College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 2 - Problems - Page 68: 72

Answer

The normal force is $152.8~N$ The magnitude of the force of static friction exerted on the crate is $88.2~N$ and this force is directed up the ramp at an angle of $30^{\circ}$ to the horizontal.

Work Step by Step

The normal force $F_N$ is the component of the crate's weight that is directed straight into the surface of the ramp. $F_N = mg~cos~\theta$ $F_N = (18.0~kg)(9.80~m/s^2)~cos~30^{\circ}$ $F_N = 152.8~N$ The normal force is $152.8~N$ Since the crate is not moving, the force of static friction is exerted on the crate and it is directed up the ramp. The force of static friction $F_f$ exerted on the crate is equal in magnitude to the component of the crate's weight directed down the ramp. $F_f = mg~sin~\theta$ $F_f = (18.0~kg)(9.80~m/s^2)~sin~30^{\circ}$ $F_f = 88.2~N$ The magnitude of the force of static friction exerted on the crate is $88.2~N$ and this force is directed up the ramp at an angle of $30^{\circ}$ to the horizontal.
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