The \"Giant Swing\" at a county fair consists of a vertical central shaft with a

Question

The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. (See the figure http://session.masteringphysics.com/problemAsset/1260042/2/YF-05-57.jpg) Each arm supports a seat suspended from a 5.00m -long cable, the upper end of which is fastened to the arm at a point 3.00m from the central shaft.



1. Find the time of one revolution of the swing if the cable supporting the seat makes an angle of 30 with the vertical.

2. Does the angle depend on the weight of the passenger for a given rate of revolution?
Does the angle depend on the weight of the passenger for a given rate of revolution?
A. Yes
B. No

Explanation / Answer

The radius is the distance from the person to the point rotation. Radius,r = 5 sin30 + 3.00m = 5.5 m The centripetal force is actually caused by the horizontal tension in the 5.00m cable. Centripetal force,F = T sin 30 (mv^2) / r = T sin 30 -------------(1) where, m = mass of person + seat v = tangential velocity r = radius The weight of the person and seat are balanced by the vertical tension in the 5.00m cable. mg = T cos 30 ----------------(2) Combine both equation (1) / (2), tan 30 = v^2 / rg v^2 = rg tan30 = 31.12 v = 5.57846m/s v = rW , where W is the angular velocity 5.57846 = (5.5)(W) W = 1.0143 rad/s 2(pi)(f) = W, where f is the frequency f = 0.16143 1/T = f , where T is the period. T = 1/f = 6.2s

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