Question

A 38 kg child on a 1.4 m long swing is released
from rest when the swing supports make an
angle of 21.2 with the vertical.
The acceleration of gravity is 9.81 m/s2 .
a) What is the maximum potential energy
associated with the child?
Answer in units of J

Answer 1

Let's make following denominations:

α = 21.2°
L = 1.4 m
M = 38 kg

Now let's find the height a child moved up:

H = L*cosα = 1.4*cos(21.2) ≈ 1.3053 m.

So, the maximum potential energy of a child is

E = MgH = 38*9.81*1.3053 = 486.5723 J.