Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 32

32 In Fig. 12-36, a 55 kg rock climber is in a lie-back climb along a fissure, with hands pulling on one side of the fissure and feet pressed against the opposite side. The fissure has width $w = 0.20 \text{ m}$, and the center of mass of the climber is a horizontal distance $d = 0.40 \text{ m}$ from the fissure. The coefficient of static friction between hands and rock is $\mu_1 = 0.45$, and between boots and rock it is $\mu_2 = 1.2$. (a) What is the least horizontal pull by the hands and push by the feet that will keep the climber stable? (b) For the horizontal pull of (a), what must be the vertical distance $h$ between hands and feet? If the climber encounters wet rock, so that $\mu_1$ and $\mu_2$ are reduced, what happens to (c) the answer to (a) and (d) the answer to (b)?