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I Ball rebounding off a wall

  1. Aug 10, 2017 #1
    An elastic spherical ball of mass m and radius a moving with velocity v strikes a rigid surface at an angle θ to the normal. Assuming the ball skids while in contact with the surface, the tangential reaction force being a constant fraction μ of the normal reaction force, and assuming the perpendicular velocity of the ball is reversed, show that
    1. the ball is reflected at an angle Φ to the normal where |tanθ - tanΦ| = 2μ
    2. the angular velocity of the ball changes by an amount 5μvcosθ/a

    Now the solution I have for this says that the ball can't skid if it is not rotating prior to colliding with the surface. I don't understand why this has to be the case. Could someone help explain why this is?

    Thanks
     
  2. jcsd
  3. Aug 10, 2017 #2

    jbriggs444

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    So the claim is that if a ball is hitting the surface at a non-perpendicular angle and if it is not rotating as it arrives, then it cannot skid.

    That claim is obviously false. Take the limiting case of a glancing impact at an angle of 89+ degrees from the normal with a greased ball. The ball will darned sure skid.
     
  4. Aug 10, 2017 #3
    That's what it says, and as you suggest, this seems very counter-intuitive. The solution is from a book by a Cambridge professor though so I was reluctant to question it. Could it be a mistake?
     
  5. Aug 10, 2017 #4

    jbriggs444

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    Mistake or misinterpretation. It is difficult to say without seeing the exact claim in context.
     
  6. Aug 10, 2017 #5
    Here is the quote from the book:

    "The problem refers to a change in angular velocity of the ball, so it is presumably not safe to assume that the ball is not initially rotating (and in fact if the ball were not rotating, it could not skid against the surface so the angles θ and Φ would be identical)."

     
  7. Aug 10, 2017 #6

    jbriggs444

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    That claim is indeed incorrect and confused. The author of that quote could be correct to point out that a ball with an inadequate rotation rate might start the collision in a skidding condition and end the collision in a rolling-without-slipping condition. But the problem poser ruled that possibility out with the careful phrasing:
    However, the error is cosmetic. It does not change the solution.

    Whether one assumes that the ball starts with sufficient back spin that the skid persists throughout the collision or whether one assumes that the collision is at a sufficiently glancing angle it's still skidding when it rebounds, the important thing is that the force of friction between ball and surface persists throughout the collision and is given by the normal force multiplied by the coefficient of kinetic friction.
     
  8. Aug 10, 2017 #7
    Thanks! And if the question had not said to assume that the ball slips during the collision, how would one go about solving the subsequent motion of the ball? If it doesn't slip during the collision, does that mean it no longer receives an impulse parallel to the wall? Would you be able to conserve kinetic energy in that circumstance?
     
  9. Aug 10, 2017 #8

    jbriggs444

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    One would need additional details on the collision and the ball. For instance, the elasticity of the ball could figure in.

    If you have ever bounced a sticky rubber ball (do they still make "superballs"?), you will understand that spin makes a huge difference in rebound angle for a ball that rebounds elastically and without slipping.

    Just because the ball does not slip does not mean that there is no friction. Nor does it mean that there is no energy loss.
     
  10. Aug 10, 2017 #9

    russ_watters

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    Looks to me like the writer got lost in a grammatical loop of too many "nots".
     
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