Question

A box is dragged at constant speed across a surface with coefficient o kinetic riction Hint: The minimum force occurs when the dF/ds 0 and d2F/de2 >0. It is assential that you show all your wark. 1 the orce s app d at an angle 6 above horizontal, determine the ano e as a function of only uk that the applied force is at its minimum

Answer 1

Horizontal component of force is equal to kinetic friction because the box is moving with constant speed f cos theta = f F cos theta = mu_k mg F = mu_k mg sec theta tan theta dF/D Theta = 0 Rightarrow tan theta = 0 Rightarrow theta = 0 d62f/d theta 62 = mu_k mg (sec theta sec^2 + tan theta sec theta tan theta) when theta = 0 d^2 F/d theta^2 = mu_k mg > 0 so the force is minimum when theta = 0 minimum force, F = mu_k mg sec theta = mu_k mg sec theta F_n in = mu_k mg