In the swing carousel amusement park ride, riders sit in chairs that are attached by a chain to a large rotating drum as shown in (figure 1). as the carousel turns, the riders move in a large circle with the chains tilted out from the vertical. in one such carousel, the riders move in a 15-m-radius circle and take 7.9 s to complete one revolution.

what is the angle of the chains, as measured from the vertical?

The angle the chains measures from the vertical is 44.1⁰.

The given parameters;

The vertical component of the tension on the rope;

The horizontal component of the tension on the chain;

The coefficient of friction is calculated as;

where;

is the centripetal acceleration of the riders

The velocity of the riders is calculated as;

The centripetal acceleration is calculated as;

The angle the chain measures from the vertical is calculated as;

Thus, the angle the chains measures from the vertical is 44.1⁰.

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Explanation:

Given

time taken to complete the circle=7.9 s

radius of circle(r)=15 m

velocity of rider is given by

Let us suppose T is the tension in the chain and is the angle which chain makes with vertical

Therefore

--2

Divide 1 & 2 we get