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Chapter 6
Momentum
1. MOMENTUM
 Momentum
- inertia in motion
 Momentum = mass times velocity


p  mv
Units - kg m/s or sl ft/s
2. IMPULSE

Collisions involve forces (there is a Dv).

Impulse = force times time.
 
I  FDt
Units - N s or lb s
3.
IMPULSE CHANGES MOMENTUM
Impulse = change in momentum


F  ma 

Dv
F m
Dt


FDt  mDv


FDt  mDv

 
FDt  m(v f  vi )



FDt  (mv f  mvi )



FDt  ( p f  pi )


I  Dp
Case 1
Increasing Momentum
Follow through
 
Dt  I  Dp



FDt  I  Dp
Examples:
Long Cannons
Driving a golf ball
Can you think of others?
Video Clip
Tennis racquet and ball
Case 2
Decreasing Momentum over a Long Time

 
Dp  I  F
Dt

F
Dt
Warning – May be dangerous
Examples:
Rolling with the Punch
Bungee Jumping
Can you think of others?
Case 3
Decreasing Momentum over a Short Time

 
Dp  I  F
Dt
Examples:
Boxing (leaning into punch)
Head-on collisions
Can you think of others?
4. BOUNCING
There is a greater impulse with
bouncing.
Example:
Pelton Wheel
Demo – Impulse Pendulum
Consider a hard ball and a clay ball that
have +10 units of momentum each just
before hitting a wall.
 The clay ball sticks to the wall and the hard
ball bounces off with -5 units of momentum.
 Which delivered the most “punch” to the
wall?

Initial momentum of the clay ball is 10.
Final momentum of clay ball is 0.
The change is 0 - 10 = - 10.
It received - 10 impulse so it
applied + 10 to the wall.
Initial momentum of the hard ball is 10.
Final momentum of hard ball is - 5.
The change is - 5 - 10 = - 15.
It received - 15 impulse so it
applied + 15 to the wall.
5. CONSERVATION OF MOMENTUM
Example:
Rifle and bullet
Demo - Rocket balloon
Demo - Clackers
Video - Cannon recoil
Video - Rocket scooter
Consider two objects, 1 and 2, and assume that
no external forces are acting on the system
composed of these two particles.



Impulse applied to object 1
F1Dt  m1v1 f  m1v1i



Impulse applied to object 2
F2 Dt  m2 v2 f  m2 v2 i


Apply Newton’s Third Law
F1   F2


or F1Dt   F2 Dt
Total impulse
applied
to system
or




0  m1v1 f  m1v1i  m2 v2 f  m2 v2 i




m1v1i  m2 v2 i  m1v1 f  m2 v2 f
 Internal
forces cannot cause a
change in momentum of the
system.
 For conservation of momentum, the
external forces must be zero.
6. COLLISIONS
 Collisions
involve forces internal to
colliding bodies.
 Elastic
collisions - conserve energy and
momentum
 Inelastic
 Totally
collisions - conserve momentum
inelastic collisions - conserve
momentum and objects stick together
Demos and Videos
Terms in parentheses represent what is conserved.
Demo
– Air track collisions (momentum & energy)
Demo
- Momentum balls (momentum & energy)
Demo
- Hovering disks (momentum & energy)
Demo
- Small ball/large ball drop
Demo
- Funny Balls
Video
- Two Colliding Autos (momentum)
Simple Examples of Head-On Collisions
(Energy and Momentum are Both Conserved)
Collision between two objects of the same mass. One mass is at rest.
Collision between two objects. One at rest initially has twice the mass.
Collision between two objects. One not at rest initially has twice the mass.
Head-On Totally Inelastic
Collision Example
vtruck  60mph
vcar  60mph
Let the mass of the truck be 20 times the
mass of the car.
 Using conservation of momentum, we get

initial momentum of system = final momentum of system
20 m(60 mph)  m(60 mph)  (21 m)v
19(60 mph)  21v
19
v  (60 mph)
21
v  54.3 mph
Remember that the car and the truck exert
equal but oppositely directed forces upon
each other.
 What about the drivers?
 The truck driver undergoes the same
acceleration as the truck, that is

(54.3  60) mph  5.7 mph

Dt
Dt

The car driver undergoes the same
acceleration as the car, that is
54.3 mph  (60 mph) 114.3 mph

Dt
Dt
The ratio of the magnitudes of these two accelerations is
114.3
 20
5.7
Remember to use Newton’s Second Law to
see the forces involved.

For the truck driver his mass times his
acceleration gives
ma F
For the car driver his mass times his greater acceleration
gives
a F
m

Don’t mess with T
TRUCKS, big trucks that is.

Your danger is of the order of twenty times
greater than that of the truck driver.
7. More Complicated Collisions
Vector Addition of Momentum
Example of Non-Head-On Collisions
(Energy and Momentum are Both Conserved)
Collision between two objects of the same mass. One mass is at rest.
If you vector add the total momentum after collision,
you get the total momentum before collision.
Examples:
Colliding cars
Exploding bombs
Video - Collisions in 2-D
Chapter 6 Review Questions
The product of mass times velocity is most
appropriately called
(a) impulse
(b) change in momentum
(c) momentum
(d) change in impulse
You jump off a table. When you land on the
floor you bend your knees during the landing
in order to
(a) make smaller the impulse applied to
you by the floor
(b) make smaller the force applied to you by
the floor
(c) both (a) and (b)
An egg dropped on carpet has a better chance
of surviving than an egg dropped on concrete.
The reason why is because on carpet the time
of impact is longer than for concrete and thus
the force applied to the egg will be smaller.
(a) True
(b) False
In which type of collision is energy
conserved?
(a) elastic
(b) inelastic
(c) totally inelastic
(d) All of the above
(e) None of the above
A Mack truck and a Volkswagen have a
collision head-on. Which driver experiences
the greater force?
(a) Mack truck driver
(b) Volkswagen driver
(c) both experience the same force