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

Answers ( )

    0
    2021-08-29T20:19:57+00:00

    Answer:

    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

    0
    2021-08-29T20:19:59+00:00

    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

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