Static friction and maximum/minimum force

[Poetria]

Homework Statement

A block of mass m is at rest on an inclined plane of angle θ with respect to the horizontal. There is friction between the block and the inclined surface (μk and μs).

Now, assume that the value of θ is less than the value in part A) (so that the block will remain stationary if no other forces act on it). What is the maximum magnitude of a horizontal Force F that(with respect to ground) can be applied without causing the block to move up the incline?

Homework Equations

The Attempt at a Solution

I have found a similar thread here:
https://www.physicsforums.com/threads/block-wedge-problem.698343/#post-4424430
and here: https://www.physicsforums.com/threa...-friction-min-and-max-forces-involved.619902/

I understand everything except one significant detail. I have to choose between several options:
mg(sinθ−μ*cosθ)/(cosθ+μ*sinθ)

or mg(sinθ+μ*cosθ)/(cosθ+μ*sinθ)

Friction is static. I don't understand the numerator. Why is there -/+μ*sinθ or -/+μ*cosθ?? Could you give me a hint?

 

[siddharth23]

Why don't you draw a Free Body Diagram of the block on the incline

 

[Poetria]

Oh, you are right. I did it. I understand it now. Silly me.
Many thanks. :)

 

[siddharth23]

Oh, you are right. I did it. I understand it now. Silly me.
Many thanks. :)

You did it yourself mate! Cheers!

 

[hjkchorong]

Oh, you are right. I did it. I understand it now. Silly me.
Many thanks. :)
View attachment 78203

Could you please explain that Fcos(theta) bit?

 

[hjkchorong]

Could you please explain that Fcos(theta) bit?

Nevermind, I've understood it now.