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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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

the answer is mosques. they are an important part of islamic culture.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards