Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 4 - Dynamics: Newton's Laws of Motion - Problems - Page 102: 25

Answer

(a) The tension in the upper cord is 63 N and the tension in the lower cord is 31 N. (b) The tension in the upper cord is 71 N and the tension in the lower cord is 35 N.

Work Step by Step

(a) The upper cord is holding the weight of both buckets. $F_T = mg$ $F_T = (6.4 ~kg)(9.8 ~m/s^2)$ $F_T = 63 ~N$ The lower cord is holding up the weight of the lower bucket. $F_T = mg$ $F_T = (3.2 ~kg)(9.8 ~m/s^2)$ $F_T = 31 ~N$ (b) The upper cord is causing both buckets to accelerate. $F_T - mg = ma$ $F_T = m(g+a)$ $F_T = (6.4 ~kg)(1.25 ~m/s^2 + 9.8 ~m/s^2)$ $F_T = 71 ~N$ The lower cord is causing the lower bucket to accelerate. $F_T - mg = ma$ $F_T = m(g+a)$ $F_T = (3.2 ~kg)(1.25 ~m/s^2 + 9.8 ~m/s^2)$ $F_T = 35 ~N$
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