In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5

Question

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing 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 in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70.
What is the minimum rotational frequency, in rpm, for which the ride is safe?

Explanation / Answer

for minimum speed when the floor may be removed the friction is thelimiting force which is equal to sN
so sN=mg
but N=mv*v/r
so s*mv*v/r=mg
hence v=rg/s=2.5*9.8/0.6=6.39 m/sec
so angular velocity==v/r=2.55rad/sec
rotational frequency=/2
so rotational frequency=0.4060 rot/sec
in rpm the value is 0.4060*60=24.36 rpm

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