2011 F = ma Contest Question # 25

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SUMMARY

The problem involves a hollow cylinder and a block sliding down an inclined plane, both reaching the bottom simultaneously. The solution reveals that the coefficient of kinetic friction between the block and the plane is (1/2)tan(theta). The relevant equations include K = (1/2)MV^2 + (1/2)IW^2, with I = MR^2 and W = V/R. The analysis confirms that the acceleration of the rolling cylinder is crucial to solving the problem.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Familiarity with rotational dynamics and moment of inertia (I = MR^2)
  • Knowledge of the relationship between linear and angular velocity (W = V/R)
  • Basic trigonometry, specifically the tangent function (tan(theta))
NEXT STEPS
  • Study the dynamics of rolling motion and the effects of friction on acceleration
  • Explore the derivation of the moment of inertia for various shapes
  • Learn about the relationship between linear and angular motion in physics
  • Investigate problems involving inclined planes and friction in classical mechanics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for illustrative examples of friction and motion on inclined planes.

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Homework Statement



A hollow cylinder with a very thin wall (like a toilet paper tube) and a block are placed at rest at the top of a plane with inclination  above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found that both objects reach the bottom of the plane simultaneously. What is the coefficient of kinetic friction between the block and the plane?

Homework Equations



K = (1/2)MV^2 + (1/2)IW^2 for I = MR^2 and W = V/R

The Attempt at a Solution



Answer is: (1/2)tan(theta)
I have tried many different approaches: F = ma as well as assuming the same mass and/or velocity at the end of the ramp, but have had no success. Thanks for your time and consideration!
 
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Start by finding the acceleration of the rolling cylinder.
 
Hey, thanks for the response! That really helped and I was able to figure this one out finally.
 

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