In an amusement park ride called The Roundup, passengers stand inside a 17.0 m -

Question

In an amusement park ride called The Roundup, passengers stand inside a 17.0 m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure (Figure 1) .

Part A

Suppose the ring rotates once every 5.10 s . 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?

Part B

Suppose the ring rotates once every 5.10 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?

Part 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.

Express your answer with the appropriate units.


Express your answer with the appropriate units.

Explanation / Answer

a)

Here , at the top od ride

force from ride , N

N = m*(2pi/T)^2 * R - M*g

N = 53 * ( (2pi/5.1)^2 *(17/2) - 9.8)

N = 163.7 N

the force ring applies on person at the top is 163.7 N

b)

at the bottom of the ride

force from ride , N

N = m*(2pi/T)^2 * R -+ M*g

N = 53 * ( (2pi/5.1)^2 *(17/2) + 9.8)

N = 1202.5 N

the force applied by ring at the bottom is 1202.5 N

c)

for longest duration , at the top of ride ,

N = 0

0= m*(2pi/T)^2 * R - M*g

0 = 53 * ( (2pi/T)^2 *(17/2) - 9.8)

solving for T

T = 5.85 s

the longest duration of round is 5.85 s

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