Problem 7-51 Energy cons. - Part 8 - 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 rope with angles and lengths indicated.

At point 2, \(E_P = 0\)

At point 2, \(E_K = (1/2)mv^2\)

\(h = 3.7(1 - \cos48) \;m = 1.22 \;m\)

E at point  \(1 = 0 + mgh\)

E at point  \(2 = (1/2)mv{_2}{^2} + 0\)

\(v_2 = 4.9 \;m/s\)    (answer to part (a))


He would rise to his original height.  (answer to part (b))


You have completed this problem.