In a popular amusement park ride, a rotating cylinder of radius R = 3.60 m is se

Question

In a popular amusement park ride, a rotating cylinder of radius R = 3.60 m is set in rotation at an angular speed of 5.60 rad/s, as in the figure shown below. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rider from slipping? Hint: Recall that the magnitude of the maximum force of static friction is equal to sn, where n is the normal force—in this case, the force causing the centripetal acceleration.

s =

Explanation / Answer

The mass of the rider is common to both the vertical force of gravity and the horizontal force from centripetal acceleration. We can therefore work only with accelerations as a substitute for force.

centripetal acceleration is
ac = ²r

find such that the upward force of friction, which is the friction coefficient times the normal force ( a product of centripetal acceleration) is equal to the gravity force

(ac) = g

= g / (ac)

= g / (²r)

= 9.81 / (5.60²(3.60))

= 0.0868

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