A"swing" ride at a carnival consists of chairs that are swung in a circle by 10.1 m cables attached to a vertical rotating pole, as the drawing shows. suppose the total mass of a chair and its occupant is 164 kg. (a) determine the tension in the cable attached to the chair. (b) find the speed of the chair.

Missing picture: find it in attachment.

(a) 3214 N

To find the tension in the cable, we just need to analzye the forces along the vertical direction.

We have:

- The vertical component of the tension, which is , acting upward

- The weight of the passenger + the chair, mg, acting downward

Since there is equilibrium along this direction, we can write

where:

T is the magnitude of the tension

m = 164 kg is the total mass of the chair and the occupant

is the acceleration of gravity

Solving for T,

(b) 12.2 m/s

To find the speed of the car, we have to analyze the forces in the horizontal direction.

The component of the tension in the cable provides the centripetal force that keeps the chair in circular motion, so:

where

v is the speed

r is the radius of the circular path

We know that the length of the cable is

L = 10.1 m

So, the radius of the circle is

So now we can solve the equation to find v, the speed:

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