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Frictional forces and the angle for minimum frictional force

  1. Feb 26, 2015 #1

    Yam

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    1. The problem statement, all variables and given/known data
    A person is dragging a packing crate of mass 100 kg across a rough floor where the coefficient of kinetic friction is 0.400. He exerts a force F just sufficient to keep the crate moving at a constant velocity. At what angle above the horizontal should his pulling force F be for it to be minimum?

    2. Relevant equations
    Frictional Forces = UkN

    3. The attempt at a solution
    Frictional Force = Uk(mg)(cosx)

    Im stuck.
     
  2. jcsd
  3. Feb 26, 2015 #2

    BvU

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    I like the "I'm stuck" (you wouldn't post if you weren't). But ##F_{fric} = \mu_k mg\cos\theta## doesn't count as an attempt.

    What forces play a role and how can you express the constant speed in an equation ?
     
  4. Feb 26, 2015 #3

    Yam

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    Forces that play a role:
    1) Pulling force F
    2) Frictional force

    Constant speed means that there is no acceleration.
    F = ma = m(0) = 0
     
  5. Feb 26, 2015 #4

    BvU

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    Frictional force is horizontal, pulling is in some theta direction. What else ? (hint: you already wrote mg -- and there's no vertical acceleration either). So we have a few equations. Magnitude of pulling force might depend on theta. If so, there might be a minimum !
     
  6. Feb 26, 2015 #5

    Yam

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    Forces that play a role:
    1) Pulling force F at an angle
    2) Horizontal Frictional force
    3) Weight of the block

    Yes i understand that the magnitude of the puling force depends on theta, however, how do i relate it to the minimum force?
     
  7. Feb 26, 2015 #6

    BvU

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    One force missing still.
    If |F| depends on theta like, say ##2-\cos^2\theta## then zero degrees would give a nice minimum, wouldn't it ?
     
  8. Feb 26, 2015 #7

    Yam

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    Is it the upward force generated by the pull at an angle?
     
  9. Feb 26, 2015 #8

    BvU

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    Wouldn't that mean that if you don't pull, the box drops down like a brick ?
     
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