Question

illustrates a method for solving this problem. A "swing" ride at a carnival consists of chairs that are swung in a circle by 19.6 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 250 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair.

Answer 1

Explanation:

Given that,

Length of the cable is 19.6 m, l = 19.6 m

Let us assume that the angle with vertical rotating pole is 63 degrees.

The total mass of a chair and its occupant is 250 kg.

(a) Let T is the tension in the cable attached to the chair. So,

$T\cos\theta=mg\\\\T=\dfrac{mg}{\cos\theta}\\\\T=\dfrac{250\times 9.8}{\cos(63)}\\\\T=5396.58\ N$

(b) The centripetal acceleration acts on it such that,

$\dfrac{v^2}{r}=g\tan\theta\\\\v=\sqrt{Rg\tan\theta} \\\\v=\sqrt{l\sin\theta g\tan\theta}\\\\v=\sqrt{19.6\times \sin(63)9.8\times \tan(63)}\\\\v=18.32\ m/s$

Hence, this is the required solution.