Chapter 7 - Potential Energy and Energy Conservation - Problems - Exercises - Page 232: 7.53

(a) v = 7.00 m/s (b) T = 8.82 N

(a) $K_2+U_2 = K_1+U_1$ $\frac{1}{2}mv^2+0 = 0+ mgh$ $v^2 = 2gh$ $v = \sqrt{2gh}$ $v = \sqrt{(2)(9.80~m/s^2)(2.50~m)}$ $v = 7.00~m/s$ (b) $\sum F = \frac{mv^2}{R}$ $T-mg = \frac{mv^2}{R}$ $T = \frac{mv^2}{R} + mg$ $T = \frac{(0.300~kg)(7.00~m/s)^2}{2.50~m} + (0.300~kg)(9.80~m/s^2)$ $T = 8.82~N$