1. Two boards are bolted together with two bolts, as shown. The squeeze force between the boards is 500 lbs. If the shear strength of each bolt is 5000 lbs and the coefficient of static friction between the boards is μs = 0.5, what is the maximum force F that can be applied to the boards and not pull them apart?
2. Two children throw a rope over a tree branch and hang off each end. The children have a mass of 40 kg and 50 kg. What is the minimum coefficient of static friction between rope and tree branch so that the rope doesn't slip? To solve this consider the general equation T2 = T1eμθ, where T1 and T2 are the rope tensions on the two ends (with T2 > T1), μ is the coefficient of static friction between rope and tree branch, and θ is the angle of contact between rope and branch, in radians. For example, if the rope wraps completely around the branch then the angle θ = 2π.