Page 107 - Schaum's Outline of Theory and Problems of Applied Physics

92 MOMENTUM [CHAP. 8

COLLISIONS
Momentum is also conserved in collisions. If a moving billiard ball strikes a stationary one, the two move off in
such a way that the vector sum of their momenta is the same as the initial momentum of the first ball (Fig. 8-1).
This is true even if the balls move off in different directions.

m v
1 1
1 m v m v
2 2
1 1
1 2 m v
m v 1 0
1 0
2
m v
2 2

Fig. 8-1

An elastic collision is one in which the bodies involved move apart in such a way that kinetic energy as well
as momentum is conserved. In a perfectly inelastic collision, the bodies stick together and the kinetic energy
loss is the maximum possible consistent with momentum conservation. Most collisions are intermediate between
these two extremes and are simply called inelastic.

SOLVED PROBLEM 8.11

A 1000-kg car moving at 80 km/h collides head-on with a 1500 kg car moving at 30 km/h, and the two
cars stick together. Which way does the wreckage move?
The 1000-kg car had the greater initial momentum, so the wreckage moves in the same direction it had.

SOLVED PROBLEM 8.12
A 0.5-kg snowball moving at 20 m/s strikes and sticks to a 70-kg man standing on the frictionless surface
of a frozen pond. What is the man’s final velocity?
Let v 1 = snowball’s velocity and v 2 = final velocity of man plus snowball. Then

Initial momentum of snowball = final momentum of man + snowball
m s v 1 = (m m + m s )v 2

m s 0.5kg
v 2 = (v 1 ) = (20 m/s) = 0.14 m/s
m m + m s 70.5kg
SOLVED PROBLEM 8.13
A 40-kg skater traveling at 4 m/s overtakes a 60-kg skater traveling at 2 m/s in the same direction and
collides with her. (a) If the two skaters remain in contact, what is their final velocity? (b) How much
kinetic energy is lost?
(a) Let v 1 = initial velocity of 40-kg skater, v 2 = initial velocity of 60-kg skater, and v 3 = final velocity of the two
skaters. Then

Initial total momentum = final total momentum
m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v 3
m 1 v 1 + m 2 v 2 (40 kg)(4 m/s) + (60 kg)(2 m/s)
v 3 = = = 2.8 m/s
m 1 + m 2 40 kg + 60 kg