Chapter 12, Problem 51P

You’re investigating ladder safety for the Consumer Product Safety Commission. Your test case is a uniform ladder of mass m leaning against a frictionless vertical wall with which it makes an angle θ. The coefficient of static friction at the floor is μ. Your job is to find an expression for the maximum mass of a person who can climb to the top of the ladder without its slipping. With that result, you’re to show that anyone can climb to the top if μ ≥ tan θ land but that no one can if $\mu <\frac{1}{2}\tan \theta$.