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(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)))