(Like 5.50, but symbolic) The \"Giant Swing\" at a county fair consists of a ver
ID: 583516 • Letter: #
Question
(Like 5.50, but symbolic) 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 of length L2 and the upper end of the cable is fastened to the arm at a point L1 from the central shaft. As a result of the uniform circular motion, the cable makes an angle of 0 from the vertical. Find an expression for the speed v in terms of L1, L2, theta, the rider's mass m, and/or the acceleration due to gravity g.Explanation / Answer
here,
let the tension in the cable be t
equatig the forces vertically
t * cos(theta) = m*g .....(1)
and equating the forces horizontally
t * sin(theta) = m * v^2 /(L1 + L2 *sin(theta)) ......(2)
from equation (1) and (2)
tan(theta) = v^2 / g(L1 + L2 *sin(theta)
v = sqrt(g * tan(theta) *(L1 + L2 *(sin(theta)))
the expression for v is
v = sqrt(g * tan(theta) *(L1 + L2 *(sin(theta)))
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