## A child with a weight of 230 N swings on a playground swing attached to 1.90 m long chains. What is the gravitational potential energy (in J

Question

A child with a weight of 230 N swings on a playground swing attached to 1.90 m long chains. What is the gravitational potential energy (in J) of the child-earth system relative to the child’s lowest position at the following times?

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1 year 2021-08-29T20:18:48+00:00 2 Answers 0 views 0

437 J

Explanation:

Parameters given:

Weight of child, W = 230 N

Height of swing, h = 1.9 m

Gravitational Potential Energy is given as:

P. E. = m*g*h = W*h

m = mass

h = height above the ground

W = weight

P. E. = 230 * 1.9

P. E. = 437 J

2. The question is incomplete! The complete question along with answers and explanation is provided below!

Question:

A child with a weight of 230 N swings on a playground swing attached to 1.90 m long chains. What is the gravitational potential energy (in J) of the child-earth system relative to the child’s lowest position at the following times?

(a)when the ropes are horizontal

(b) when the ropes make a 25.0° angle with the vertical

(c) when the child is at the bottom of the circular arc

Given Information:

Weight = W = 230 N

Length of rope = L = 1.90 m

Required Information:

a) Gravitational potential energy when the ropes are horizontal  = ?

(b) Gravitational potential energy when the ropes make a 25.0° angle with the vertical   = ?

(c) Gravitational potential energy when the child is at the bottom of the circular arc

a)   GPE = 437 J

(b)  GPE = 41.07 J

(c)
GPE = 0 J

Explanation:

As we know, gravitational potential energy is given by

GPE = mgh

Where mg = W and h = L(1 – cosθ)

a) Gravitational potential energy when the ropes are horizontal  = ?

In this case, the ropes are perpendicular with respect to vertical therefore, the angle θ is 90°

GPE = 230*1.90(1 – cos(90°))

GPE = 230*1.90(1 – 0)

GPE = 437 J

(b) Gravitational potential energy when the ropes make a 25.0° angle with the vertical   = ?

In this case, the ropes are at 25° with respect to vertical therefore, the angle θ is 25°

GPE = 230*1.90(1 – cos(25°))

GPE = 437(1 – 0.906)

GPE = 41.07 J

(c) Gravitational potential energy when the child is at the bottom of the circular arc

In this case, the ropes are aligned with respect to vertical therefore, the angle θ is 0°

GPE = 230*1.90(1 – cos(0°))

GPE = 437(1 – 1)

GPE = 437(0)

GPE = 0 J