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

(a) The spring scale reads 49 N (b) $k = 1450~N/m$ (c) The scale will read zero when the spring is compressed by 3.4 cm
(a) The spring scale will show the weight of the object. Let $T$ be the tension from the scale pulling up on the object. $T = mg$ $T = (5.0~kg)(9.80~m/s^2)$ $T = 49~N$ The spring scale reads 49 N. (b) Let $F_s$ be the force of the spring pushing up on the object. $F_s +T = mg$ $F_s = mg-T$ $F_s = 49~N-20~N$ $F_s = 29~N$ We can find the spring constant of the spring. $kx = F_s$ $k = \frac{F_s}{x}$ $k = \frac{29~N}{0.020~m}$ $k = 1450~N/m$ (c) The scale will read zero when the spring is supporting the full weight of the object. $F_s = mg$ $F_s = 49~N$ We can find the distance the spring is compressed when the spring is pushing with this force. $kx = F_s$ $x = \frac{F_s}{k}$ $x = \frac{49~N}{1450~N/m}$ $x = 0.034~m = 3.4~cm$ The scale will read zero when the spring is compressed by 3.4 cm.