Question

A 5m rope is tied to a tree limb and used as a swing. Tarzan holds the rope in horizontal orientation. Assuming that the frictional force is zero and there is no air resistance, determine the speed of Tarzan at the lowest point on the circular arc of the swing. Show complete solution.

Answer 1

The law of conservation of energy says

$$\frac{mv_1^2}{2}=\frac{mv_2^2}{2}+mgh$$

The velocity of Tarzan at the highest point satisfies Newton's second law

$$\frac{mv_2^2}{R}=mg$$

Hence

$$\frac{mv_1^2}{2}=\frac{mgR}{2}+mg2R$$

$$v_1^2=5gR$$

$$v_1=\sqrt{5gR}=\sqrt{5*9.8*5}=15.7\:\rm m/s$$