Question

In another version of the "Giant Swing" (see Exercise 5.50), the seat is connected to two cables, one of which is horizontal(Figure 1) . The seat swings in a horizontal circle at a rate of 28.0 rev/min. If the seat weighs 255 N and a 825-N person is sitting in it, find the tension in each cable.

Answer 1

Note => weighs = mass /g

$T= 60/28 sec\\ \omega =(2*\pi)/T$

so total mass = (255+825) * 9.8 Kg

suppose upper cables have tension T1 and lower cables have tension T2 then

vertical force balance

T1 *cos40 = 255+825

T1 = 1409.83 N

horizontal force balance

T1 *sin 40 + T2 = $m\omega^2*r$

$T_2 = {((255+825)/9.8)}*(2\pi/T)^2*7.50 -T_1sin(40)$

r= 7.50

then

T2=6199.893 N