A Ferris wheel has a radius R of 6.64 m and rotates four times each minute. Ther

Question

A Ferris wheel has a radius R of 6.64 m and rotates four times each minute. There is a rider with a mass of 41.5 kg. The seat exerts a force on the rider that includes both the normal force and friction so that the rider stays on the seat during the entire ride. a) What is the magnitude of the centripetal acceleration of the rider? b) What is the magnitude of the force that the seat exerts on the rider at the lowest point of the ride? c) What is the direction of the force that the seat exerts on the rider at the lowest point of the ride? (reference angles to upward being 0 degrees) d) What is the magnitude of the force that the seat exerts on the rider at the highest point of the ride? e) What is the direction of the force that the seat exerts on the rider at the highest point of the ride? (reference angles to upward being 0 degrees) f) What is the magnitude of the force that the seat exerts on the rider half way between top and bottom of the ride? g) What is the direction of the force that the seat exerts on the rider half way between top and bottom of the ride? (Take the upwards direction to be 0 degrees. The computer is looking for a positive angle.)

Explanation / Answer

similar problem with mass = 33 kg and radious = 12 m hope u will follow it (a) 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) plsz rate me 1st

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