In one day, a $75$-kg mountain climber ascends from the $1500$-m level on a vertical cliff to the top at $2400$ m. The next day, she descends from the top to the base of the cliff, which is at an elevation of $1350$ m. What is her change in gravitational potential energy on the first day?

The maximum height a typical human can jump from a crouched start is about $60$ cm. By how much does the gravitational potential energy increase for a $72$-kg person in such a jump? Where does this energy come from?

Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length $20$ m that makes an angle of $45°$ with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of $30°$ with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan's speed just before he reaches Jane. Ignore air resistance and the mass of the vine.

A spring of negligible mass has force constant $k=800$ N/m. How far must the spring be compressed for $1.20$ J of potential energy to be stored in it?

A spring of negligible mass has force constant $k = 1600$ N/m. How far must the spring be compressed for $3.20$ J of potential energy to be stored in it?

A spring of negligible mass has force constant $k=1600$ N/m. You place the spring vertically with one end on the floor. You then drop a $1.20$-kg book onto it from a height of $0.800$ m above the top of the spring. Find the maximum distance the spring will be compressed.