Question

The Cosmo Clock 21 Ferris wheel in Yokohama, 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.
(b) A passenger weighs 882 N at the weight-guessing booth on the ground. What is his apparent weight at the highest and at the lowest point on the Ferris wheel?
(c) What would be the time for one revolution if the passenger’s apparent weight at the highest point were zero?
(d) What then would be the passenger’s apparent weight at the lowest point?

Answer 1

Answer:

Explanation:

a ) speed of passenger = circumference / time

= 2π R / Time

= 2 x 3.14 x 50 / 60

= 5.23 m /s

b )

centrifugal force = m v² /R

= (882 /9.8 ) x 5.23² / 50

= 77.47 N

Apparent weight at the highest point

real weight  - centrifugal force

= 882 - 77.47

= 804.53 N

Apparent weight at the lowest point

real weight  + centrifugal force

= 882 +77.47

= 959.47 N

c )  if the passenger’s apparent weight at the highest point were zero

centrifugal force = weight

mv² /R = mg

v² = gR

= 9.8 X 50

v = 22.13 m /s

d )

apparent weight

mg - mv² / R

= 882 - (882 / 9.8 )x 22.13²/50

= 882 +  882

= 1764 N  

=