Question

A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion? ( type in your answer with no units in form xx0)

Answer 1

The apparent weight of the person as she pass the highest point is
`N = 458.8 \ N`

Step-by-step explanation:

From the question we are told that

The radius of the Ferris wheel is
`r = 5.0 \ m`

The period of revolution is
`T = 8.0 \ s`

The weight of the person is
`W = 670 \ N`

Generally the speed of the wheel is mathematically represented as

`v = (2 \pi r)/(T )`

substituting values

`v = (2 * 3.142 * 5)/(8 )`

`v = 3.9 3 \ m/s`

The apparent weight (the normal force exerted on her by the bench) at the highest point is mathematically evaluated as

`N = mg - (mv^2)/(r)`

Where m is the mass of the person which is mathematically evaluated as

`m = (W)/(g)`

substituting values

`m = (670)/(9.8)`

`m = 68.37 \ kg`

So

`N = 68.37 * 9.8 - \frac{68.37 * {3.93}^2}{5}`

`N = 458.8 \ N`