Question

Unlike a roller coaster, the seats in a Ferris wheel swivel so that the rider is always seated upright. An 80-ft-diameter Ferris wheel rotates once every 24 s.

What is the apparent weight of a 60 kg passenger at the lowest point of the circle?

What is the apparent weight of a 60 kg passenger at the highest point of the circle?

Answer 1

Part A.

At the lowest point of the circle:

Using Force balance on passenger:

Fnet = N - W = Fc

N = Normal force direct upwards

W = Weight of person directed downwards

Fc = Centripetal force upwards = m*V^2/R

V = w*R = 2*pi*f*R

Fc = m*(2*pi*f)^2*R

f = frequency of roller coaster = 1/24 = 0.042 Hz

R = radius of wheel = diameter/2 = 80/2 = 40 ft = 12.19 m

Since 1 ft = 0.3048 m

m = mass of passenger = 60 kg

So,

N = Fc + W

N = m*(2*pi*f)^2*R + m*g

Using known values:

N = 60*(2*pi*0.042)^2*12.19 + 60*9.81

N = apparent weight = 639.5 N

Part B.

When passenger is at the highest point

Using Force balance on passenger:

Fnet = -N - W = Fc

N = Normal force direct downwards

W = Weight of person directed downwards

Fc = Centripetal force downwards

N = Fc - W

N = m*(2*pi*f)^2*R - m*g

Using known values:

N = 60*(2*pi*0.042)^2*12.19 - 60*9.81

N = -537.7 N

Apparent weight = 537.7 N

Please Upvote.

N = apparent weight = 639.5 N