Suppose you place a spring, spring constant k, exactly vertical and then place a

Question

Suppose you place a spring, spring constant k, exactly vertical and then place a mass m on it. Initially the elastic energy in the spring is zero and the kinetic energy of the mass is zero. Obviously the mass will compress the spring until the speed of the mass is again zero. Call this distance the spring is compressed d (a positive number). Use conservation of energy to find what d, the compression of the spring, will be.
The problem above is what will be graded but you should think about your answer: is the situation “compressed spring + mass at rest” in equilibrium? If not, what will happen next?

Explanation / Answer

mgd = .5Kd^2 so d = 2mg/K

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