In an amusement park ride called The Roundup, passengers stand inside a 14.9 m d

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In an amusement park ride called The Roundup, passengers stand inside a 14.9 m diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in Figure P7.47.style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">color="red">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">

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http://www.webassign.net/knight/P7.47.gifstyle="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">color="red">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">

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(a) Suppose the ring rotates every 4.5 s. If a rider's mass is 58 kg, with how much force does the ring push on her at the top of the ride?
N
How much force the does the ring push on her at the bottom of the ride?
N
(b) What is the longest rotation period of the wheel that will prevent riders from falling off at the top?
s

In an amusement park ride called The Roundup, passengers stand inside a 14.9 m diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in Figure P7.47. Suppose the ring rotates every 4.5 s. If a rider's mass is 58 kg, with how much force does the ring push on her at the top of the ride? How much force the does the ring push on her at the bottom of the ride? What is the longest rotation period of the wheel that will prevent riders from falling off at the top?

Explanation / Answer

Part A)

The centripetal force at the top is found from mw^2r

w = 2pi/4.5 = 1.4 rad/s

Fc = (58)(1.4)^2(7.45) = 846.9 N

The weight = 58(9.8) = 568.4 N

The net force is 846.9 - 568.4 = 278.5 N

At the bottom, the forces add, so

846.9 + 568.4 = 1415.3 N

Part B

Fc would be the weight = 568.4

568.4 = (58)(w^2)7.45

w = 1.147 rad/s

1.147/2pi = .183 rev/s

1/.183 = 5.48 sec

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In an amusement park ride called The Roundup, passengers stand inside a 14.9 m d

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