In an amusement park ride called The Roundup, passengers stand inside a 18.0m -d

Question

In an amusement park ride called The Roundup, passengers stand inside a 18.0m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts intoa vertical plane, as shown in the figure (Figure 1) .

Part A

Suppose the ring rotates once every 4.80s . If a rider's mass is 52.0kg , with how much force does the ring push on her at the top of the ride?

Part B

Suppose the ring rotates once every 4.80s . If a rider's mass is 52.0kg , with how much force does the ring push on her at the bottom of the ride?

Part C

What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?

Explanation / Answer

a) v = 2 pi r/T = pi*18/4.8

at top N + mg = mv^2/r

N = 52*( (pi*18/4.8)^2/9 - 9.81)= 291.8 N

b) at bottom N - mg = mv^2/r

so N= 52*( (pi*18/4.8)^2/9 + 9.81) = 1312 N

c) at max period N top = 0

so mg = mv^2/r

9.81 = (pi*18/T)^2/9

T=6.02 s

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