Chapter 2.6, Problem 70ES

The force $F$ (in pounds) acting at an angle $\theta$ with the horizontal that is needed to drag a crate weighing $W$ pounds along a horizontal surface at a constant velocity is given by

$F=\frac{\mu W}{\cos \theta +\mu \sin \theta }$

Where $\mu$ is a constant called the coefficient of sliding friction between the crate and the surface (see the accompanying figure). Suppose that the crate weighs $150\text{ lb}$ and that $\mu =\mathrm{0.3.}$

(a) Find $dF/d\theta$ when $\theta =30°$ if $\theta$ is decreasing at the rate of $0.5°\text{/s}$ at this instant.