Finding spring constant in elastic collision of equal masses

[ss85]

Homework Statement

Two identical cars approach each other on a straight road. The red car has a velocity of 40MPH to the left and the green car has a velocity of 80MPH to the right.

A spring is attached to the front bumper so that a head-on collision will be elastic. If the maximum indentation of each bumper is 5cm, what is the spring constant of the bumpers?

Homework Equations

KE= 1/2 m v²
EPE = 1/2 k x²

The Attempt at a Solution

The kinetic energy must be absorbed by the two springs, so KE_{red car} + KE_{green car} = 2 * EPE, correct? Doing this I get a value of 320410m, but this doesn't seem right. Shouldn't I be able to get an answer that is not in terms of the mass? Did I set up the equation wrong and somehow the masses should cancel?

 

[Doc Al]

The kinetic energy must be absorbed by the two springs, so KE_{red car} + KE_{green car} = 2 * EPE, correct?

You cannot assume that all of the kinetic energy goes into the springs at the point of maximum compression. (Consider momentum conservation.)

(No reason to think that the masses will cancel from your final answer.)