Question

A Ferris wheel has diameter of 10 m and makes one revolution in 8.0 seconds. A woman weighing 670 N is sitting on one of the benches attached at the rim of the wheel. What is the net force on this woman as she passes through the highest point of her motion?

Answer 1

208 N

Step-by-step explanation:

The net force on the woman is equal to the centripetal force, which is given by

`F=m(v^2)/(r)`

where

m is the mass of the woman

v is her speed

r is the radius of the wheel

here we have:

r = d/2 = 5 m is the radius of the wheel

`m=(W)/(g)=(670 N)/(9.8 m/s^2)=68.4 kg` is the mass of the woman (equal to her weight divided by the acceleration of gravity)

The wheel makes one revolution in t=8.0 s, so the speed is:

`v=(2\pi r)/(t)=(2\pi (5.0 m))/(8.0 s)=3.9 m/s`

so now we can find the centripetal force:

`F=(68.4 kg)((3.9 m/s)^2)/(5.0 m)=208 N`