Block on a Plane (Classical Mechanics)

[vcm1992]

I've taken intro to classical mechanics, but am really not sure about how this example calculates the friction force and the normal force...I usually break down the force vector into components, and I understand that this is probably a much more simple way to calculate the perpendicular and parallel forces, I just can't really grasp how the author is coming to these conclusions. Sorry if this is a really simple problem! Any help or other textbooks that might explain this would be appreciated! Thanks.

 

[tnich]

You have shown us the solution from your textbook, but not the problem that it's a solution for. From the third sentence of the solution and the drawing, it appears that there is a horizontal force $Mg$ applied to the block in addition to the vertical force of gravity. Given that, the equations for $F_f$ and $N$ are just the force balance equations in the tangential and normal directions.

 

[Dr.D]

We might very well ask why Mg acts in both the horizontal and vertical directions. This looks like a mistake to me.

 

[tnich]

We might very well ask why Mg acts in both the horizontal and vertical directions. This looks like a mistake to me.

We won't know until we see the problem statement.

 

[A.T.]

I just can't really grasp how the author is coming to these conclusions.

By balancing all forces parallel and perpendicular to the plane, as the text says. It might help you to draw the parallel and perpendicular components as separate arrows.

 

[vcm1992]

You have shown us the solution from your textbook, but not the problem that it's a solution for. From the third sentence of the solution and the drawing, it appears that there is a horizontal force $Mg$ applied to the block in addition to the vertical force of gravity. Given that, the equations for $F_f$ and $N$ are just the force balance equations in the tangential and normal directions.

The problem states that "A block of mass M rests on a fixed plane inclined at an angle theta. You apply a horizontal force Mg on the block. Assume friction force is enough to keep the block at rest. What are the normal and friction forces that the plane exerts on the block? For what range of angles will the block remain at rest?"

I understand that these are the force balance equations and I have no doubt that they are correct, I think that my question is more why are they correct? As I said, my professor taught breaking down force vectors into x and y components, so I do not understand HOW this balance equation is true. What is the assumption here? Thanks!

 

[vcm1992]

By balancing all forces parallel and perpendicular to the plane, as the text says. It might help you to draw the parallel and perpendicular components as separate arrows.

Hi, thank you so much for this advice! Although I did break it up into components before, I finally grasp the logic. I really feel like this way should have been taught as it does make it easier to orient the components with respect to the plane and not the x and y axis. Thank goodness this finally makes sense.