Finding spring constant in elastic collision of equal masses

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In the elastic collision of two identical cars, the red car travels at 40 MPH left and the green car at 80 MPH right, with a maximum bumper indentation of 5 cm. The kinetic energy of both cars must be equated to the potential energy stored in the springs, leading to the equation KEred car + KEgreen car = 2 * EPE. However, it's important to note that not all kinetic energy is converted into spring energy at maximum compression due to momentum conservation. The setup of the equation may need adjustment, and the masses do not cancel out in the final calculation. Understanding these principles is crucial for accurately determining the spring constant.
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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 KEred car + KEgreen 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?
 
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ss85 said:
The kinetic energy must be absorbed by the two springs, so KEred car + KEgreen 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.)
 

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