## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $F_g = 4.90~N$ (b) $T = 2.9~N$ (c) $T = 32.5~N$
(a) We first find the gravitational force acting on the ball; $F_g = mg$ $F_g = (0.500~kg)(9.80~m/s^2)$ $F_g = 4.90~N$ (b) We use the equation for centripetal force to find the tension in the string at the top; $\sum F = \frac{mv^2}{r}$ $T+mg = \frac{mv^2}{r}$ $T = \frac{mv^2}{r} - mg$ $T = \frac{(0.500~kg)(4.0~m/s)^2}{1.02~m} - (0.500~kg)(9.80~m/s^2)$ $T = 2.9~N$ (c) We can use the equation for centripetal force to find the tension in the string at the bottom; $\sum F = \frac{mv^2}{r}$ $T-mg = \frac{mv^2}{r}$ $T = \frac{mv^2}{r} + mg$ $T = \frac{(0.500~kg)(7.5~m/s)^2}{1.02~m} + (0.500~kg)(9.80~m/s^2)$ $T = 32.5~N$