# Speed of Center of Mass

1. Homework Statement
A loaded coal car with a mass of 120 metric tons traveling at 2 m/s collides and couples with an empty, stationary coal car with a mass of 8 metric tons. (1 metric ton = 103 kg)

(c) What is the speed of the center of mass of the system of two cars throughout the process?

2. Homework Equations

I am not sure of any relevant equations for part c but I know that M1r1=M2r2 deals with center of mass systems.

3. The Attempt at a Solution
I already solved parts a and b which are about final speed of two cars, and change in kinetic energy respectively.

Thanks for the help

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The total momentum of the system tends to be the momentum of the center of mass. Using that, just find the velocity of the center of mass. The velocity of the center of mass should technically remain the same throughout the entire process (before and after collision).

internal forces cant change the velocity or position of center of mass.

tiny-tim
Homework Helper
… just use ordinary geometry …

(c) What is the speed of the center of mass of the system of two cars throughout the process?

I am not sure of any relevant equations for part c but I know that M1r1=M2r2 deals with center of mass systems.
ok - so you know where the center of mass is (before the collision)!

Just use ordinary geometry to work out how fast it is moving!

I still don't understand the problem. I know that the moving coal car is moving at 2m/s and it hits the stationary coal car. But the problem does not specify which direction the moving coal car is coming from or how far it is initially.

I don't know if I could use the final velocity of the two coupled cars or the change in kinetic energy to help find part c.

You don't know to know which direction the moving coal car is heading; the direction is arbitrary here. You don't need to know how far the coal car moved, either, this is a momentum problem, so use conservation of momentum.

Ok, I got it now. I realized that the speed of the center of mass was the same as the final velocity of the two cars, which happened to be the same answer to part a. Thanks for the help.