A 34.0-kg child takes a ride on a Ferris wheel that rotates four times each minu

Question

A 34.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 22.0 m.

(a) What is the centripetal acceleration of the child?

(b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride?

(c) What force does the seat exert on the child at the highest point of the ride?

(d) What force does the seat exert on the child when the child is halfway between the top and bottom? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.)

magnitude      m/s2 direction      ---Select--- toward the center of the path away from the center of the path tangent to the path The magnitude is zero.

Explanation / Answer

a) = 4rev/min * 2 rad/rev * 1min/60s = 0.42 rad/s
a = ² r = (0.42rad/s)² * 11m = 1.94 m/s²

b) F = Fg + Fc = 34kg * (9.8m/s² + 1.94m/s²) = 399.16 N up   

c) F = Fg - Fc = 34kg * (9.8m/s² - 1.94m/s²) = 267.24 N

d) F = (Fg² + Fc²) = ((34 * 9.8)² + (34 * 1.94)²) N = 339.7 N

= arctan(Fg/-Fc) = arctan(9.8/-1.94) -78.8º or 101.2º to put in quadrant II

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