Question

A child with a weight of 230 N swings on a playground swing attached to 2.20-m-long chains. What is the gravitational potential energy of the child-Earth system relative to the child's lowest position at the following times?

(a) when the chains are horizontal (in J)
(b) when the chains make an angle of 33.0° with respect to the vertical (in J)
(c) when the child is at his lowest position (in J)

Answer 1

a) U = 506 J, b) U = 37.11 J, c) U = 0

Step-by-step explanation:

The gravitational power energy is given by the expression

U = m g (y -y₀)

In general, a reference system is set that allows the expression to be simplified, in this case let's assume the reference system at the child's lowest point, therefore y₀ = 0

Let's use trigonometry to find the child's height

h = y = L - L cos θ

we substitute

U = m g L (1 - cos θ)

a) when the chain is horizontal θ = 90 and cos 90 = 0

U = mg L

weight and mass are related

W = mg

m = W / g

U = 230 2.20

U = 506 J

b) θ = 33.0º

cos 33 = 0.83867

U = 230 (1 - 0.83867)

U = 37.11 J

c) in this case θ = 0 cos 0 = 1

U = 0