# A child's pogo stick stores energy in a spring with a force constant of 2.5×104N/m. At position A, the spring compression is a maximum and the child is momentarily at rest. At position B, the...

A child's pogo stick stores energy in a spring with a force constant of 2.5×104N/m.

At position A, the spring compression is a maximum and the child is momentarily at rest. At position B, the spring is in its equilibrium position and the child is moving upward.At position C, the child is again momentarily at rest at the top of the jump. The combined mass of child and pogo stick is 25.0 kg. If xA is10cm below the line shown find out the distance xC.

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It is a little difficult to visualize your question, but as best we can do:

The compression of the pogostick's spring is going to given by Hook's Law F = -kx where k is the spring constant and x is measured from the equlibrium point. The work done in compressing the spring can also be determined from W = 1/2kx^2

From conservation of energy and the work energy theorem we can determine the maximum height of the system above the deepest compression:

W = mg(Hf - Hi)

1/2kx^2 = mg(Hf - x)

Hf = 1/2kx^2/(mg) + x

Hf = 1/2X2.5X10^4N/mX0.100m^2/(25kgX9.8m/s^2) + (-0.100m)

Hf = 0.426m or 42.6 cm