An 80-lb child is sitting on a swing suspended by a rope that passes over a tree branch as shown. The coefficient of friction between the rope and the branch is 0.5, and the weight of the rope can be ignored. Determine the minimum force that must be applied to the other end of the rope to keep the child suspended.

Suppose the child is holding the other end of the rope as shown in the righthand side figure. Determine the minimum force he must exert on the rope to keep himself suspended.