Question

Asked Jan 22, 2020

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The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 5.00 m long, the upper end of the cable being fastened to the arm at a point 3.00 m from the central shaft. (Figure 1)

Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 30.0∘ with the vertical.

Step 1

Consider the angular speed of the swing be *ω*, the length of the arm be *R*, the length of the cable be *L*, the radius of the circular path of the swing be *r*, the tension in the cable be *T*, the mass of the passenger at swing be *m*, the acceleration of the swing be *a*, and time period be *t*.

The radius of the circular path of the swing can be calculated as,

Step 2

The free-body diagram of the passenger on the swing is,

Step 3

From the free-body diagram, the horizontal component of the tension...

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