Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 3

You drop a 2.00 kg book to a friend who stands on the ground at distance \( D = 10.0 \text{ m} \) below. If your friend’s outstretched hands are at distance \( d = 1.50 \text{ m} \) above the ground (Fig. 8.13), (a) how much work \( W_g \) does the gravitational force do on the book as it drops to her hands? (b) What is the change \( \Delta U \) in the gravitational potential energy of the book–Earth system during the drop? If the gravitational potential energy \( U \) of that system is taken to be zero at ground level, what is \( U \) (c) when the book is released and (d) when it reaches her hands? Now take \( U \) to be 100 J at ground level and again find (e) \( W_g \), (f) \( \Delta U \), (g) \( U \) at the release point, and (h) \( U \) at her hands.