How Fast Can a Merry-Go-Round Spin Before a Child Slides Off?

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AI Thread Summary
To determine the maximum speed of a merry-go-round before a child slides off, one must calculate the centripetal force required to keep the child in place. Given the child's mass of 30 kg and a static friction coefficient of 0.56, the frictional force must be sufficient to counteract the centripetal force. The diameter of the merry-go-round is 12 meters, which is crucial for calculating the radius and subsequent forces. Utilizing standard equations for centripetal motion and static friction will lead to the solution. Understanding these concepts is essential for solving the problem effectively.
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Homework Statement


A child with mass m = 30 kg is sitting on a 12-m diameter merry-go-round. What is the maximum speed the merry-go-round can travel and the child not slide with a static friction coefficient of 0.56?


Homework Equations



To be honest, I had to miss a day of class because I was sick. I have no idea where to start on this problem. Any help or formulas would be much appreciated!


The Attempt at a Solution



See #2
 
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It's about centripetal force. If you really haven't heard of that or don't know any equations concerning it, search the net. Calculate the centripetal force required to keep the child from spinning off, then use your usual statics equations to determine the frictional force, the normal force, and thus the minimum coefficient of static friction.
 

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