The figure shows an 8.3 kg stone at rest on a spring. The spring is compressed 1

Question

The figure shows an 8.3 kg stone at rest on a spring. The spring is compressed 12 cm by the stone. (a) What is the spring constant? (b) The stone is pushed down an additional 30 cm and released.What is the elastic potential energy of the compressed spring just before that release? (c) What is the change in the gravitational potential energy of the stone–Earth system when the stone moves from the release point to its maximum height? (d) What is that maximum height, measured from the release point?

Explanation / Answer

a) k = mg/x = 8.3*9.8/0.12 = 677.833 N/m
b) P.E. = 0.5*k*x^2 = 0.5*677.833*(0.42)^2 = 59.78 J
c) change in gravitational potential energy = 59.78 J
d) h = 59.78/m*g = 0.735m

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