Determine the force involving static coefficient

[goldfish9776]

Homework Statement

A force P acts as shown on a 200kg block placed on an inclined plane. The static coefficient of friction between the block and plane are Us= 0.5 . Determine the force of P to ensure he block is in the verge of moving down. The ans given is P = 560.4 N
i have done in 2 ways , but my ans is incorrect ... why am i wrong ?

Homework Equations

The Attempt at a Solution

[/B]
1. ) P cos 20 = Fs

Pcos20 =0.5x9.81x200xcos10

P= 1028N

2. ) Wsin10 + P cos20 = 0.5x9.81x200xcos10

Pcos20 = 0.5x9.81x200xcos10 - Wsin10

Pcos20 = 0.5x9.81x200xcos10 – 200x9.81 sin10

P= 665.5N

 

[BvU]

What about the maximum friction if P were at 90 degrees instead of 20 ?

 

[haruspex]

Go through the standard procedure:
Draw the free body diagram of the block. List the forces with horizontal components, write out expressions for their values and the force balance equation. Then do the same for vertical components.