Friction ( Inclined plane)

[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 !