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

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SUMMARY

The discussion focuses on calculating the maximum compression of a spring in an inelastic collision scenario involving a 10,500 kg freight car and a 9,400 kg car moving at 7.5 m/s. The spring constant is given as k = 3.4 x 10^N/m. The solution for part b was successfully determined using the equation m1v1 + m2v2 = V(m1 + m2), yielding a speed of 3.5 m/s for the coupled cars after the collision. The primary challenge remains in calculating the maximum compression of the spring, which requires the application of energy conservation principles.

PREREQUISITES
  • Understanding of inelastic collisions and momentum conservation
  • Familiarity with Hooke's Law and spring constants
  • Knowledge of energy conservation in mechanical systems
  • Basic algebra for solving equations
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  • Study the principles of energy conservation in inelastic collisions
  • Learn how to apply Hooke's Law to calculate spring compression
  • Review examples of momentum conservation in collision problems
  • Explore the relationship between kinetic energy and potential energy in spring systems
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Students studying physics, particularly those focusing on mechanics and collision problems, as well as educators seeking to enhance their understanding of spring dynamics in inelastic collisions.

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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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