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## Homework Statement

Two objects are placed in a 1 dimensional box with springs of different constants at each end of the box. The box is made of wood and has a length of L. The first object has a mass of M and is initially compressed a distance of xinitial onto spring 1 of spring constant k. When M is released it collides elastically with a second object of 6M with is initially at rest. Both objects recoil in opposite directions and ignoring friction how far will the initial spring recompress when M strikes it. How far will the second spring compress when 6M hits it knowing that the spring constant is 2k. The total length of each spring is 1.5m at equilibrium.

## Homework Equations

1/2kx^2

1/2mv^2

energy balance

momentum balance

## The Attempt at a Solution

This is a problem I am having trouble getting started. I know the concept but I can't get it to the paper. The 1st spring has a potential energy that will be converted into a kinetic energy of the object M. This will give M momentum equal to its velocity X mass. This will collide with 6M transferring some energy. Since the momentum is conserved the the 6M will have a positive velocity and the m will now have a negative velocity and less momentum. This velocity can then be used to find out how much spring potential energy is needed to obtain this, and then find the compression needed.