Friction ( Inclined plane)

  • #1

Homework Statement


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.

Homework Equations



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

The Attempt at a Solution



I just don't know where to start . Any hints would be appreciated.
 

Answers and Replies

  • #2
gneill
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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.
 
  • #3
Thanks gneill , I finally proved it !
 

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