Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 10

Problem 3: You drop a $2.00\text{ kg}$ book to a friend who stands on the ground at distance $D = 10.0\text{ m}$ below. Your friend's outstretched hands are at distance $d = 1.50\text{ m}$ above the ground (Fig. 8-19). (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 $100\text{ J}$ at ground level and again find (e) $W_g$, (f) $\Delta U$, (g) $U$ at the release point, and (h) $U$ at her hands. Problem 10: (a) In Problem 3, what is the speed of the book when it reaches your friend's hands? (b) If we substituted a second book with twice the mass, what would its speed be? (c) If, instead, the book were thrown down, would the answer to part (a) increase, decrease, or remain the same?