Ok, you go up but how far?

Take a solid cylinder of radius RR , roll it with angular velocity ω0\omega_{0} and carefully keep it on an inclined plane having inclination θ\theta , and coefficient of kinetic friction μk\mu_{k} , such that μk>tanθ\mu_{k} > \tan \theta. Find the maximum height attained by the cylinder above the initial position in mmmm to the nearest integer

Details and Assumptions

  • ω0=50rads1\omega_{0} = 50 rad s^{-1}
  • R=25cmR = 25cm
  • μk=13\mu_{k} = \frac{1}{3}
  • tanθ=14\tan \theta = \frac{1}{4}
  • g=9.8m/s2g=9.8 m/s^2
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