A clever engineer designs a "sprong" that obeys the force law F_{x}=-q(x-x_{e})^{3}, where x_{e} is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, well let x_{e}=0. Then _{x}=-qx^{3}.

Find an expression for the potential energy of a stretched or compressed sprong.

A sprong-loaded toy gun shoots a 21 g plastic ball. What is the launch speed if the sprong constant is 4.3×10^{4} N/m^{3} and the sprong is compressed 13 cm ? Assume the barrel is frictionless.

What are the units of q?

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