Question

You are on a Ferris wheel moving in a vertical circle. When you are at the bottom of the circle, how does the magnitude of the normal force n exerted by your seat compare to your weight mg? n = m g n > m g , but cannot be exactly calculated without more information. n < m g , but cannot be exactly calculated without more information. n = m g / 2 n = 2 m g SSM

Answer 1

N > mg

Step-by-step explanation:

When we are at the bottom of the circle, there are two forces acting on the passenger:

- The normal force, N, upward

- The weight of the passenger (+ the cabin), mg, downward

So, the equation of the forces is

`N-mg=m(v^2)/(r)`

where

`m(v^2)/(r)` is the centripetal force, which points towards the centre of the wheel, so upward (as the normal force)

m is the mass

v is the speed

r is the radius of the wheel

Re-arranging the equation,

`N=mg+m(v^2)/(r)`

We can notice that the term
`m(v^2)/(r)` is always positive, therefore we have

`N>mg`

So, the normal force is larger than the weight.