What is the Correct Formula for Static Friction on an Inclined Box?

[physgirl]

Homework Statement

On a box (of mass "m"), force "F" is applied at "theta" degree angle above the horizontal. The box has static friction coefficient of "u." When this force is applied, and the box remains stationary, what expression describes the frictional force?

Homework Equations

F=uN??
(N is normal force)

The Attempt at a Solution

I came down to 2 choices:
F=umg
or
F=uFcos(theta)

I initially thought the former, because I keep remember being drilled the equation F=uN, and about how it's all about the normal force when it comes to friction.

But then when I thought about it, forces must balance out... so if there's no net acceleration, applied force (i.e. Fcos(theta)) MUST balance out frictional force, no?

And now I'm just confusing myself.

 

[rock.freak667]

Right, yes the forces must balance out.

When you split the force into vertical and horizontal components what do you get?

 

[physgirl]

right, so if the box isn't moving (yet), then for vertical, we just have normal force = gravity force (i think?), which is just mg=mg... then for horizontal, we have applied force (Fcos(theta))=frictional opposing force (u*F*cos(theta))...

i think i get the confusion. so the normal force equation is only relevant for *maximum* static frictional force equation, where that's the force at which the box moves b/c it overcomes static friction. yes?

 

[rock.freak667]

yes but you see, your normal reaction is not just N=mg since the vertical component of the force F_y is present and depending how the force is applied, the normal reaction will change.