In an old fashion amusement park ride, passengers stand inside a 3.0m tall,5.0m

Question

In an old fashion amusement park ride, passengers stand inside a 3.0m tall,5.0m diameter, hollow steel cylinder with their backs against the wall. 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

Given that radius r = 2.5 m acceleration due to gravity g =9.80m/s2 coefficient of static frction is s = 0.60 ----------------------------------------------- Here frictional force is equal to the weight of the body           s(m ac) = mg Here ac = v^2/r s(m (v^2/r)) = mg    v = [rg/s]        = [(2.50m)(9.80 m/s2)/(0.60 )]         = 6.39 m/s The minimum rotational frequency in rpm, for which the ride is safe is     = (v/r)         = [(6.39 m/s)/(2.50 m)](1 rev/(2))(60s/1min)         =24.408 rev/min    

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