Question

A 300-N child is in a swing that is attached to a pair of ropes 1.80 m long. Find the gravitational potential energy of the child–Earth system relative to the child's lowest position at the following times. (a) when the ropes are horizontal=_____ J
(b) when the ropes make a 31.0° angle with the vertical= ________J(c) when the child is at the bottom of the circular arc= _________J

Answer 1

Answer:

(a) 540 J

(b) 45.9 J

Explanation:

Weight of child, W = mg = 300 N

Length of rope, L = 1.80 m

(A) Gravitational potential energy when the ropes are horizontal

U = m x g x h = 300 x 1.80 = 540 J

(B) When the ropes make an angle of 31° with the vertical.

U = m x g x L (1 - Cos31°)

U = 300 x 1.8 x ( 1 - 0.915)

U = 45.9 J

Answer 2

Answer

given,

Weight of children = 300 N

length of rope = 1.8 m

mass of children = $\dfrac{300}{9.8}$

                            = 30.61 kg

a) potential energy of the child

     PE = m g h

     PE = 30.61 x 9.8 x 1.8

     PE = 539.96 J

b) When rope made angle of 31.0° with vertical

     PE = m g h(1 - cos θ)

     PE = 30.61 x 9.8 x 1.8(1 - cos 31°)

     PE = 30.61 x 9.8 x 1.8 x 0.1428

     PE = 77.12 J

c) When child is at bottom height will be zero

    hence, potential energy of the body will be zero.