The Cosmoclock 21 Ferris wheel in Yokohama City, Japan, has a diameter of 100 m.

Question

The Cosmoclock 21 Ferris wheel in Yokohama City, Japan, has a diameter of 100 m. Its name comes from its 60 arms, each of which can function as a second hand (so that it makes one revolution every 60.0 s).

(a) Find the speed of the passengers when the Ferris wheel is rotating at this rate.
  m/s ?

(b) A passenger weighs 721 N at the weight-guessing booth on the ground. What is his apparent weight at the highest point on the Ferris wheel?
N ?

What is his apparent weight at the lowest point on the Ferris wheel?
N?
(c) What would be the time for one revolution if the passenger's apparent weight at the highest point were zero?
s?

(d) What then would be the passenger's apparent weight at the lowest point?

Explanation / Answer

a) speed = angular velocity x radius

angular velocity, w = 2pi / T = 2pi / 60 = 0.105 rad/s

v = 0.105 x (100/2) = 5.24 m/s

b) mg = 721 N

m = (721 / 9.81) = 73.50 kg

at highest point,

mg - N = mv^2 / R

N = mg - mv^2/R   = 721 - (73.50 x 5.24^2 / 50)

N = 680.67 N

at lowest point,

N - mg = m v^2 / R

N = mg + mv^2/R = 721 + (73.50 x 5.24^2 / 50)

N = 761.40 N

c) at highest point,

N = mg - mv^2/R = 0

g = v^2 / R

v = sqrt(9.81 x 50) = 22.15 m/s

T = 2piR / v = (2 x pi x 50) / 22.15

T = 14.18 s

d) N = mg + mv^2 /R

N = 721 + 73.50(22.15^2/50)

N = 1442 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.