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.]


Physic Lecture, Week 1, FRICTION!

Some of you may be interested in the material, but not know about the science behind it, or how to even begin solving such problems. This lecture is for you.

With every pop quiz there is a load of concepts integrated into the question. And a lot of material if you wish to dig deeper than the strict "how do I solve it" mentality engineers have :) So I hope to expound upon the material in the question, and hopefully explain how one solves such problems.

Things taken for granted in this particular problem are balancing of forces, an understanding of the "normal force", decomposition of vectors (well, sorta, more on that next week) and probably a few things I'm over looking due to familiarity with the subject.

So, on to the actual "lecture" and feel free to ask ?'s and discuss!

---------------------- Part 1, Types of Friction, and coefficients ------------------------------

This week's problem focuses primarily upon friction, and how it interacts with the motion of objects. To understand how to solve this problem, one must examine the various components of the frictional force that motion across a surface.

Nobody knows, precisely, what causes friction, though there are a couple of general ideas about it. Part of the problem is that there are actually two kinds of friction! There is "static" friction and "kinetic" friction. These vary in strength depending on the materials involved but always (as far as I know) the static friction is stronger than the kinetic friction.

Have you ever noticed that it's harder to start moving an object, than it is to keep pushing it once it's moving? You'll push and pull and tug on that old refrigerator until it finally budges, and then once it's moving you have a much easier time of it. Of course, at some point you stop pushing again, and once again, it's really hard to start sliding. This is due to the differences in the two types of friction.

Friction in general is believed to be a combination of the two surfaces catching and snagging against eachother, even on an atomic scale. The rougher the surfaces, the more they catch, the stronger the friction. Unfortunately there are exceptions to this rule. For instance if you take two highly polished and clean steel plates, and place them together, they can actually fuse together far stronger than if they were rough pieces of metal.

This is because there are two other mechanisms for friction. One is sorta like a suction cup action, where small cracks and fissures in the surface of a material, even a smooth material, shift and flex when the objects are brought into contact. This flexing can create a sort of suction seal that needs to be broken before the object moves.

Then there is of cold welding or bonding. This is the main cause of the two steel plates sticking together. If you bring the material close enough the molecules between the two objects will actually form weak bonds, melding the two materials together.

Of these three basic mechanisms for friction, two of them work best when the object is stationary, allowing them time to adhere (though all three work all the time). And as a stationary has 3 strong frictional mechanisms at work, the resulting force due to friction, for a stationary object, is much higher than if the object is moving, where only the "catch and snag" mechanism works efficiently.

The strength of these two types of friction are contained and communicated by their "coefficients." These are constants, reffered to with the greek letter mu (ยต) and are usually determined empirically. The larger the coefficient, the stronger the frictional force. Typically this value is less than one, however if you use adhesives, the value can exceed 1.

To calculate the frictional force then, you need to know the strength of each type of friction, and correctly use the right type! If the object is sliding past the surface, you use kinetic friction. If the object is stationary on the surface, you use the "static" friction. There are cases where this can be hard to determine. Take, for instance, a walking man. The man is moving, so you would think to use the kinetic friction coefficient. But you'd be mistaken. The key is where the man touches the ground. Usually a walking mans feet do not slide across the surface. They stick firm, an the man then sorta falls past his feet. Since his feet are not moving across the surface themselves you have to use the static friction coefficient.

Wednesday, April 30, 2008

SDC Physics Quiz, Week 1

This is a duplicate of the initial thread at SDC's physics forum.

Alrighty, time to get started. This problem is entirely out of my own head, and I haven't worked it out yet, but it should be doable. As such it's pretty plain and unimaginitive, but I figured we'd start small, and build upon it. It's also part of a multi-step problem that I plan to use to fully evaluate the physics problem we know and love, a block on a ramp! (then on to the dreaded Atwoods machine!)

If anybody has any problem suggestions...I'll figure out a way to take those without cluttering this thread or resorting to e-mail. I do plan on selecting problems that demonstrate the practical side of physics as well. For example I've got a problem in mind later that looks at how fast a car can turn, before it flips over.

Feel free to discuss the problem in this thread. For those of you aren't familiar with the actual physical concepts behind this problem (and how to apply them) I'll be posting a "mini lecture" either later in the week, or with the "official" solution.


A 12kg Aluminum cube rests upon a wooden board. The coefficient of static friction (Us) is 0.2, and the coefficient of kinetic friction is (Uk) 0.1.

a) What is the required force to cause the block to begin moving?

b) What is the position of the block after 11 seconds of appling the force in part a?

c) If we stop applying the force, what is the final position of the block after it stops moving?

d) If we change the material of the block, are our calculations affected? What if we change the shape of the block?

You may use whatever methods you desire and find applicable.


Next weeks preview: We tip the board and introduce trigonometry! :::Shudder:::

Tuesday, April 29, 2008

Test Image!

I'm just toying with blogger and Picasa to see how well I can upload pictures. For those of you waiting for my weekly physics problem threads, rejoice! For this is proof I'm working on it.

For your enjoyment this picture, from is the stock image for my SDC avatar.

You can curse me now for not actually starting said threads just yet.
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Ack! I'm a blogger!

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