Discovering the Maximum Force to Keep a Box at Rest on an Inclined Ramp

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The discussion focuses on calculating the maximum force required to keep a 22 kg box at rest on a 45-degree inclined ramp, considering static and kinetic friction coefficients of 0.78 and 0.65, respectively. The user struggles with setting up the equations correctly, specifically the normal force (Fn), applied force (Fapp), and frictional force (Ffs). The correct approach involves balancing forces along the incline and understanding the direction of friction, which opposes the motion of the box. The user needs clarification on their equations to derive the correct value for Fapp.

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This question is driving me nuts. I really need help with it, actually i just need help setting up my equations.

Mu = the weird friction sympol

A box of a mass m=22 kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficient of friction between the box and the ramp are "Mu s" = 0.78 and "Mu k" = 0.65.
a)Determine the magnitude of the largest force that can be applied upward, parallel to the ramp, if the box is to remain at rest.

My equation are:

Fn=Fgy - Fapp
Fnet = 0
also
Fnet = Fgx - Ffs

After that i end up getting two equations for Fapp but when i solve for it i get a negative answer. I also tried flipping Fapp so Fn=Fapp - Fgy but that also won't work, i get the wrong answer.

So can anyone please help get my two equations, there's something wrong with mine.
 
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Please clarify your expressions, what is Fn, what are Fapp and Ffs?

Which way does the friction act?
 

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