Potential energy?

Question

A 36 Kg child is in a swing that is attached to ropes 2.10 m long. The acceleration of gravity is 9.81 m/s^2. Find the gravitational potential energy associated with the child relative to the child's lowest position under the following conditions:

a) when the ropes are horizontak
b) when the ropes make a 32.0 angle with the vertical
c) at the bottom of the circular arc

Yes- I did attempt the problem, i just can't figure it out

Answer 1

I looked for the unit of measurement and could not find one

In principle the potential energy is mass x height

When the swing is parallel 36kg x2.1 meters = 75.6 kg/m
the unit is wrong but your book should have it

c. the swing can go no lower so the potential energy is zero.

b) the height at 32 degrees would be 2.1 x cosine 32 degrees potential energy 36 kg x 2.1 meters x cos 32
l

Answer 2

The gravitational potential energy is m*g*h, where h is the height above the reference level (lowest swing position). The problem boils down to finding h for each condition. It helps to draw a diagram to determine this. In part a), h = length of the rope L. (Only the vertical distance matters.) For part b) use trigonometry; h should come out L*cos(32º). For part c), h = 0.

EDIT: If m is kg, h is meters, and g = 9.8 meter/sec^2, the energy is in joules.