Serway & Jewett — Static Equilibrium and Elasticity: Problem 14

A 10.0-kg monkey climbs a uniform ladder with weight \(1.20 \times 10^2\text{ N}\) and length \(L = 3.00\text{ m}\) as shown in Figure P12.14. The ladder rests against the wall and makes an angle of \(\theta = 60.0^\circ\) with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N. (a) Draw a force diagram for the ladder. (b) Find the normal force exerted on the bottom of the ladder. (c) Find the tension in the rope when the monkey is two-thirds of the way up the ladder. (d) Find the maximum distance d that the monkey can climb up the ladder before the rope breaks. (e) If the horizontal surface were rough and the rope were removed, how would your analysis of the problem change? What other information would you need to answer parts (c) and (d)?