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## Homework Statement

The block resting on the inclined plane shown has a mass of 40kg. Determine the maximum and minimum value for P for which the block is in equilibrium. (f

_{s}= 0.35 and θ=25°)

## Homework Equations

ΣFx = 0

ΣFy=0

F

_{max}=(f

_{s})(N)

## The Attempt at a Solution

w

_{x}= (392.4)(sin(25)) = 165.84

w

_{y}= (392.4)(cos(25)) = 355.64

F

_{max}= (0.35)(355.64) = 124.47

-P

_{max}+ F

_{max}+ w

_{x}= 0

P

_{max}= 290.31 N

-P

_{min}- F

_{max}+ w

_{x}= 0

P

_{min}= 41.37 N

Okay so the problem isn't that I couldn't solve it: I followed my notes by my professor and got the answers right. My problem is my understanding of the concept behind some points in the equations. My questions are:

1) What exactly are Pmin and Pmax?

2) When solving for Pmin and Pmax, I understand that it is just the equilibrium equation for the whole system (in this case ΣFx because the friction is parallel to the surface) right?

3) If so, why does the F

_{max}turn to negative when solving for the minimum? I can see why it is positive since it is in the positive direction (right), but why does it turn negative all of a sudden?