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 s).

A passenger weights 702 N at the weight guessing booth on the ground. What is his apparent weight at the highest point on the ferris wheel?

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

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

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

Explanation / Answer

= 1rev/60s * 2 rad/rev = 0.1 rad/s angular velocity
v = r = 0.1rad/s * 50m = 5.2 m/s tangential velocity, (A)

(B) m = 702N / 9.8m/s² = 71.63 kg
a = ²r = (0.1 rad/s)² * 50m = 0.55 m/s²
At the lowest point, apparent W = ma = 71.63kg * (9.8 + 0.55)m/s² = 741.37 N

(C) At the highest point, apparent W = ma = 71.63kg * (9.8 - 0.55)m/s² = 662.6 N

(D) for the apparent weight to = 0, centripetal accel = g
²r = ² * 50m = 9.8m/s²
= sqrt(9.8/50s) = 0.44 rad/s
T = 2/ = 14.2 s

(E) If accel = 0 at top, then accel = 2g at bottom:
apparent weight = 71.63kg * (2 * 9.8m/s²) = 1403 N

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