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

when the floor is removed
the forces on the passengers are
1)weight mg acts downwards
2)normal force N due to the wall
3)frictional force parallel to the wall
when the passengers are moving in a circular path accelerationtowards the centre is r2 where iasthe angular speed
for minimum speed
smr2=mg==>2=g/sr==>=9.8/0.6*[5.0/2] = 2.5560 rad/sec

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