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.

Figure
1 of 1
3.00m
130.0°
5.00m
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Figure 1 of 1 3.00m 130.0° 5.00m

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Expert Answer

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,

Physics homework question answer, step 1, image 1
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Step 2

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

Physics homework question answer, step 2, image 1
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Step 3

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

Physics homework question answer, step 3, image 1
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Science

Physics

Angular Motion