How much energy (in J) is stored in the spring under this circumstance?

Question

A 38 kg child uses a pogo stick to bounce up and down. The spring constant, k, of the toy equals 9,300 N/m.

How much energy (in J) is stored in the spring under this circumstance?

Answer 1

If you think about the spring in its compressed condition when the child is "down" in her up/down cycle, then the free body diagram looks like this:

where W = mg = 38(9.81) = 372.78 N

and F_S = kx = 9300x

At that instantaneous moment, there is no velocity and there is no acceleration (acceleration on the "going down" phase is negative and the acceleration on the "going up" phase is positive meaning and the bottom of the motion, the acceleration is zero). So if a = 0 then ∑F = 0 so F_S = W so:

372.78 = 9300x

x = 0.04 m

The potential energy stored in a spring is found by the equation U_S = 1/2kx² = (1/2)(9300)(0.04)² = 7.5 joules