A 24.0 kg child plays on a swing having support ropes that are 1.90 m long. A fr

Question

A 24.0 kg child plays on a swing having support ropes that are 1.90 m long. A friend pulls her back until the ropes are 39.0 from the vertical and releases her from rest.

What is the potential energy for the child just as she is released, compared with the potential energy at the bottom of the swing?

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Part B

How fast will she be moving at the bottom of the swing?

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Part C

How much work does the tension in the ropes do as the child swings from the initial position to the bottom?

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Explanation / Answer

Given,

Mass, m = 24 kg

Length, l = 1.90 m

Part A)

PE = mgh

With a 1.90 m long rope, when up at a 39 degree angle, it forms a triangle with sides of 1.9 x cos39 = 1.48 m long.

Therefore the child will be 1.9 - 1.48 m = 0.423 m above the lowest point of the swing, which is the height.

PE = (24) x (9.8)(0.423) = 99.59 J

Part B)

From law of conservation of energy

KE = PE

0.5mv^2 = mgh

v = sqrt[(2)(9.8)(0.423)]

v = 2.88 m/s

Part C)

Work done by rope will be zero.

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