A 30.0-kg child takes a ride on a Ferris wheel that rotates four times each minu

Question

A 30.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 26.0 m. (a) What is the centripetal acceleration of the child? magnitude? (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? magnitude? (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 and direction? I JUST NEED HELP ON PART D, I have answers to part a through c so you can just solve part d

Explanation / Answer

(a)
Angular speed is 4 rpm = 4/60 revs per second = 0.0667 rps, diameter D = 26m, radius r = 13m
Tangential speed v = 0.0667 *2pi*r m/s = 5.445 m/s
Centripetal acceleration a = v^2/r = (5.445)^2 / 13 m/s^2 = 2.28 m/s^2

(b)
The centripetal accelerating force is always towards the center of the Ferris wheel
But the apparent centrifugal force experienced by the child is in the opposite direction.
So its a downward force assisting gravity at the lowest point of the ride, upward against gravity at the highest point of the ride, and horizontal at right angles to gravity at the halfway point (so the seat then only has to resist gravity).

The apparent centrifugal force is F = m*v^2/r = 30kg * (5.445m/s)^2 / 13m = 68.429 N
The force of gravity is f = mg = 30kg * 9.81m/s^2 = 294.3 N

At the lowest point of the ride, force exerted by seat = 294.3 N + 68.429 N = 362.73 N STRAIGHT UP

(c)
At the highest point of the ride, force exerted by seat = 294.3 N - 68.429N = 225.87 N STRAIGHT UP

(d)
At the halfway point of the ride, force exerted by seat = 294.3 N toward center (resisting gravity only)

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