Question

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?

Answer 1

Answer:$\theta =44.068^{\circ}$

Explanation:

Given

time taken to complete the circle=7.9 s

radius of circle(r)=15 m

velocity of rider is given by $=\frac{2\pi r}{t}$

$v=\frac{2\pi 15}{7.9}=11.93 m/s$

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

Therefore $T\sin \theta =\frac{mv^2}{r}-1$

$T\cos \theta=mg$ --2

Divide 1 & 2 we get

$tan\theta =\frac{v^2}{rg}$

$tan\theta =0.968$

$\theta =44.068^{\circ}$