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B Question about static friction adjusting itself

  1. Apr 24, 2016 #1
    incline_wpulley.gif
    In a situation like this, there are two equilibrium's,
    For just about to accelerate downwards:
    mgsinθ - Ffriction - T = 0
    For just about to accelerate upwards:
    T - Ffriction - mgsinθ = 0

    Is there a situation where there is no static friction i.e. when
    mgsinθ = T?
     
  2. jcsd
  3. Apr 24, 2016 #2

    PhanthomJay

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    Sure. For the equilibrium condition with or without friction, T is always equal to Mg. The m/M ratio is key.
     
  4. Apr 24, 2016 #3

    A.T.

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    This are the limiting cases. There are infinitely many equilibriums in between.
     
  5. Apr 25, 2016 #4
    if m>M
    first set angle to 0
    then increase angle by tiny amounts and after each increase reset the system to original condition( ie bodies at rest) and check if mass 'm' is at rest
    let x = 1st angle at which equilibrium is achieved (body just about to accelerate down)
    on further increase , for a small interval of angle , system will stay at rest
    let y = 1st angle at which system again starts moving (body just about to accelerate up)
    note that on increasing angle above x , tendency of m to go down decreases and to go up increases
    on decreasing angle below y , tendency of m to go down increases and to go up decreases
    so there must be an angle bet x and y at which both tendency balanced so no static friction needed for equilibrium
     
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