains the same, while
the velocity changes.
• Dp = mDv
• Dv  acceleration
a = Dv/t  Dv=at
• Dp = mDv becomes Dp = m x a x t
• Dp = Force x time = Ft
F
• This is called Impulse
– I = Ft
Example #3
If a baseball bat applies a 22-N force to a
baseball for 0.13 s, what is the impulse
experienced by the ball?
Impulse & Momentum
• Impulse equals a change in momentum
• I = Dp
• Variations
Ft = mDv
Ft = mvf – mvi
I = mDv
I = mvf – mvi
Ft = Dp
Example #4
What is the impulse needed to stop a 10kg bowling ball moving at 6 m/s?
Example #5
A car crashes into a wall at 25 m/s and is
brought to a rest in 0.1 s. Calculate the average
force exerted on a 75-kg test dummy by the seat
belt.
Impulse & Momentum
Increasing Momentum 
mDv = Ft
Increase the time to increase the velocity
• Examples:
– Follow through in sports
•
•
•
•
Basketball shoot
Baseball hit
Soccer kick
Golf swing
– Long-range cannons have long barrels
Impulse & Momentum
Decreasing Force 
mDv = Ft
Increase the time to decrease the Force
• Examples:
– Catching
• Egg toss
• Water balloon
• Football
–
–
–
–
–
–
–
Cars: Crumple Zones & Air Bags
Roll with the punches
Mighty Ducks
Jumping and landing (sprung floors)
Running Shoes
Any padding
Bungee Jumping
Problems
• Review Questions
1-11, 13
• Exercises
1-4, 6, 9, 10
• Problems
1, 2, 5
Conservation of Momentum
• Newton’s Second Law…
– If we want an object to accelerate, we must
apply a force.
• Impulse and Momentum…
– If we want a change in momentum, we must
apply an impulse.
• In both cases, the force or impulse must be
exerted on the object or any system of
objects by something external.
Conservation of Momentum
• If we define the system to include all the
objects we want to study…
 all forces become internal;
 there can be no impulse;
 no impulse means no change in momentum!
• When a physical quantity remains
unchanged during a process, that quantity is
said to be…
CONSERVED.
Collisions
• Momentum is conserved 
Momentum before = Momentum after
• Three types of collisions…
– Elastic  objects rebound off each
other without lasting deformation.
– Inelastic  objects are deformed by
the collision; think car crashes.
– Perfectly inelastic  both objects
stick together
Example #1a
The blue car is moving at 10 m/s, with a mass m.
The orange car, also mass m, is at rest. If the
freight cars are coupled together by the collision,
what is their combined velocity?
v = 10 m/s
v=?
v=0
Example #1b
If the freight cars in the previous example do not
couple and experience an elastic collision, what is
the velocity of the orange car?
v = 10 m/s
v=?
v=0
v=0
Example #2
Two trucks with equal masses, m, experience a head
on collision. After collision, the coupled wreck remains
at the point of impact with zero momentum. If the
green truck was moving at 10 m/s, how fast was the
red truck moving?
v = 10 m/s
v=?
v=0
Example #3
A 3 kg object traveling at 5 m/sec collides head-on with a 2
kg object that is traveling at 2 m/sec in the opposite
direction. What is the velocity of the second object after
the collision if the first object is moving at 1 m/sec?
Problems
• Review Questions
18-23
• Exercises
13, 21
• Problems
6-10