Calculating Force on Inclined Plane with Friction

[NumberTheory]

Homework Statement

A body of weight W rests on a rough inclined plane and a force P acting at angle \alpha with the inclined plane just prevents the body from sliding down . If the inclined plane makes an angle \phi with the horizontal , prove that

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

where \lambda is the angle of friction.

Homework Equations

F = \mu N

The Attempt at a Solution

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

 

[gneill]

Start with determining how \lambda is related to \mu. 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.

 

[NumberTheory]

Thanks gneill , I finally proved it !