Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 10 - Energy - Exercises and Problems: 17

Answer

(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

Work Step by Step

(a) The spring scale will show the weight of the object. Let $T$ be the tension of 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 as; $kx = F_s$ $k = \frac{F_s}{x}$ $k = \frac{29~N}{0.020~m}$ $k = 1450~N/m$ (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.
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