Walker, Halliday & Resnick — Force and Motion-II: Problem 14

14 Figure 6-20 shows the cross section of a road cut into the side of a mountain. The solid line AA' represents a weak bedding plane along which sliding is possible. Block B directly above the highway is separated from uphill rock by a large crack (called a joint), so that only friction between the block and the bedding plane prevents sliding. The mass of the block is \(1.5 \times 10^7 \text{ kg}\), the dip angle \(\theta\) of the bedding plane is \(24^{\circ}\), and the coefficient of static friction between block and plane is \(0.63\). (a) Show that the block will not slide under these circumstances. (b) Next, water seeps into the joint and expands upon freezing, exerting on the block a force \(\vec{F}\) parallel to AA'. What minimum value of force magnitude \(F\) will trigger a slide down the plane?