When we discuss normal forces, I drum into the students’ heads that the force is perpendicular to the surface. They get that eventually. Where they get into trouble is on an incline when the angled component of the weight of an object F(i)=mg*cos(Θ). I called this force F(i) meaning the force exerted on the incline (and the (i) is really a subscript, but I can’t make that work in this blog).
This is sometimes the normal force, but not always. If there are any other forces, like F(x), in the angled Y-axis, then the normal force is not the same as F(i).
Here is what I tell them: imagine there is a scale under the object in question, what would it read? If it is only the object and no other forces, then F(n) is F(i). From the drawing above, it’s fairly clear that there are two forces down that combine to create our normal force up. The scale under the block would read the value of F(i) + F(x), so that is our F(n).
