Download Chapter 6 - SFA Physics

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 v).
Impulse = force times time
 
I  Ft
Units – Ns or lbs
3.
IMPULSE CHANGES MOMENTUM
Impulse = change in momentum



v
F  ma  m
t


Ft  mv


I  p
Case 1: Increasing Momentum
Follow through
 
t  I  p

F
Examples: long cannons, driving a golf ball, can you think of others?
Video – Tennis racquet and ball

F  t
Case 2: Decreasing Momentum over a Long Time
 
p  I 
t

F
Examples: rolling with the punch, bungee jumping, can you think of others?
Case 3: Decreasing Momentum over a Short Time
 
p  I 

F
t
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
5.
CONSERVATION OF MOMENTUM
Example - Rifle and bullet
Demo – Rocket balloon
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.



F1 t  m1v1 f  m1v1i
Impulse applied to object 1
Impulse applied to object 2
Apply Newton’s Third Law
Total impulse
applied
to system
or



F2  t  m 2 v 2 f  m 2 v 2i


F1   F2




0  m1v1 f  m1v1i  m 2 v 2 f  m 2 v 2i




m1v1i  m 2 v 2i  m1v1 f  m 2 v 2 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 collisions - conserve momentum
Totally inelastic collisions - conserve momentum and objects stick together
Demo - Collisions on air track
Demo - Momentum balls
Demo - Small ball/large ball drop
Demo - Funny Balls
Video - Two Colliding Autos
20 m (60mph )  m ( 60 mph )  ( 21m )v
19(60mph)  21v
19
(60mph)
21
v  54.3mph
v
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

t
t
Remember to use Newton’s Second Law to
see the forces involved.

The car driver undergoes the same
acceleration as the car, that is
54.3mph  ( 60mph) 114.3mph

t
t
The ratio of these two accelerations is
114 .3
 20
5 .7
7
MORE COMPLICATED COLLISIONS
Vector Addition of Momentum
Examples - Colliding cars and exploding bombs
Video – Collisions in 2-D
Video – Two different masses

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