A 20.0 kg child plays on a swing having support ropes that are 2.10 m long. A fr

Question

A 20.0 kg child plays on a swing having support ropes that are 2.10 m long. A friend pulls her back until the ropes are 43.0 from the vertical and releases her from the rest. 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? B. How fast will she be moving at the bottom of the swing? C. How much work does the tension in the ropes do as the child swings from the initial position to the bottom? A 20.0 kg child plays on a swing having support ropes that are 2.10 m long. A friend pulls her back until the ropes are 43.0 from the vertical and releases her from the rest. 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? B. How fast will she be moving at the bottom of the swing? C. How much work does the tension in the ropes do as the child swings from the initial position to the bottom? 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? B. How fast will she be moving at the bottom of the swing? C. How much work does the tension in the ropes do as the child swings from the initial position to the bottom?

Explanation / Answer

A) considering potential energy at bottom zero.

height of initial position = L ( 1 - cos@)

            = 2.10 (1 - cos43 ) = 0.564 m

PE = mgh = 20 x 9.8 x 0.564 = 110.57 J

B) Using energy conservation,

total energy at initial position (PE + KE) = energy at bottom

0 + 110.57 = m v^2 /2 + 0

v = sqrt(2 x 110.57 / 20) = 3.32 m/s

C) Tension is always perpendicular so work done by tension is zero.

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