Box resting on an inclined plane

[JamesW]

Homework Statement

A box with a mass of 22kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficient of static friction is 0.78

determine the magnitude of the smallest force that can be applied onto the top of the box, perpendicular to the ramp if the box is to remain at rest?

Homework Equations

F=ma

The Attempt at a Solution

F f (static friction) + Fgx = 0

F n = Fgy + F a

Fa = F n - Fgy

I have viewed a thread and to calculate F n (normal force) they divided Fgx/mu static. I was wondering why this was?

 

[JamesW]

WHY IS Fn = Fgx/ mu static ?

 

[JamesW]

because Fs=(mu static)(Fn)

 

[lightgrav]

which is valid if friction _exactly_ cancels "g sin theta" ...