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A uniform cylinder of mass M and radius R rolls without slipping down a slope of angle a(theta) to the horizontal. The cylinder is connected to a spring constant K while the other end of the spring is connected to a rigid support at P The cylinder is released when the spring is unstretched. The maximum distance that the cylinder travels is?

Vincent Thacker
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insanegovind
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  • Hello there, and welcome to the Physics Stack Exchange! Homework and "check my work" questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. Please read this post on asking homework questions and this post for "check my work" questions. – Vincent Thacker Nov 08 '20 at 14:24
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  • I have found the answer and I am only asking the concept , I have neither asked anyone to provide the solution nor to find my mistake, the question below is only for reference. – insanegovind Nov 08 '20 at 15:59
  • The question isn't asking the how can you solve? But its how is its possible that this has happened? – insanegovind Nov 08 '20 at 16:06

2 Answers2

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The friction in this situation is static friction. It provides a torque which causes an angular acceleration (first positive and later negative), but it does not dissipate energy.

R.W. Bird
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  • But why is the friction static and not kinetic – insanegovind Nov 08 '20 at 15:43
  • For a cylinder rolling freely on a surface, at the point of contact, the cylinder is not moving relative to the surface. (Consider the bottom of a wheel on your car.) There may be a small "rolling friction" associated with the deformation of the surfaces. – R.W. Bird Nov 09 '20 at 18:30
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Friction always acts to oppose the actual or impending motion. The maximum frictional force in this case is the coefficient of sliding friction times the normal force. However, this maximum frictional force occurs when the mass slips; for rolling without slipping, the frictional force is less and may not be constant. You can search this exchange for more details on friction; for example see https://physics.stackexchange.com/questions/509358/why-do-the-expressions-for-an-object-rolling-down-an-incline-not-depend-on-the-c?r=SearchResults&s=2|46.4439. Also, The Halliday and Resnick physics textbooks discuss this.

John Darby
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