Fricition: Block on inclined plane

[yellowsnow]

Homework Statement

What is the maximum angle (theta) for which the block of mass m in (figure) will not slide down the incline if the coefficient of static friction is 0.30 and ||P|| = 0?

Figure:

Homework Equations

I know this isn't a hard problem, but I just seem to be stuck on it.

The Attempt at a Solution

I started by replacing the force "P" with it's X and Y components, then adding the 2 forces to the block, "mg" and "N", the normal force.

After that I'm stumped. I'd appreciate if anyone can help me.

 

[tiny-tim]

Welcome to PF!

Hi yellowsnow! Welcome to PF!

What is the maximum angle (theta) for which the block of mass m in (figure) will not slide down the incline if the coefficient of static friction is 0.30 and ||P|| = 0?
…
I started by replacing the force "P" with it's X and Y components, then adding the 2 forces to the block, "mg" and "N", the normal force.

(do you really mean ||P|| = 0 ?)

It's a lot easier if you replace g, by its slope and normal components

 

[Mene]

I would first start by clarifying the problem and making sure all the necessary information is provided. In this case, I would ask for the mass of the block and the angle of the incline.

Once all the necessary information is provided, I would then begin by drawing a free body diagram of the block on the inclined plane. This would help me visualize all the forces acting on the block and their directions.

Next, I would write out the equations of motion for the block in both the x and y directions. This would involve using Newton's second law and the equations for friction and the normal force.

Since the block is not sliding down the incline, we can set the net force in the x direction equal to 0. This would give us an equation with the coefficient of static friction, the normal force, and the weight of the block. We can then solve for the maximum angle by substituting in the given values.

Therefore, my response to this content would be to clarify any missing information, draw a free body diagram, and use the equations of motion to solve for the maximum angle. I would also suggest checking the calculations and making sure all units are consistent.