Halliday, Resnick & Walker — Force and Motion–II: Problem 98_BIO

Rock climbing chalk. Many rock climbers, whether outdoors or in a gym, periodically dip their fingers into a chalk bag hanging from the back of their belt to coat their fingers (Fig. 6.51a). (The chalk is magnesium carbonate, not classroom chalk.) Climbers claim that the chalk dries their fingers from sweat, allowing better grips on the holds but other climbers doubt that effect. In a research experiment, experienced climbers supported their weight on a hang bar, something commonly used in training. However, this hang bar could be tilted (Fig. 6.51b). On its wood support, researchers attached a stone plate from which a climber would hang by one hand, and then the researchers increased the tilt angle \(\theta\) until the climber slipped off. From the slip angle \(\theta_{\text{slip}}\) we can calculate the coefficient of static friction \(\mu_s\) between the fingers and the stone plate. What is \(\mu_s\) for limestone when \(\theta_{\text{slip}}\) is (a) \(32.6^\circ\) for unchalked fingers and (b) \(37.2^\circ\) for chalked fingers? What is \(\mu_s\) for sandstone when \(\theta_{\text{slip}}\) is (c) \(36.5^\circ\) for unchalked fingers and (d) \(41.9^\circ\) for chalked fingers?