Problem 7-51 Energy cons. - Part 2 - A

A boy is playing with a rope tied to a tree near his favourite swimming hole. Initially the boy is stationary and the rope (of length \(3.7 \;m\)) makes an angle of \(48^\circ\) with the vertical. He then lifts his feet slightly and starts to swing freely. If air resistance is neglected, use conservation of energy to determine:

(a) his speed at the bottom of the swing
(b) the minimum height, relative to his initial position, to which he can swing.

Diagram of a tree on the edge of a cliff with water below. A rope hangs from a branch hanging over the water.

Accumulated Solution

Diagram of angle of rope

At point 2, \(E_P = 0\)

Correct.

At point 2, \(E_P = 0\)

What is the kinetic energy \(E_K\) at point 2?

(A)   \(0\)

(B)   \(mgh\)

(C)   \((1/2)mv^2\)