Finding the possible values of a force pushing a block

[AryRezvani]

Homework Statement

Homework Equations

I believe the only necessary equations would be those utilized to find the X and Y components of a certain force as well as the formula used to find μ_s

µ = f_friction/f_normal

The Attempt at a Solution

Attempt:

I'm not really sure where to start. If someone could just give me a push in the right direction, it'd be much appreciated.

 

[PeterO]

Homework Statement

Homework Equations

I believe the only necessary equations would be those utilized to find the X and Y components of a certain force as well as the formula used to find μ_s

µ = f_friction/f_normal

The Attempt at a Solution

Attempt:

I'm not really sure where to start. If someone could just give me a push in the right direction, it'd be much appreciated.

In all cases, the Normal Reaction Force [to be used in the Friction = μN] is the horizontal component of the applied Force, which they called P.

Also in all cases, the vertical forces acting on the block are: mg, down, P_vert, up plus friction.

If you push with too small a force, the block will slip down, so friction will act up. When the force becomes big enough to stop the slip, P_vert, up + friction, up will equal mg, down.

If you push too hard, the block will slip up, so friction will act down. At the point of slipping

P_vert, up will equal mg, down plus friction, down

Note: P_vert, up means the vertical component of the applied force P

 

[Simon Bridge]

The applied force P presses into the surface as well as along the surface.
Since the block has no acceleration into (or away from) the surface, there must be another force pointing away from the surface to oppose this.

Some people call this the "normal" force, and some the "reaction" force, at the surface.
PeterO has a slightly different picture - where the applied force is divided into normal and parallel components - which works just as well for this situation.

I'm not really sure where to start. If someone could just give me a push in the right direction, it'd be much appreciated.

The starting point is to draw a free body diagram.
It will have force arrows for weight (W), the applied force (P), and the normal/reaction (N) force and static friction (f).
[I like to give friction a lower-case "f", and I don't like subscripts.]