Question

In the Vomitus carnival ride, passengers travel in a horizontal 4.0 m radius circle. For safe operation, the maximum sustained acceleration that riders may experience is 20 m/s2 , approximately twice the free fall acceleration. What is the period of the ride when it is being operated at the maximum acceleration?

Answer 1

The period of the ride when it is being operated at the maximum acceleration is T=2.81 s.

Step-by-step explanation:

We can use the centripetal acceleration here:

`a_(c)=(v^(2))/(R)=\omega^(2)R`

Let's find the angular velocity ω at the maximum acceleration.

`20=\omega^(2)*4`

`\omega=2.24 rad/s`

The period is given by:

`T=(2\pi)/(\omega)`

`T=(2\pi)/(2.24)`

Therefore, the period will be T=2.81 s.

I hope it helps you!