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).

Part A

Find the speed of the passengers when the Ferris wheel is rotating at this rate.

Part B

A passenger weighs 882 N at the weight-guessing booth on the ground. What is his apparent weight at the lowest point on the Ferris wheel?

Part C

What is his apparent weight at the highest point on the Ferris wheel?

Part D

What would be the time for one revolution if the passenger's apparent weight at the highest point were zero?

Part E

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

Explanation / Answer

A)Speed of passenger v = r = (2rads / 60s) * (100m / 2) = 5.24 m/s

B) mass of passenger =weight/gravity =(m*g)/g =882/9.81 =89.908kg

F = m(g + a) = m(g + v²/r) = 89.908 *(9.8m/s² + (5.24)² / 50m) = 931.37N

C) F = m(g - a) = 89.908*(9.81-5.24^2/50) =832.62N

D) F = 0 when g - a = 0, or g = ²r i.e acceleration due to gravity =centripetal acceleration
9.8 m/s² = ² * 50m
angular velocity = 0.443 rad/s
time for one revolution T = 2/ = 2 / 0.443rad/s = 14.2 s

E) If g - a = 0=>a=g, then g + a = 2g and apparent weight = 2 * 882N = 1764 N

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