Find an expression for the max speed of circular motion of a car in a circular horizontal track of radius R. The cofficient of static friction between the car tyres and the road along the surfaces is u
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Answer:
Consider the following diagram,
We have,
N= mg
and
![\frac{mv^{2} }{R} \leq uN\\\frac{mv^{2} }{R} \leq umg\\\\\ Solving it furthur,\\\frac{v^{2} }{R} =ug\\v=\sqrt{ugR} \\ \frac{mv^{2} }{R} \leq uN\\\frac{mv^{2} }{R} \leq umg\\\\\ Solving it furthur,\\\frac{v^{2} }{R} =ug\\v=\sqrt{ugR} \\](https://tex.z-dn.net/?f=%5Cfrac%7Bmv%5E%7B2%7D+%7D%7BR%7D+%5Cleq+uN%5C%5C%5Cfrac%7Bmv%5E%7B2%7D+%7D%7BR%7D+%5Cleq+umg%5C%5C%5C%5C%5C+Solving+it+furthur%2C%5C%5C%5Cfrac%7Bv%5E%7B2%7D+%7D%7BR%7D+%3Dug%5C%5Cv%3D%5Csqrt%7BugR%7D+%5C%5C)
Hence your solution.
NOTE: r in the diagram is equal to R in the question.
Apologies for my silliness ^_^".
Consider the following diagram,
We have,
N= mg
and
Hence your solution.
NOTE: r in the diagram is equal to R in the question.
Apologies for my silliness ^_^".
Attachments:
![](https://hi-static.z-dn.net/files/d61/34a67b36b602613b394437a9fbc4f373.png)
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