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Deriving µs = tan θ

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data

    Deriv µs = tan θ
    For when a block is put on a wooden plank and the plank is lifted at one side.
    2. Relevant equations

    tan = sin/cos
    Ff = µFn

    3. The attempt at a solution
    Ff = µFn
    -mgsinθ= µ (-mgcosθ)
    µ =(-mgsinθ) /(-mgcosθ)
    µ = tan θ

    Where i am confused is why Ff = -mgsinθ. Is it because the block has an acceleration of zero when falling down the plank?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 28, 2007 #2

    cristo

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    Staff Emeritus
    Science Advisor

    Yes, the block is assumed not to move, and so the frictional force must balance the component of the weight of the block parallel to the plank.
     
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