Chapter 4.1, Problem 58E

An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle θ with the plane, then the magnitude of the force is

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

where μ is a positive constant called the coefficient of friction and where 0 ≤ θ ≤ π/2. Show that F is minimized when tan θ = μ.