physics help?

Question

In the railroad freight yard, an empty freight car of mass m rolls along a straight level track at 1 m/s and collides with an initially stationary, fully loaded boxcar of mass 3.5m. The two cars couple together upon collision.

(a) What is the magnitude of the velocity of the two cars after the collision?

(b) Suppose instead that the two cars are at rest after the collision. With what speed was the loaded boxcar moving before the collision if the empty one was moving at 1 m/s?

Answer 1

Conservation of momentum...

a) 1 M m/s = 4.5 X
X = 2/9 m/s

b) 1 M m/s = 3.5 X
X = 2/7 m/s

Answer 2

This involves the conservation of momentum.

(mass) (initial velocity) for each element = (mass) (final velocity) for each element. Because the cars couple afterwards, the problem becomes the following:

M1*V1 +M2*V2 = (M1+M2)*Vf

where M1= m, V1 =1m/s, M2=3.5m, V2=0, Vf=final velocity

for part (a),

(m) * 1m/s + 3.5m * 0 = (m +3.5m) Vf
4.5m*Vf = m * 1m/s
Vf = .222m/s

for part (b), same equation, just Vf = 0, and you're solving for V2

m*1m/s + 3.5m*V2=(3.5m + m)*0
m*1m/s=-3.5m*V2
V2= -.2857m/s = -.29m/s

Hope this helps. Good luck!