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?

Answer 1

The friction force ( µ . N ) must be enough to counter the gravity force ( m . g ) The Normal force from the rotating wall is the centripetal force = mv^2 / r so with the lowest coefficient of friction ( 0.4 ) 0.4 . v^2 / 2.5 = g v^2 = 2.5 . 9.8 / 0.4 v = 7.83 m/s T = 5π / 7.83 = 2.007 s f = 0.5 Hz = 30 rpm