A clever engineer designs a “sprong” that obeys the force law F_x = -q(x - x_eq)³, where x_eq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we’ll let x_eq = 0 m. Then F_x = -qx³.

a. What are the units of q?
b. Find an expression for the potential energy of a stretched or compressed sprong.
c. A sprong-loaded toy gun shoots a 20 g plastic ball. What is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10 cm? Assume the barrel is frictionless.