Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 4 - Forces and Newton's Laws of Motion - Focus On Concepts - Page 112: 15

Answer

(b) $f_{s,A}=f_{s,B}=\frac{1}{2}f_{s,C}$

Work Step by Step

Let, the masses of each block is $m$. According to the given diagram, The static friction on C arises only from the contact with B $f_{s,A}=\mu mg$, directed towards right The static friction on B arises from the contact with C and A The static friction on B arises at the contact with A: $f^{1}_{s,B}=\mu mg$, directed towards left The static friction on B arises at the contact with C: $f^{2}_{s,B}=\mu (m+m)g$, directed towards right Therefore resultant static friction on B $f_{s,B}=f^{2}_{s,B}-f^{1}_{s,B}=\mu mg$, directed towards right. The static friction on A arises only from the contact with B $f_{s,C}=\mu (m+m)g=2\mu mg$, directed towards left Thus, $f_{s,A}=f_{s,B}=\frac{1}{2}f_{s,C}$
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