The figure below shows a Ferris wheel that rotates three times each minute. It c

Question

The figure below shows a Ferris wheel that rotates three times each minute. It carries each car around a circle of diameter 18.0 m.

(a) What is the centripetal acceleration of a rider?_______

(b) What force does the seat exert on a 36.0 kg rider at the lowest point of the ride?_______

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

(d) What force (magnitude and direction) does the seat exert on a rider when the rider is halfway between top and bottom, going up?

2 answers here. I know that one of them is 360.07 N, but what is the other.

please triple check your work. I asked this question and ended up wrong. I tried doing it but not getting anywhere. state your answer and show work please. Thank you

Explanation / Answer

a) Angular velocity w = 3 rev/min = 3 * 2pi/60 rad/s
= pi/10 rad/s
Or w = 0.314 rad/s
Radius r = 18.0 m/2 = 9 m
Centripetal acceleration a = w^2 * r
= 0.314^2 * 9
= 0.887364 m/s^2

b) Mass M = 36.0 kg
Let force = F
F is upward and weight Mg is downward. Centripetal force is upward.
F - Mg = Ma
Or F = M(a+g) = 36 * (9.8 + 0.887364) = 384.745104 N

c) Mass M = 36.0 kg
Let force = F
F is upward and Mg is downward. Centripetal force is downward.
Mg - F = Ma
Or F = M(g - a) = 36 * (9.8 - 0.887364) = 320.854896 N

d) Let force = F at angle theta below vertical.
Vertical component of F = F cos(theta) upward.
Horizontal component of F = F sin(theta)

There is no acceleration in vertical direction.
Therefore F cos(theta) = Mg--------------------------(1)
Centripetal force is horizontal.
Therefore F sin(theta) = Ma---------------------------(2)
Dividing (2) by (1),
tan(theta) = a/g
Or theta = atan(a/g) = atan(0.887364/9.8) = 5.173871724 deg
From (1),
F = Mg/cos(theta) = 36 * 9.8/cos(5.173871724 deg) = 354.2433199 N
Therefore, force by the seat is 354.2433199 N at 5.173871724 deg below vertical.
(Note: I do not know what exactly is meant by inward from vertical. I have calculated the angle from vertically upward. If you want the angle from vertically downward, then it is 180 - 5.173871724 = 174.8261283 deg

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