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
Answer:
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