Question

Christine, with mass m rides on a Ferris wheel

as shown in the figure. Christine moves in a

vertical circle of radius 10.0m with constant

speed of 3.00 m/s. Determine the force exerted

by the seat on Christine at the bottom of the

ride. Express your answer in terms of weight of

Christine, mg

Answer 1

The centripetal force is

$$F_c=m\frac{v^2}{R}.$$

The weight is

$$F_g=mg.$$

The normal force is

$$N=F_c+F_g=\\\space\\ =m\bigg(g+\frac{v^2}{R}\bigg).$$

Expressed terms of weight of Christine, mg, it is

$$N_{mg}=\bigg[\frac{N}{mg}\bigg]=\bigg[1+\frac{v^2}{gr}\bigg]mg=1.09mg.$$