1. Chapter 6: Momentum and Collisions

2. Objectives Understand the concept of momentum.
Use the impulse-momentum theorem to solve problems.
Understand how time and force are related in collisions.

3. Momentum momentum: inertia in motion; the product of mass and velocity
p = m · v
How much momentum does a
2750 kg Hummer H2 moving at
31 m/s possess?
Note: momentum is a vector; units are kg·m/s

4. Impulse Changes Momentum
Newton actually wrote his second law in this form:
SF · Dt = m · Dv
The quantity SF·Dt is called impulse.
The quantity m·Dv represents a change in momentum.
Thus, an impulse causes a change in momentum SF
SF · Dt = m · Dv = Dp
“impulse-momentum theorem”

5. Impulse Problem A 1750 kg car traveling at 21 m/s
hits a concrete wall and stops in
0.62 s.
What is the Dp?
How much impulse is applied to
the car?
How much force does the
wall apply to the car?
What would be the
force applied to the car
if you used the brakes and
took 4.5 seconds to stop?

6. Impulse Problem The face of a golf club applies an average force of
5300 N to a 49 gram golf ball. The ball leaves the
clubface with a speed of 44 m/s. How much time is
the ball in contact with the clubface?
SF · Dt = m · Dv SF

7. Bouncing Which collision involves more force: a ball bouncing
off a wall or a ball sticking to a wall? Why?
The ball bouncing because there is a greater Dv.
SF · Dt = m · Dv so
SF ~ Dv

8. Highway Safety and Impulse
Water-filled highway
barricades increase
the time it takes to stop
a car. Why is this safer?
They reduce the force
of impact!
SF = (m · Dv) / Dt
Seatbelts and
airbags also
increase the
stopping time
and reduce the
force of impact.

9. Objectives Understand the concept of conservation of momentum.
Understand why momentum is conserved in an interaction.
Be able to solve problems involving collisions.

10. Conservation of Momentum
conservation of momentum: in any interaction (such
as a collision) the total combined momentum of the
objects remains unchanged (as long as no external
forces are present).
system: all of the objects involved in an interaction

11. Conservation of Momentum
system
Conservation of
Momentum
ma·vai + mb·vbi = Spi mb ma
vai
vbi
Dp = -SF · Dt
-SF
+SF
Dp = +SF · Dt Dt
DpTOTAL = ( -SF·Dt ) + ( +SF·Dt ) = 0
ma·vaf + mb·vbf = Spf mb ma
S pi = S pf
vaf
vbf
Law of Conservation
of Momentum:
ma·vai + mb·vbi = ma·vaf + mb·vbf

12. Types of Collisions elastic: objects collide without being permanently
deformed and without
releasing heat or sound
ma·vai + mb·vbi = ma·vaf + mb·vbf
perfectly inelastic: objects
become tangled or combined
together
ma·vai + mb·vbi = (ma+ mb) ·vf

13. Conservation of Momentum Problem
A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg target ball. The bocce ball slows to 2.6 m/s. How fast does the target ball move? Assume all motion is in one dimension.
ma·vai + mb·vbi = ma·vaf + mb·vbf

14. Conservation of Momentum Problem
Victor, who has a mass of 85 kg, is trying to make a
“get-away” in his 23-kg canoe. As he is leaving the
dock at 1.3 m/s, Dakota jumps into the canoe and sits
down. If Dakota has a mass of 64 kg and she jumps
at a speed of 2.7 m/s, what is the final speed of the
the canoe and its passengers?

15. Conservation of Momentum in Two-Dimensions
Collisions in 2-D
involve vectors.
paf ma
initial ma mb
final
Spi mb
pbf

16. Equal Mass Collision
A cue ball (m = 0.16 kg) rolling at 4.0 m/s hits a
stationary eight ball of the same mass. If the cue
ball travels 25o above its original path and the eight
ball travels 65o below the original path, what is the
speed of each ball after the collision?

17. Unequal Mass Collision
A 0.85 kg bocce ball rolling at 3.4 m/s hits a stationary 0.17 kg target ball. The bocce ball slows to 2.8 m/s and travels at a 15o angle above its original path. What is the speed of the target ball it travels at a 75o below the original path?

18. Slingshot Manuever NASA has made use of conservation of momentum
on numerous missions.
The spacecraft substantially
increased its momentum
(as speed) and Jupiter
lost the same amount
of momentum, but because
Jupiter is so massive,
its overall speed remained
virtually unchanged.
Jupiter
S pi = S pf
The spacecraft is pulled
toward Jupiter by gravity,
but as Jupiter moves along
its orbit, the spacecraft just
misses colliding with the
planet and continues it trip.