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Problem about friction

  1. Oct 24, 2014 #1
    1. The problem statement, all variables and given/known data
    The following problem appeared in our test:
    A box of mass m is moving with a constant velocity v along a smooth frictionless surface.When the box passes the boundary the frictional force acts on the box.The coefficient of kinetic friction between the box and the surface is μk and the box covers a distance x after crossing the boundary.
    Find the dependence of acceleration on x.
    LIL6BbS.png



    2. Relevant equations
    ∑Fx=max

    3. The attempt at a solution
    I really did not know how to begin the solution.All I did know was that the acceleration would be equal to a=-μkg by Newton's Second law
     
  2. jcsd
  3. Oct 24, 2014 #2

    Orodruin

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    Why dont you start from the realization you had about the acceleration? How do you relate the acceleration to the travelled distance?
     
  4. Oct 24, 2014 #3
    By any chance, do they give you the length of the box (like L)?

    Chet
     
  5. Oct 24, 2014 #4

    haruspex

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    Not quite. You have cancelled out the mass, without considering whether the masses on the two sides of the equation are the same. See Chet's hint/question.
     
  6. Oct 27, 2014 #5
    Actually I do not remember properly but I think the length of the block was L.
     
  7. Oct 27, 2014 #6

    haruspex

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    I don't think it matters. The lower diagram implies x < L. If you have to allow for x > L as well it gets a little more complicated.
    Let's assume x < L for now. Start again with ∑Fx=max. What do you have for the force(s)?
     
  8. Oct 31, 2014 #7
    The only force is the frictional force F=-uk*mg
     
  9. Oct 31, 2014 #8
    What fraction of the mass is situated over the frictional surface, and what fraction of the mass is situated over the frictionless surface? What is the normal force over the frictional surface?

    Chet
     
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