A block of mass m 1 = 1.5 kg initially moving to the right with a speed of 2.6 m

Question

A block of massm1 = 1.5 kg initially moving to the right with a speed of 2.6 m/s on a frictionless, horizontal track collides with a spring attached to a second block of mass m2 = 3.7 kg initiall at rest. The spring constant is 569N/m.

(a) Find the maximum spring compression in this case.
x =  m

What will be the individual velocities of the two masses (v1 and v2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete.)

Use the relations implied by the having the same total kinetic energy and same total momentum at the end to solve this problem.

Explanation / Answer

The trick to these problems is in recognizing that the maximum spring compression occurs when the velocities of the two blocks are equal (otherwise the spring is either compressing or decompressing). Begin by conserving momentum:
1.5 kg * 2.6 m/s + 0 = (1.5 + 3.7)kg * v
v = 0.75 m/s

Next, conserve energy:
initial KE =

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