A box with weight w is pulled at constant speed along a level floor by a force that is at an angle θ above the horizontal. The coefficient of kinetic friction between the floor and box is μ_k.

(a) In terms of θ, μ_k, and w, calculate F.

(b) For w = 400 N and μ_k = 0.25, calculate F for θ ranging from 0º to 90º in increments of 10º. Graph F versus θ.

(c) From the general expression in part (a), calculate the value of θ for which the value of F, required to maintain constant speed, is a minimum.