How Do You Calculate Maximum Spring Compression in an Inelastic Collision?

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To calculate the maximum spring compression in an inelastic collision involving a freight car and a spring bumper, the initial momentum of the moving car must be conserved when the two cars couple together. The equation m1v1 + m2v2 = V(m1 + m2) is used to determine the combined speed after the collision, which has been found to be 3.5 m/s. The next step involves applying energy conservation principles, where the kinetic energy of the coupled cars is converted into potential energy stored in the spring at maximum compression. The spring's potential energy can be expressed as (1/2)kx^2, where k is the spring constant. The solution for maximum compression requires setting the kinetic energy equal to the potential energy of the spring.
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Homework Statement



A 10500kg freight car rests against a spring bumper at the end of a raildroad track. The spring has constant k = 3.4 x 10^N/m. The car is hit by a second car of 9400 kg mass moving at 7.5 m/s, and the two cars couple together.

a) what is the maximum compression of the spring?
b) what is the speed of the two cars together when the rebound from the spring?

Homework Equations





The Attempt at a Solution


For starters, I know this is an elastic collision problem since the 2 cars stick together. Perhaps the equation m1v1=V(m1+m2) has some relevance. I also know the initial energy of the first car is 0 since it's at rest. But I'm not sure how to factor the spring here. What equation or equations can I use to solve this problem?
 
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Ok correction, I solved part b. I did use m1v1+ m2v2=v(m1+m2), and I got 3.5 m/s, which is correct. But how do I solve part a? What equation should I use
 

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