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).
Part A: Find the speed of the passengers when the Ferris wheel is rotating at this rate (in m/s)
Part B: A passenger weighs 834 N at the weight-guessing booth on the ground. What is his apparent weight at the highest point of the Ferris wheel? (in N)
Part C: What is his apparent weight at the lowest point on the Ferris wheel?
Part D: What would be the time for one revolution if the passeger's apparent weight at the highest point were zero? (in s)
Part E: What then would be the passenger's apparent weight at the lowest point? (in N)

Answer 1

Answer:

Explanation:

A ) angular velocity ω = 2π / T

= 2 x 3.14 / 60

= .10467 rad / s

linear velocity v = ω R

=  .10467 x 50

= 5.23 m / s

centripetal force = m v² / R

= mg v² / gR

= 834 x 5.23² / 9.8 x 50

= 46.55 N

B )

apparent weight

= mg - centripetal force

= 834 - 46.55

= 787.45 N

C ) apparent weight

= mg + centripetal force

= 834 + 46.55

= 880.55 N.

D )

For apparent weight to be zero

centripetal force = mg

mg = mv² / R

v² = gR

= 9.8 x 50

= 490

v = 22.13 m /s

time period of revolution

= 2π R /v

2 x 3.14 x 50 / 22.13

= 14.19 s