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 - General Problems - Page 106: 76

Answer

(a) $F_T = \frac{Mg}{2}$ (b) $F_{T1} = \frac{Mg}{2}$ $F_{T2} = \frac{Mg}{2}$ $F_{T3} = \frac{3Mg}{2}$ $F_{T4} = Mg$

Work Step by Step

(a) Since the tension in the rope is the same all along the rope, $F = F_{T1} = F_{T2}$. The tension in $F_{T1}$ and $F_{T2}$ pulls up the piano, therefore the sum of these two tension forces must be at least equal to the weight of the piano: $F_{T1} + F_{T2} = Mg$ $2 F_T = Mg$ $F_T = \frac{Mg}{2}$ (b) $F_{T1} = F_{T2} = F_T = \frac{Mg}{2}$ $F_{T3} = F_{T1} + F_{T2} + F_T = \frac{3Mg}{2}$ $F_{T4} = F_{T1} + F_{T2} = Mg$
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