Saturday, May 3, 2008

Friction and the Normal Force

Okay, so I’ve discussed the cause(s) of friction, and why there are two different types. But what determines the strength of the friction? The answer is twofold. First, is the materials in question, and their specific properties. Are you looking at rubber on paper? Or metal on concrete? Sheep on various surfaces? Etc… Then you have to consider things like is it rough, smooth, how it’s textured, yada yada yada…

Only serious nuts actually try to figure these things out from scratch. Most of the time the answer is determined empirically. You drag the object and measure the forces required to start it moving, and to keep it moving. This is all wrapped up in the coefficients I discussed in my last post.

The other key factor is pressure, namely how hard the two objects are pressed together. This can be as simple as the weight of the object (on a level surface), to how hard you press the objects together (like sand paper and wood). It can also get a bit more complicated, say if you’re concerned about the object on a tilted surface (a.k.a. ramp). If the two surfaces are pressed together harder, then all three sources of friction I mentioned above work better. Things deform and snag more often, the molecules bond together better, and more miniscule stress fractures arise to help “suction cup” the surfaces together.

This force pressing the two objects together is characterized as the “Normal Force.” This normal force is actually the force exerted by the surface, on the object. It’s related to gravity, and to other forces bringing the objects together, but it is explicitly independent as it can be proportional to combinations, or only portions, of many of these other forces. This Normal Force is the force the surface exerts to prevent the object from passing through it. For example it’s the force your chair is exerting upon your derrier keeping you from falling to the floor.

The reason it’s called the “Normal” force is because of the way the force is oriented compared to the surface creating it. It is always, always, always, 90 degrees to the surface (perpendicular, orthogonal or, gasp! NORMAL to the surface). On a flat level table, the normal force is pointed straight up. If you tilt the table, the normal force is also tilted (by the exact same amount!)

The magnitude (read “strength” for those not steeped in physics lingo) of this force is exactly equal to, and opposite of any forces pressing straight down into the surface (i.e. also NORMAL to the surface, but pointed towards the surface). Take our chair, derrier example. The chair pushes up against your body with the exact same force that your body pushes down upon it. They completely balance out and so you don’t move at all. If they didn’t balance out you’d have one of two consequences:

A) The chair does not push back hard enough, meaning the “downward” force of gravity isn’t completely nullified, and so you accelerate downwards…through the chair. I.e. you broke the chair!

B) The chair pushes back harder than you are pressed down into it, causing you to accelerate upwards, and be launched out of the chair. Now, this doesn’t happen unless somebody spring loaded your chair as a nasty practical joke, so we can rule this one out.

Now, if the surface is tilted, you have to do a bit of math on the forces involved to figure out how much of the forces exerted upon the object are directed straight into the surface below. Basically you have to break apart each force into separate components, a “vertical” and “horizontal” component. The “vertical” components are directed perpendicular to the surface…which is why I put “s around the word vertical. Afterall, in physics any way I want to call up, is up. It’s only required that I be consistent. These “vertical” portions of the force push the object straight into the surface, acting only to increase the friction. They do nothing to move the object. The “horizontal” portions are aligned parallel to the surface and do nothing to add the friction. These horizontal portions act only to move the object!

If that last paragraph confused you a bit, you’re not alone. Thousands of first years physics students struggle with the concept every semester. I’ll also work to clear this up next week.

Luckily, this weeks problem is on a flat and level surface, and the force being applied is directly down (gravity) or directly across (pulling/pushing to move it). As no force is at an angle, we don’t have to hurt our brains.

So, the normal force in todays problem is just like our chair-derrier example. Gravity acts upon the block down towards the surface. The surface exerts the Normal force, straight up and directly countering gravity. So the normal force = gravity in this case. To determine to the force of gravity…I’ll leave up to you for now.


Jack Harvey, John Culvenor, Warren Payne, Steve Cowley, Michael Lawrance, David Stuart, and Robyn Williams of Australia, for their irresistible report "An Analysis of the Forces Required to Drag Sheep over Various Surfaces."
[PUBLISHED IN: Applied Ergonomics, vol. 33, no. 6, November 2002, pp. 523-31.]


1 comment:

Anonymous said...

Good post.