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

Step-by-step 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=(mg)/(\cos\theta)\\\\T=(250* 9.8)/(\cos(63))\\\\T=5396.58\ N`

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

`(v^2)/(r)=g\tan\theta\\\\v=√(Rg\tan\theta) \\\\v=√(l\sin\theta g\tan\theta)\\\\v=√(19.6* \sin(63)9.8* \tan(63))\\\\v=18.32\ m/s`

Hence, this is the required solution.