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

Explanation / Answer

maximum compression when both mass have same velocity. momentum conservation 3 x 4 = (3+2)x v v = 12/5 m/s energy conservation 1/2 m1v1^2 = 1/2 (m1+m2)v^2 + 1/2 k x^2 3 x 16 = 5 x144 /25 + 480 x2 max compression , x = .2 m or 20 cm

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