Question: 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

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 \(150 \mathrm{lb}\) and that \(\mu=0.3\)

1. Find \(d F / d \theta\) when \(\theta=30^{\circ}\). Express the answer in units of pounds/degree.
2. Find \(d F / d t\) when \(\theta=30^{\circ}\) if \(\theta\) is decreasing at the rate of \(0.5 \% / \mathrm{s}\) at this instant.

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