Determine the force involving static coefficient

AI Thread Summary
A force P is applied to a 200kg block on an inclined plane with a static coefficient of friction of 0.5, and the goal is to find P to keep the block on the verge of moving down. The correct answer for P is 560.4 N, but the user calculated values of 1028 N and 665.5 N using two different methods, both of which were incorrect. The user is prompted to reassess their calculations by drawing a free body diagram and listing the forces involved, including both horizontal and vertical components. The discussion emphasizes the importance of accurately applying the equations of motion and friction in static scenarios. Understanding the balance of forces is crucial for solving such problems effectively.
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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
 

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