Halliday, Resnick & Walker — Force and Motion–II: Problem 30_M_CALC

A toy chest and its contents have a combined weight of 180 N. The coefficient of static friction between toy chest and floor is 0.42. The child in Fig. 6.24 attempts to move the chest across the floor by pulling on an attached rope. (a) If \(\theta\) is 42°, what is the magnitude of the force \(\vec{F}\) that the child must exert on the rope to put the chest on the verge of sliding? (b) Write an expression for the magnitude \(F\) required to put the chest on the verge of sliding as a function of the angle \(\theta\). Determine (c) the value of \(\theta\) for which \(F\) is a minimum and (d) that minimum magnitude.