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

Question

In an amusement park ride called The Roundup, passengers stand inside a 18.0 m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, Suppose the ring rotates once every 4.90 s .

a) If a rider's mass is 53.0 kg , with how much force does the ring push on her at the top of the ride?

b) Suppose the ring rotates once every 4.90 s . If a rider's mass is 53.0 kg , with how much force does the ring push on her at the bottom of the ride?

Express your answer with the appropriate units.

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

Express your answer with the appropriate units.

Explanation / Answer

Here ,

radius of ride , r = 18/2 = 9 m

time period , T = 4.90 s

angular speed , w = 2pi/T

w = 2pi/4.90 s

w = 1.282 rad/s

a) at the top of the ride

force pushed by ring = m * (g - w^2 * r)

force pushed by ring = 53 * (9.8 - 1.282^2 * 9)

force pushed by ring = -265 N

the ring is pushed by 265 N at the top of ride

b)

at the bottom

Force = m * (g + w^2 * r)

Force = 53 * (9.8 + 1.282^2 * 9)

Force = 1304 N

the applied at the bottom of the ring is 1304 N

c)

let the minimum angular speed is w

for Force = 0

m * (g - w^2 * r) = 0

9.8 - w^2 * 9 = 0

w = 1.043 rad/s

period = 2pi/w

period = 2pi/1.043 s

period = 6.02 s

the longest rotation period of the wheel is 6.02 s

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