Harmonic Motion physics problem

Question

After a hard day at school Mr. Wellman swings on a swing so that his center of mass is located 2.4 m from the point where the rope is attached to the tree. If he swings so that his maximum amplitude causes the rope to make an angle of 47° with the vertical, calculate the Mr. Wellman’s maximum speed during the swing.

Answer 1

A swinging mass always balances its kinetic and potential energies

mv²/2 = mgh,

where v is its speed and (after drawing a careful diagram)

h = (1 – cosθ)r

is its height. Therefore the maximum speed can be found by solving the energy-balance equation using maximum height:

v = √(2gh)

= √(2(1 – cosθ)gr),

which involves 3 parameters whose values you know.