Question

(a) As you ride on a Ferris wheel, your apparent weight is different at the top and at the bottom. Explain. (b) Calculate your apparent weight at the top and bottom of a Ferris wheel, given that the radius of the wheel is 7.2 m, it completes one revolution every 28 seconds, and your mass is 55 kg.

Answer 1

Answer:

a. The component of the net force which make up the apparent weight are added to each other at the bottom and subtracted (the centripetal force from the weight) at the top)

b. Apparent weight at the top is approximately 519.06 N

Apparent weight at the bottom is approximately 558.94 N

Explanation:

a. The apparent weight at the top is different from the apparent weight at the bottom of a moving Ferris wheel because of the opposite direction in which the centripetal force acts at the top and the bottom, which are upwards and downwards respectively, while the weight acts downwards constantly

b. The given parameters are

The radius of the Ferris wheel, r = 7.2 m

The period for one complete revolution, t = 28 seconds

The angle covered in one revolution, θ = 2·π radian

The mass of the person riding on the Ferris wheel, the passenger  = 55 kg

Therefore, we have;

The angular speed, ω = Δθ/Δt = 2·π/(28)

From which we have;

Centripetal force, $F_c$ = m × ω² × r

Substituting the known values, we have $F_c$ = 55 kg × (2·π/(28 s))² × 7.2 m ≈ 19.94 N

The centripetal force, $F_c$ = 19.94 N always acting outward from the center

Weight = Mass × Acceleration due to gravity

The weight of the passenger = 55 kg × 9.8 m/s² = 539 N

The weight of the passenger = 539 N always acting downwards

At the top of the Ferris wheel the the centripetal force is acting upwards and the weight is acting downwards

Therefore;

The net force, which is the apparent weight of the passenger at the top $F_{NET_{Top}}$ = 539 N - 19.94 N ≈ 519.06 N

Apparent weight at the top ≈ 519.06 N

At the bottom of the Ferris wheel the weight is acting downwards and the centripetal force is also acting downwards

Therefore;

The net force at the bottom, which is the apparent weight of the passenger at the bottom $F_{NET_{bottom}}$ = 539 N + 19.94 N ≈ 558.94 N

Apparent weight at the bottom ≈ 558.94 N.