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University of Washington

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Problem 73 Hard Difficulty

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, 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 msn, where n is the normal force—in this case, the force causing the centripetal acceleration.

Answer

0.13

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Video Transcript

this question. We have this, uh, situation, this rotating cylinder, Uh, radios 3 m, rotating at Angela's B of five against for a second. Okay, then we want to find a minimum coefficient of friction between the writers clothing at the wall so that the writer will not sleep. Okay, So to do this problem, uh, we need to draw a free body diagram of the writer. Okay, Because we want to determine, uh, something really? The two forces. Okay, so maybe I'll just draw dot Okay, so we have the weight. Okay. We have the normal force from the wall. Yes, I have, uh, friction or static friction. And so this is the free body diagram. And then we also know that this is the central butte of exaggeration. He is on the diagram that we have drawn. So, um, we can use our a c Chris, too. Uh, our only got square, right. And then FC is, uh lemme see And the normal force from everybody that ground. Okay. And it goes to FC goes to m r. Omega Square. Okay. And then, uh, since we need to find a minimum coefficient of friction, So f s s equal to us. And this is equal to us. Uh, m R oh, my God. Square and prevent sleeping. Okay. F s nice. Equal to w. Okay, so u S m r Omega Square. He goes to m g cancer. The M, um us is Judy by by our only gas. Where goes to 9.8. Bye bye. Tree times. Um, five square. Okay, so you get 0.131 Okay, this is our minimum us in this case, and that's all for this question.

University of Washington
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