Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 6 - Applications of Newton's Laws - Problems and Conceptual Exercises - Page 178: 12

Answer

(a) $0.49$ (b) no change to the angle ($26^{\circ}$)

Work Step by Step

(a) We can find the coefficient of static friction as $\Sigma F_y=N-mgcos\theta=0$ $\implies N=mgcos\theta$ Now the horizontal component of force is $F_x=\mu_sN-mgsin\theta=ma_x=0$ $\implies \mu_s(mgcos\theta)-mgsin\theta=0$ This simplifies to: $\mu_s=tan\theta$ $\implies \mu_s=tan26^{\circ}$ $\mu_s=0.49$ (b) We know that the angle does not depend on the mass. Thus, if mass is doubled, the angle remains the same.
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