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

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skyluke89 skyluke89 · Answer 1 · 2019-11-04T04:20:45+01:00

Answer:

N > mg

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

[tex]N-mg=m\frac{v^2}{r}[/tex]

where

[tex]m\frac{v^2}{r}[/tex] 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,

[tex]N=mg+m\frac{v^2}{r}[/tex]

We can notice that the term [tex]m\frac{v^2}{r}[/tex] is always positive, therefore we have

[tex]N>mg[/tex]

So, the normal force is larger than the weight.