Normal force always point perpendicular to the plane?

[aaaa202]

Why is it that the normal force always point perpendicular to the plane? If I imagine the ground as made up of a bunch of particles I find it hard to see, why they should necessarily direct their forces perpendicular to the plane. Consider as a classical example a box sliding down a slope. The gravity acts straight downwards on the particle. What is it that in total makes this downwards press direct upwards with an angle?

 

[tiny-tim]

Why is it that the normal force always point perpendicular to the plane?

it's a mathematical definition

alternative answer: it isn't the normal force, it's the normal component of the reaction force

the whole force from the surface is the reaction force …

it can be at any angle, but we choose to simplify it by calling the normal component the normal force, and the parallel component the friction force

 

[aaaa202]

hmm okay... But if it's only the component of the reactionforce what then happens to the total reaction force? Surely the box slides, because there isn't any component balancing the projection of the gravity along the slope. So the total reaction force must be the normal force...

 

[tiny-tim]

… Surely the box slides, because there isn't any component balancing the projection of the gravity along the slope. So the total reaction force must be the normal force...

no, the box slides (ie stays on the surface) because the normal force (ie the normal component of the reaction force) is balanced by the normal component of the weight

 

[aaaa202]

yes yes.. All that is basic classical mechanics. What I want to know is different, so let me try to explain again.
When gravity acts on the box, it will push directly downwards on the layers of atoms on the slope. Agreed so far?
Good, now by Newtons 3rd law these atoms will push back on the box. I want to know this:
Why doesn't the reaction force from the atoms point in the same way as the downwards gravity? This would be quite bizarre of course since the box then wouldn't slide. But I want to know what limits them from pressing directly upwards.
Please try not give an answer in terms of the ideal physical world presented in clasiccal mechanics, but rather an answer in terms of what actually happens between the molecules. I have studied several lectures in both ordinary Newtonian mechanics and lagrangian mechanics, and I'm not looking for trivial answers :P

 

[tiny-tim]

When gravity acts on the box, it will push directly downwards on the layers of atoms on the slope. Agreed so far?

nope!

gravity acts on the molecules in the box

the molecules in the box also act on each other via the electromagnetic force

they also act on the molecules in the slope via the electromagnetic force

the resultant can be in any direction

… rather an answer in terms of what actually happens between the molecules.

hmm … you do know that, on that level of mangification, neither the box nor the slope is rigid?

 

[aaaa202]

hmm I see what you mean by splitting it up into a friction force and normal force, but consider then if the surface was totally smooth. The downards action on the molecules is somehow still translated into a force perpendicular to the surface. How does that happen.

Edit: hmm.. maybe it doesn't really make sense theoretically to talk about the box pressing directly down on the molecules if the surface is smooth.

 

[tiny-tim]

how does any individual box molecule know whether the friendly slope molecule next to it is in a nice neat line with its neighbours?

and what makes you think they're going to be normally in-line, with a normal reaction force, anyway? ​

 

[aaaa202]

hmm you are right... When it comes to understanding physics on the intuitive basic level, that is often the hardest (compared to for instance lagrangian mechanics which is just math..)
Here's how I understand it:
When the box molecules meet the slope molecules they interact. The nature of these interactions is very hard to describe because it essentially involves all kinds of forces. What we however CAN see is:
The box doesn't break through the slope, i.e. the total force from the molecules must sum to a normal force that balances the component of gravity perpendicular to the slope. Similarly we observe that there is a force of friction which must be the rest of the resulting force...

 

[tiny-tim]

yes

unfortunately, with solids, the molecular level really isn't very practical!