   Chapter 7, Problem 73AP

Chapter
Section
Textbook Problem

In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s, as in Figure P7.73. The floor then drops away, leasing 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 μsn, where n is the normal force—in this case, the force causing the centripetal acceleration. Figure P7.73

To determine
The minimum co-efficient of friction.

Explanation

Given info: Radius of the cylinder (r) is 3.00 m. The angular speed of rotation ( ω ) is 5.00 rad/s.

Explanation:

The normal force provides the centripetal acceleration. Therefore,

N=mω2r

• m is the mass of the person.

The maximum static force of friction equals the weight of the person. Hence,

fs=mg

• fs is the force of friction.
• g is the acceleration due to gravity.

The force of friction is,

fs=μsN

From the above equations,

mg=μsmω2r

On Re-arrang

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