Steve, with mass m , is ready to squat jump Kale’s insecurities—represented by n moles of a solid with total mass M —out of Earth’s atmosphere. He decides to model his squat as a spring with constant k compressing vertically down a distance d from equilibrium, and the jump as releasing that spring, launching himself and Kale’s insecurities to a maximum height h above equilibrium. He does everything perfectly.

a) When he gets to that maximum height, he finds that Kale’s insecurities have heated by ∆T. How much energy went into heating them?

b) Assuming Steve’s temperature did not change and no other interactions were present, how far did Steve compress his model spring?