A 23.0 kg child plays on a swing having support ropes that are 2.30 m long. A fr

Question

A 23.0 kg child plays on a swing having support ropes that are 2.30 m long. A friend pulls her back until the ropes are 45.0 from the vertical and releases her from rest.

PART A:What is the potential energy for the child just as she is released, compared with the potential energy at the bottom of the swing? U =? J

PART B:How fast will she be moving at the bottom of the swing? V=? m/s

PART C:How much work does the tension in the ropes do as the child swings from the initial position to the bottom? W=? J

Explanation / Answer

As she moves from her initial height to her lowest height, her potential energy decreases as her kinetic energy decreases.

Change of PE = mass * g * height
height = length of cord – length of cord * cos
height = 2.3 – 2.3 * cos 45

Change of PE = 23 * 9.8 * (2.3 – 2.3 * cos 45)
This is her initial potential energy.

Change of KE = ½ * mass * (vf^2 – vi^2), vi = 0 m/s
Change of KE = ½ * mass * vf^2 = ½ * 23 * vf^2

Change of KE = Change of PE
½ * 23 * vf^2 = 23 * 9.8 * (2.3 – 2.3 * cos 45)
solve for the final velocity vf

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