A 3 kg mass moving at 4 m/s along a horizontal, frictionless surface collides wi

Question

A 3 kg mass moving at 4 m/s along a horizontal, frictionless surface collides with a spring, with a spring constant of 480 N/m, which is attached to a 2 kg mass as shown in the figure below. The 2 kg mass and the spring are stationary prior to the collision. What is the maximum compression of the spring (in m) that results from the collision? HINT #1: try solving for the displacement of the spring using energy conservation and then use calculus to determine when this displacement is at a maximum. HINT #2: Newton’s 3rd Law will be helpful.

Explanation / Answer

Maximum compression happen when both block move with same velocity.

By conservation of momentum:

3*4+2*0=(3+2)*V

V= 2.4 m/s

By conservation of Energy:

0.5*3*4^2=0.5*3*2.4^2+0.5*2*2.4^2+0.5*480*X^2

3*4^2=3*2.4^2+2*2.4^2+480*X^2

19.2=480*X^2

X=0.2 m

Maximum compression = 0.2 m

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