p150c5:1

Chapter 5: Momentum

Momentum: a measure of motion

Force: a cause of change in motion

What changes when a force is applied?

F ma mv

t

Fmv

tmv

;

;

but mass does not change

changes with time

Linear Momentum: p = mv

the tendency of an object to pursue straight line motion

Kinetic Energy in terms of momentum:

KEp

m

2

2

p150c5:2

Impulse: the change in motion

I p m v

v a t

F ma

I F t p mv

since

and

Example: The head of a golf club is in contact with a 46 g golf ball for 0.50 ms, which results in the golf ball flying off at 70 m/s. Find the impulse and the average force acting on the ball during the impact.

p150c5:3

Conservation of momentum

two bodies + action/reaction + no other forces

FAB = - FBA

=> equal but opposite impulses

=> pA + pB = 0

When the vector sum of the external forces acting on a system of particles equals zero, the total linear momentum remains constant.

p1 + p2 + p3 + ... is constant

p150c5:4

An application of conservation of momentum: explosions

initially:

mv = 0

after explosion:

m1v1 + m2v2 + ...= 0

or (for two fragments)

m1v1 = m2v2 same size p, opposite directions

Example: An astronaut just outside of the space shuttle throws her 800 g camera away when it jams. If she and her space suit have a combined mass of 100 kg and the speed of the camera is 20 m/s, how far is she from the shuttle in 10 seconds?

m

m1 m2 v1 v2

p150c5:5

Rocket propulsion (note: no problems)

“continual explosion”

continual conservation of momentum:

All space propulsion systems depend upon conservation of momentum.

most require some “reaction mass”

combustion chamber

ejected gases: m at speed v

Fmv

tv

m

t

( )

p150c5:6

Collisions

Elastic Collisions

conserve KE (total KE is same before and after collision)

Inelastic Collisions

some KE is lost during collision (heat, sound, etc.)

Completely Inelastic Collisions

objects stick together

maximum possible loss of KE

In all collisions, the total momentum is conserved!

p150c5:7

Example 5.4 A 5.0 kg lump of clay that is moving at 10 m/s to the left strikes a 6.0 kg lump of clay moving 12 m/s to the right. The two lumps stick together after they collide. Find the final speed of the composite lump of clay and the kinetic energy lost during the collisions.

Example 5.5 (discussion only) A 60 kg man sliding east on a frictionless surface of a frozen pond at a velocity of .50 m/s is struck by a 1 kg snowball whose velocity is 20 m/s towards the north. If the snowball sticks to the man, what is his final velocity?

p150c5:8

Elastic collisionsconservation of KE + conservation of momentum=> initial relative velocity = -(final relative velocity)

v1 v2 = (v1' v2 ')

For an object striking head-on a second object (initially at rest)

212

12

1

2

121

121

21

211

22112211

2121

2

)1()(4'

2''

algebra

''

)''(

0

mmmm

KEKE

vmm

mvv

mmmm

v

vmvmvmvm

vvvv

v

p150c5:9

Example: A 5.0 Kg mass moving at 10 m/s collides elastically head-on with a stationary 10 Kg mass. What are the final velocities of both masses? What is the initial KE of the 5.0 kg mass? What is the final KE of the 10 kg mass?

Example: A 10 Kg mass moving at 10 m/s collides elastically head-on with a stationary 5.0 Kg mass. What are the final velocities of both masses? What is the initial KE of the 10 kg mass? What is the final KE of the 5.0 kg mass?