A block of mass $m$ is moving on a horizontal frictionless surface with a speed $v_0$ as it approaches a block of mass $2m$ which is at rest and has an ideal spring attached to one side.
When the two blocks collide, the spring is completely compressed and the two blocks momentarily move at the same speed, and then separate again, each continuing to move.

Question

A block of mass $m$ is moving on a horizontal frictionless surface with a speed $v_0$ as it approaches a block of mass $2m$ which is at rest and has an ideal spring attached to one side.
When the two blocks collide, the spring is completely compressed and the two blocks momentarily move at the same speed, and then separate again, each continuing to move.(a) Briefly explain why the two blocks have the same speed when the spring is completely compressed.
, (b) Determine the speed $v_f$ of the two blocks while the spring is completely compressed.
, (c) Determine the kinetic energy of the two blocks as they move together with the same speed.
, (d) When the spring expands, the blocks are again separated, and the spring returns its compressed potential energy to kinetic energy in the two blocks. On a graph, sketch a graph of kinetic energy vs. time from the time block $m$ approaches block $2m$ until the two blocks are separated after the collision. *You can describe the graph in the answer section.
, (e) Write the equations that could be used to solve for the speed of each block after they have separated. It is not necessary to solve these equations for the two speeds.
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Jason · Accepted Answer

When the spring is compressed, both blocks have 0 relative velocity, meaning they move at the same speed. This is similar where two objects move at the same speed after an inelastic collision.
$ v_0/3 $
$ \frac{1}{6} mv_0^2 $
The graph of KE should be a horizontal line followed by a downwards curved dip, followed by a horizontal line at the original position on the KE axis.
$ mv_0 = mv_{f1} + mv_{f2} \quad \text{and} \quad \frac{1}{2}mv_0^2 = \frac{1}{2}mv_{f1}^2 + \frac{1}{2}mv_{f2}^2 $

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