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Friction ( Inclined plane)

  1. Aug 6, 2011 #1
    1. The problem statement, all variables and given/known data
    A body of weight [tex]W[/tex] rests on a rough inclined plane and a force [tex]P[/tex] acting at angle [itex]\alpha[/itex] with the inclined plane just prevents the body from sliding down . If the inclined plane makes an angle [itex]\phi[/itex] with the horizontal , prove that

    [tex]P = W\frac{sin(\phi - \lambda)}{cos(\alpha + \lambda)} [/tex]

    where [itex]\lambda[/itex] is the angle of friction.

    2. Relevant equations

    [tex] F = \mu N [/tex]

    3. The attempt at a solution

    I just don't know where to start . Any hints would be appreciated.
  2. jcsd
  3. Aug 6, 2011 #2


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    Staff: Mentor

    Start with determining how [itex]\lambda[/itex] is related to [itex]\mu[/itex]. Then use a Free Body Diagram to identify all the forces involved, and how they must combine to achieve a static condition (no motion for the block). Solve for P.

    There will be some simple trig identities involved in simplifying the expression for P.
  4. Aug 7, 2011 #3
    Thanks gneill , I finally proved it !
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