# If friction disregard area, why the direction you drag a long object matters?

I am talking here about dry friction between solid objects, for example a ruler and a table, not anything lubricated or fluid.

I noticed that with a ruler and a table for example, if you drag the ruler like it was a knife, it is much easier to do it than if still holding the ruler in the same position you drag it sideways (like if you are scrapping something).

Also I noticed that when I am washing dishes, if I leave two metal objects (ie: to flat metal areas) in contact, they don't move much, but the same objects, if I try to find deformations that make the area of contact between them smaller, then they can be easily pushed around from rest, or spun.

This also applies to tyre sizes (ie: for dramatic effect, dragster cars with HUGE rear tyres and tiny front tyres).

Also I did some experiments with a paper, ie: holding it down with a finger make it much easer to slide than if I make sure more of its area is in contact, but doing that also is a downforce on the paper, so I guess I can sum that on the normal force.

My best guess is that it all has to do with the normal force, but I am not sure at all... Can someone quench my curiosity here?

• The physics 101 friction that does not depend on area is an approximation good in select regimes (where neither object deforms much and all deformations are elastic). Tire in particular fail the second requirement as you leave some of the tire on the road surface. Note, however, that your ruler case doesn't change the area of contact. Commented Dec 13, 2013 at 16:36
• Real-world materials often are nonuniform -for an extreme example, consider a cheese grater. Move one way, you shred the cheese. Move the opposite way and pretty much nothing happens. Commented Dec 13, 2013 at 16:42
• More on friction and area: physics.stackexchange.com/q/16213/2451 and links therein. Commented Dec 13, 2013 at 21:34
• Contact among elastic bodies is area dependent. Commented Dec 13, 2013 at 23:02
• I believe its the lateral force you apply and gravity that makes a little torsion of the whole object, so that object "hits" (or "tries to sink into") the table on a larger side (when moving sideways), hence have more friction along that larger edge... It's just a guess. Imagine you do this in water : the waves around the object are very non-uniform, and the edge in the front is where more thing happens. I believe it's the same for real life objects, the edge will be hitting the table (at a small angle, but an angle nonetheless, atoms hitting atoms along a larger side when moving sideways) Commented Jul 17, 2014 at 7:42

To state it simply, friction is the resistance to motion of an object within a system, in this case a ruler on a desk.

As you suggest in your question the normal force to the surface is important to friction, the equation is:

Coefficient of friction = force required to maintain constant velocity / normal force

however turning the ruler on its side does not change the force on the desk, as the weight of the ruler is unchanged.

Unfortunately this coefficient is not calculated from a formula, it is empirically measured for each system for which it is needed to be known.

All this means is that your two systems, ruler on side, and ruler on flat have different coefficients of friction.

I realise this may have not have fully satified your curiosity, but I think it is all I can accurately say.

Hope this was in some way helpful.

• I doubt noone could figure yet WHY a certain combination of materials and shapes have a certain coefficient... It is THAT hard? It does not explain for example why bigger tires are better, or why very smooth objects (like two large sheets of metal) seem to get more friction when you ensure more of them are in contact... Commented Dec 13, 2013 at 19:53
• @speeder It's not friction that makes wide tires better. It's stiffness, heat capacity, and wear. Commented Jul 16, 2014 at 12:37
• – user4552
Commented Oct 23, 2014 at 15:33

Deformities in the surface cause more friction. As it's rightly said friction is a necessary evil, friction between the surface helps in forward movement as well. Like when we walk on a rough surface we get more forward push.A slippery and smooth surface is really difficult to walk on. A very nice article with Free Body Diagram is here, which you can check pls: How friction helps in walking