Question

In an old fashioned amusement park ride, passengers stand inside a 5.0-m diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about the vertical axis. Then, the floor that the passengers are standing on suddenly drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel that ranges from 0.60 to 1.0 and a kinetic coefficient in the range of 0.4 to 0.7. A sign next to the ride says “No children under 30-kg allowed!” What is the minimum angular speed, in rpm, for which the ride is safe?

Answer 1

Not sure what speed is safe, because we do not control what clothing riders wear, and hence their coefficient of friction.

According to the data, assuming them to be accurate, you will need to have the friction to overcome the weight of the customers. Minimum coefficient of friction is μ=0.4 (kinetic), so you will need the centripetal acceleration to be g/0.4=2.5g for the poor screaming rider to be 'sustained' by the frictional force.

Centripetal acceleration is
a=2.5g=rω²
Solve for ω and convert to RPM.

Note:
1. Investigate the effect of 2.5g on the physiological functioning of the bladder.
2. A 10% slanting slope (wider near the top) to make the "cylinder" a truncated cone will help to keep the customer in his place, and gives him a chance to survive for an "encore".

Answer 2

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