Question

. A ride at a county fair spins in a circle of radius (in meters). The centripetal force experienced by one of the passengers on the ride is modeled by the equation below, where is the number of seconds the ride takes to complete one revolution and is the mass (in kilograms) of the passenger. Tom, whose mass is kilograms is on a ride that is spinning in a circle at a rate of seconds per revolution. The radius of the circle is meters. Letting , how much centripetal force does Tom experience

Answer 1

150 Newtons

Explanation:

Given

`t = \sqrt{(4\pi^2mr)/(F)}`

`t = 12`

`r =6.5`

`\pi = 3.14`

`m = 84.4`

See attachment

Required

Find F

We have:

`t = \sqrt{(4\pi^2mr)/(F)}`

Square both sides

`t^2 = (4\pi^2mr)/(F)`

Multiply both sides by F

`Ft^2 = 4\pi^2mr`

Divide both sides by
`t^2`

`F = (4\pi^2mr)/(t^2)`

Substitute known values

`F = (4*3.14^2*84.4*6.5)/(12^2)`

`F = (21635.90624)/(144)`

`F = 150.249348889`

`F = 150N`