Ok, you go up but how far?

Take a solid cylinder of radius \(R\) , roll it with angular velocity \(\omega_{0}\) and carefully keep it on an inclined plane having inclination \(\theta\) , and coefficient of kinetic friction \(\mu_{k}\) , such that \(\mu_{k} > \tan \theta\). Find the maximum height attained by the cylinder above the initial position in \(mm\) to the nearest integer

Details and Assumptions

  • \(\omega_{0} = 50 rad s^{-1}\)
  • \(R = 25cm\)
  • \(\mu_{k} = \frac{1}{3}\)
  • \(\tan \theta = \frac{1}{4}\)
  • \(g=9.8 m/s^2\)

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