In an amusement park ride called The Roundup, passengers standinside a 17.5-m-di

Question

In an amusement park ride called The Roundup, passengers standinside a 17.5-m-diameter rotating ring. After the ring has acquiredsufficient speed, it tilts into a vertical plane, as shown inFigure.
Suppose the ring rotates once every 4.04 s. If arider's mass is 57 kg, with how much force does the ring push onher at the top of the ride?
Suppose the ring rotates once every 4.04 s. If arider's mass is 57 kg, with how much force does the ring push onher at the bottom of the ride?
What is the longest rotation period of the wheelthat will prevent the riders falling off at the top?

Explanation / Answer

time taken for one round T = 4.04 s angular speed w = 2 / T = 1.555 rad / s mass m = 57 kg At top weight act downward anf centripetal force actdownward So, required pushing force F = weight + mrw^2                                             = mg + mrw^2 where r = raidus = diameter / 2= 17.5 m / 2= 8.75 m So, F = 558.6+ 1206.36                                      =1764.96 N At bottom pushing force F = mrw^2 - mg                                          = 647.76 N

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