Question

5-2) Consider a Ferris wheel that is 100m in diameter and which rotates once every 60 seconds. a) b) Find the (tangential) speed of a passenger If said passenger has a weight of 880 N, what will be his apparent weight at the top of the wheel? What will be his apparent weight at the bottom of the wheel? In what time would the wheel need to rotate once (the period) if the passenger's apparent weight at the top were to be zero? c) d) HINT: What does the question mean by 'apparent weight? What is the question actually asking for?

Answer 1

Radius of ferris wheel, r = D / 2

r = 50 m

Angular speed , w = 2*pi / T

w = 2*3.14 / 60 = 0.1047 rad/s

(a)

Tangential speed, v = wr

v = 0.1047*50

v = 5.23 m/s

(b)

Centripetal force, F = mw^2*r

here, m = 880 / 9.8 = 89.7 kg

F = 89.7*( 0.1047)^2*50 = 49.16 N

apparent weight at the top of the wheel,

Fa = W - F

Fa = 880 - 49.16

Fa = 831 N

(c)

apparent weight at the bottom of the wheel,

Fa = W + F

Fa = 880 + 49.16

Fa = 929 N

(d)

Time period of the person,

T = 2*pi*sqrt (r / g)

T = 2*pi*sqrt(50 / 9.8)

T = 14.2 s