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

Question

34.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 24.0 m. (a) What is the centripetal acceleration of the child? 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. (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? magnitude N direction ---Select--- up toward the center down away from the center tangent to the left tangent to the right The magnitude is zero. (c) What force does the seat exert on the child at the highest point of the ride? magnitude N direction ---Select--- up away from the center down toward the center tangent to the left tangent to the right The magnitude is zero. (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 N direction

Explanation / Answer

Angular speed is 4 rpm = 4/60 revs per second = 0.0667 rps, diameter D = 24m, radius r = 12m Tangential speed v = 0.0667 *pi*D m/s = 5.03 m/s Centripetal acceleration a = v^2/r = (5.03)^2 / 12 m/s^2 = 2.105 m/s^2 (b) The centripetal accelerating force is always towards the centre 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 = 33kg * (5.03m/s)^2 / 12m = 69.48N The force of gravity is f = mg = 33kg * 9.81m/s^2 = 324N At the lowest point of the ride, force exerted by seat = 324N + 69.48N = 393N STRAIGHT UP (c) At the highest point of the ride, force exerted by seat = 324N - 69.48N = 255N STRAIGHT UP (d) At the halfway point of the ride, force exerted by seat = 324N STRAIGHT UP (resisting gravity only)

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