Chapter 4.3, Problem 39E

A woman pulls a sled which, together with its load, has a mass of m kg. If her arm makes an angle of θ with her body (assumed vertical) and the coefficient of friction (a positive constant) is μ, the least force, F, she must exert to move the sled is given by

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

If μ = 0.15, find the maximum and minimum values of F for 0 ≤ θ ≤ π/2. Give answers as multiples of mg.