Determine the force involving static coefficient

1. Oct 29, 2015

goldfish9776

1. The problem statement, all variables and given/known data
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 ?

2. Relevant equations

3. The attempt at a solution

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

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2. Oct 29, 2015

BvU

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

3. Oct 29, 2015

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.

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