Halliday, Resnick & Walker — Force and Motion–II: Problem 84

In Fig. 6.47, force \(\vec{F}\) is applied to a crate of mass \(m\) on a floor where the coefficient of static friction between crate and floor is \(\mu_s\). Angle \(\theta\) is initially \(0^{\circ}\) but is gradually increased so that the force vector rotates clockwise in the figure. During the rotation, the magnitude \(F\) of the force is continuously adjusted so that the crate is always on the verge of sliding. For \(\mu_s = 0.70\), (a) plot the ratio \(F/mg\) versus \(\theta\) and (b) determine the angle \(\theta_{\text{inf}}\) at which the ratio approaches an infinite value. (c) Does lubricating the floor increase or decrease \(\theta_{\text{inf}}\), or is the value unchanged? (d) What is \(\theta_{\text{inf}}\) for \(\mu_s = 0.60\)?