The figure below shows a Ferris wheel that rotates four times each minute. It ca

Question

The figure below shows a Ferris wheel that rotates four times each minute. It carries each car around a cirde of diameter 20.0 m. What force (magnitude and direction) does the seat exert on a 41.0-kg child when the rider is halfway between top and bottom? magnitude Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N direction 798 1.76 Your r differs from the correct answer by more than 1009 measured inward from the vertical

Explanation / Answer

Angular velocity w = 4 rev/min = 4* 2pi/60 rad/s

w = 0.4189 rad/s

Radius r = 20 m / 2 = 10 m

Centripetal acceleration a = w^2*r

a = 0.4189^2 x 10

a = 1.7546 m/s^2

Let force = F at angle theta below vertical.

Vertical component of F

Fcos(theta) upward.

Horizontal component of F = F sin(theta)

There is no acceleration in vertical direction.

Therefore,

Fcos(theta) = Mg -------------------(1)

Centripetal force is horizontal.

Therefore,

Fsin(theta) = Ma ------------------(2)

Dividing (2) by (1),

tan(theta) = a/g

theta = tan^-1(a/g) = tan^-1(1.7546/9.8)

theta = 10 degree

you want the angle from vertically downward, then it is 180 - 10 = 170 degree

From (1),

F = Mg/cos(theta)

F = (41 x 9.8) / cos(10)

F = 408 N

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