What is the velocity of the cars after the inelastic collision?

Question

A 45,000 kg train car moves at 10 m/s toward a 17,000 kg train car at rest. After the two cars collide, they couple together and move along the track in the same direction.

equation for the inelastic collision: m1v1 + m2v2 = (m3 + m4)v3

Answers to choose from:

1. 5.04 m/s
2. 7.26 m/s
3. 10.0 m/s
4. 12.07 m/s

Answer 1

Hello Lily,

The equation given is the equation for conservation of momentum for the system. This equation is to be used because momentum is still conserved in an inelastic collision even though energy isn't. Since we know the masses of both vehicles and their initial velocity, the only unknown is v3. Furthermore, we know v2 is zero, so we can simply write:

m1v1=(m1+m2)v3

Dividing both sides by (m1+m2) to solve for v3 yields

v3=m1v1/(m1+m2)

v3=(45,000 kg*10 m/s)/(45,000 kg+17,000 kg)

v3= 7.258 m/s

7.26 m/s is the final answer out of the choices given. I hope this helps and good luck with your course!