How fast is the person moving at this moment ?

Question

A 67.6 kg person is riding on a Ferris wheel that has a diameter of 46.6m. When passing through the top of the Ferris wheel, the seat exerts a force of 412.4 N on the person. How fast is the person moving at this moment ?

Answer 1

m = mass of person in kg

g = 9.8 m/s²

d = diameter of wheel in meters

r = radius of wheel = d/2

N = upward normal force of seat on person in newtons

At the top, the net downward force on the person must equal the centripetal force on the person.

mg - N = mv²/r

mg - N = mv²(2/d)

(d/2)(mg - N) = mv²

v = √[(d/2)(g - N/m)]

Plug in the numbers and get v in m/s.