In a popular amusement park ride, a rotating cylinder of radius R = 2.40 m is se

Question

In a popular amusement park ride, a rotating cylinder of radius R = 2.40 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 µsn, where n is the normal force—in this case, the force causing the centripetal acceleration.

Explanation / Answer

the vertical force must equal the weight ,

centripetal force , N = m2 r

Force

f = N = mg ;

N = mg

( m2 r ) = m g

Therefore Coefficient of friction

= g / ( 2 r )

= 9.8 /( 5.6 )2 ( 2.4 )

= 0.130

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