A 55 kg person is riding a Ferris wheel that rotates 2 times per minute and has

Question

A 55 kg person is riding a Ferris wheel that rotates 2 times per minute and has a diameter of 27 m. a. What is the centripetal acceleration of the person?

Explain, in words, why this centripetal acceleration is constant throughout the persons ride.

b. What is the magnitude and direction of the normal force exerted by the seat on the person at the lowest point in the ride?

c. What is the magnitude and direction of the normal force exerted by the seat on the person at the highest point in the ride?

d. Oh no-- a psycho clown takes over the controls and speeds up the rotation! What is the minimum speed the ride would need to rotate (in revolutions/minute) for riders at the top of the ride to experience temporary weightlessness?

Explanation / Answer

r = 27/2 = 13.5m

angular speed w = 2 x 2pi /60 rad/s = 0.209 rad/s

centripital acc. = w^2 .r = 0.209^2 x 13.5 =0.592 m/s2

its constant because wheel is moving with constant speed.

B) at lowest point :

N = mg + mw^2.r = 55 ( 9.81 +0.592)

N = 572.12 N

C) at highest point :

N + mw^2.r = mg

N = 55 ( 9.81 - 0.592) = 507 N

d) rider will feel weightlessness when N =0

so N = mg - mw^2.r = 0

w = sqrt(g/r) = 0.852 rad/s = 0.852 x 60/2pi = 8.14 rev/min

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