Calculating Minimum Force for Stationary Block Against Wall

[dwan3]

The question:

A block of mass 2.00 kg is pushed up against a wall by a force p vector that makes a 50.0° angle with the horizontal as shown below. The coefficient of static friction between the block and the wall is 0.283.

Determine the possible values for the magnitude of p vector that allow the block to remain stationary.

P max vector = ?
Pmin vector = ?


I have drawn a FBD to this problem. The mass is in the middle. Branching up is the normal force and branching 50 degrees above the horizontal is P. Branching down is the Force friction and the Weight of the Mass

Summing the forces, I get Psin50-20 (Force weight)-5.66 (Force friction) = 0 and Pmax = 33.497 N. I have tried many ways, but I simply cannot get Pmin. What am I supposed to do? Am I supposed to use Pmax to find Pmin?

 

[Mattowander]

What do you mean branching up is the normal force? The normal force should be directed out horizontally from the wall.

The question:

A block of mass 2.00 kg is pushed up against a wall by a force p vector that makes a 50.0° angle with the horizontal as shown below. The coefficient of static friction between the block and the wall is 0.283.

Determine the possible values for the magnitude of p vector that allow the block to remain stationary.

P max vector = ?
Pmin vector = ?


I have drawn a FBD to this problem. The mass is in the middle. Branching up is the normal force and branching 50 degrees above the horizontal is P. Branching down is the Force friction and the Weight of the Mass

Summing the forces, I get Psin50-20 (Force weight)-5.66 (Force friction) = 0 and Pmax = 33.497 N. I have tried many ways, but I simply cannot get Pmin. What am I supposed to do? Am I supposed to use Pmax to find Pmin?

 

[dwan3]

meaning when you draw the free-body diagram, the normal force is 90 degrees above the horizontal

 

[Mattowander]

But the normal force is always perpendicular to the surface ; Hence the term "normal".

 

[dwan3]

okay, i know that the normal force is perpendicular to the surface...

then this makes it a little more complicated because Force is pushing 50 degrees at the 3rd quadrant...so imagine a brick on a wall and you are pushing from down to up...that is what this problem is about...