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About this Lesson
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- Length: 13:40
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- Posted: 07/02/2009
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This lesson was selected from a broader, comprehensive course, Physics I. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/physics. The full course covers kinematics, dynamics, energy, momentum, the physics of extended objects, gravity, fluids, relativity, oscillatory motion, waves, and more. The course features two renowned professors: Steven Pollock, an associate professor of Physics at he University of Colorado at Boulder and Ephraim Fischbach, a professor of physics at Purdue University.
Steven Pollock earned a Bachelor of Science in physics from the Massachusetts Institute of Technology and a Ph.D. from Stanford University. Prof. Pollock wears two research hats: he studies theoretical nuclear physics, and does physics education research. Currently, his research activities focus on questions of replication and sustainability of reformed teaching techniques in (very) large introductory courses. He received an Alfred P. Sloan Research Fellowship in 1994 and a Boulder Faculty Assembly (CU campus-wide) Teaching Excellence Award in 1998. He is the author of two Teaching Company video courses: “Particle Physics for Non-Physicists: a Tour of the Microcosmos” and “The Great Ideas of Classical Physics”. Prof. Pollock regularly gives public presentations in which he brings physics alive at conferences, seminars, colloquia, and for community audiences.
Ephraim Fischbach earned a B.A. in physics from Columbia University and a Ph.D. from the University of Pennsylvania. In Thinkwell Physics I, he delivers the "Physics in Action" video lectures and demonstrates numerous laboratory techniques and real-world applications. As part of his mission to encourage an interest in physics wherever he goes, Prof. Fischbach coordinates Physics on the Road, an Outreach/Funfest program. He is the author or coauthor of more than 180 publications including a recent book, “The Search for Non-Newtonian Gravity”, and was made a Fellow of the American Physical Society in 2001. He also serves as a referee for a number of journals including “Physical Review” and “Physical Review Letters”.
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You may have noticed I've been avoiding talking about friction. There's not really any deep reason for that. There's nothing fundamentally different about frictional forces than there are about any of the other forces we've been looking at. The force of gravity, the force of tension in a rope, contact force between solids, these are all just examples of physical pushes and pulls. And friction is another one. I've been avoiding friction because it's a little bit more complicated than the others. It's a little bit more difficult to quantify. And really, in the beginning of a physics course, what you're after is fundamental laws of physics, Newton's laws, universal laws, which describe the motion of any particle under any arbitrary force.
Now that we're all set up with that, we can consider any arbitrary force we want. So we're now at a stage where it's okay to consider the force of friction. So there are various different kinds of friction in the world, and perhaps one of the first ones that might become relevant in typical physical problems would be sliding friction. If you have a block and you push it along the surface, you can feel that there's something resisting the motion. It's a frictional force. It's a frictional force between the table and the block. And the direction of that frictional force is just exactly opposite the motion. If I push it this way, the force of friction is that way. If I push it this way, the force of friction is that way.
It would be nice if we could come up with a simple formula for the magnitude of the force of friction. And I'll come up with one, but it's going to be approximate. It's approximate because friction depends on a lot of subtle details. It depends, a little bit, on how rapidly the thing is moving, what's its velocity. It depends a little bit on that, but not a lot. It depends, a little bit, on the shape and size of this block. For instance, if I slide it along like so, there's a certain frictional force. If I slide it along like so, there's a certain frictional force. You can measure these frictional forces and you'll see that they're not all that different. It's a big surprise. There's a big surface area here. You'd think that would mean lots of friction. A small surface area, maybe you would think that's a small frictional force, but it's not. How do you measure the friction? There are lots of techniques.
A crude and barely effective one would be the following. I could take this scale. It's crude in part because the scale is crude, and because the force of friction is changing all of the time. Like different pieces of the paper have slightly different amounts of frictional force, because the paper isn't completely uniform. But the basic idea would be this. Supposing I start pulling this sideways with a uniform speed. So watch the needle as I do that. You see it's around two, and as I move it's pretty much constant. So think about what's going on. I'm sliding it with a uniform speed. That means no acceleration. So Newton's second law says if there's no acceleration in the x direction, the net force must be zero. The scale is reading the force that's pulling it in this direction. The only other relevant force in the x direction is the force of friction. So by Newton's second law, the force of friction and this scale reading, they'll have the same magnitude. So that's a nice simple experimental technique to measure the force of friction.
I'm telling you that it depends a little bit on speed, but not much. It depends a little bit on the details of the shape, but not much. What does it depend on? The big thing, the most important thing is this. If you stick a big old heavy weight on the top, the force of friction increases dramatically. In fact, if you double the weight, you will double the force of friction as you slide it across. So is that exact? No, it's an approximate formula. I'm afraid that I really can't give you an exact formula. But here is the rule of thumb for friction. And it's good enough to use when you're solving problems if you want to see the scale of friction and the sort of basic principles.
If you have an object and you're sliding it to the right, the force of friction is going to be to the left. This is a force diagram, so I don't want to put the velocity vector in here. I just have to remember it. Maybe I draw another diagram which tells me which way it's going. In the force diagram, there might be a force. And what should I call friction? This is friction of sliding objects. And since the word kinetic is sort of a word that implies motion, this is usually called kinetic friction. And there are different symbols people use. I use a small f[K], friction, kinetic friction. So that would be resisting the motion. This might be the only force if I launched something sideways, like a skier who has come down a hill and is now sliding across the flat. This might be the only horizontal force acting. So the object, if this is the case, will be accelerating in that direction, and will slow down and come to a halt.
What is the formula for the kinetic friction? What I just argued to you is that the kinetic friction depends on, I said, the weight. But I was thinking kind of in the vertical direction. What would happen if I pushed this against my hand and slid it up and down. It's not the weight that matters. It's how hard the two objects, that are sliding against one another, are squeezed. It's really the normal force. So let me finish this force diagram. I've only drawn the horizontal components. There's going to be a normal force, because this is sitting on some surface. And of course there will be a weight. Newton's second law says weight and normal force, in this nice simple situation, have to balance, because it's not tipped. It's not rising up or sinking down. There's no other forces. So the normal force and the weight are equal in this kind of normal ordinary situation. If I was to push down on this object, I would be adding another downward force. And the normal force would compensate, and there would be more friction sideways if I was doing that. So the frictional force depends on the normal force. It's the force of the surface upward, perpendicular to the surface on the object. So f[K]--I'm about to write an equal sign, but let[ ]me start off with proportionality. It's proportional to the normal force. Let me not put arrows on this equation, because the friction force is in a totally different direction than the normal force. It doesn't really make sense to put arrows, because that would imply that friction and normal are pointing in the same direction. So I could put absolute value signs, or just not put arrows over the top. So it's proportional to the normal force. Is it equal to the normal force? No, it depends on the surfaces. Wood on paper has fairly low friction. Skier on snow has even less friction. So, certainly, the force of friction doesn't have to equal to the normal force. So if it's proportional, what we will write is friction is equal to a constant times N. And this constant is given the name mu. It's the Greek letter mu. It's just the symbol for the coefficient of kinetic friction. And because this is sliding friction, we have to be careful to label mu with a K, it's mu[K] times N. Mu[K] is a number. Notice that this is a force, and that is a force, so mu is a dimensionless number. And you just have to either measure it, or look it up in some list of coefficients of friction. It depends on the materials involved. Is it rubber on concrete? Look that up. It's a fairly big coefficient. Big in this case means something of order one. Typically mu[K] is a number between zero and one. Zero means no friction at all. One could, in principle, be even larger, but very seldom is in nature.
So this is a nice approximate formula, and we could use it in any problem. When an object is moving, you could draw the force diagram, and you've got a lovely formula for the kinetic friction. Well what about when something is just sitting still? It's a slightly different story. If the object is just sitting there and I push, it doesn't budge. If I push harder, it still doesn't budge. Think about the force of friction. When I'm just pushing a little bit, the force of friction has to be opposing it, because it's not moving. Newton's second law says, if you're not moving, no acceleration, no net force. So if I push a little, there's a little bit of friction. If I push a lot, there's a lot of friction. So this is a weird case. I don't have a formula for what's called static friction. Static friction is when the thing is just still sitting still. So I can't tell you force of static friction equals something, because it depends on how hard I push. Static friction is always adjusting itself. The harder you push, the harder friction pushes back. It's kind of neat that way. Things really do like to stay at rest when there's friction involved. It's kind of intuitive.
There's always a breaking point. If I push hard enough, finally it will start to slide. And what's the breaking point? So that would be the maximum force of static friction. I'm going to write it with a less than or equal to sign. Static friction can get bigger and bigger, but it will never get bigger than a constant times the normal force. So a formula that looks like the kinetic friction formula, the s means static. And this is a different number. The coefficient of static friction is always a number which is always greater than the coefficient of kinetic friction. What that means is that if you're pushing, you can push harder and harder and harder, and finally, when you reach the break away point, as soon as it starts to move, since the coefficient of kinetic friction is a smaller number, it's actually easier to move once it gets moving. That's something that you may have noticed. You're pushing a box across the floor, a box full of books, and you can't get it budge, and you can't get it to budge, and finally it breaks free. Then it's really a lot easier to move. The coefficient of kinetic friction is typically smaller than the coefficient of static friction.
So how do you find the force of friction if you don't have a formula? This is just a less than sign that says the force of friction could be anything up to this. Well you've got to use Newton's second law. If you have a situation where you know that the object is just at rest, you know static friction is in play. You draw the weight and the normal force. Those two vectors are probably going to be equal and opposite if it's flat. In fact, if it's flat, they will be. There are no other forces because it's not accelerating up or down. Newton's second law says they have to balance. These two forces will have to be equal and opposite, if they are the only forces. This is your force. This is the static friction force. Again, if it's static friction, it's not budging, no acceleration. F[net] must be zero. The fact that this arrow and that one look to be about the same is just an accident of this graph. If I push a little, this would be a little arrow, and that would be a little arrow. These are just the weight of normal. And the harder I push, the bigger these get. And then there's that maximum. So you would use Newton's second law to deduce from this diagram, from the force diagram, what's static friction.
Let me show you just a little picture that summarizes this story. This is the force of friction versus the applied force. So imagine you've got a block that's sitting still, and you start to push. And as you march along this axis, you're pushing harder and harder. At first, the force of static friction will always equal F in magnitude, because it's sitting still. So the force of friction and your applied force have to balance. So this is exactly a straight line, exactly, up to a maximum f[s,max], which we've got the formula for, mu[s] times the normal force. And then suddenly it breaks free. So you will get this jagged line. Why is it jagged? Well this is not a very exact plot, it's an approximate graph over here. As I said, friction is a little bit complicated. But this is just to indicate that, roughly speaking, you will end up with a constant force of sliding friction f[K], whose value will be equal to mu[K]N. This is a little bit less than that, because mu[K] is a little bit less than mu[s].
So friction is something that you can deal with, with the two formulas , and . Remember that these refer only to magnitudes. You've got to think about the motion to decide the direction. And then, just like any other force problem, you're set to go. There's nothing fundamentally different about friction than any of the other forces we've been talking about, except that these formulas aren't quite so exact. We've been making some approximations. But given these approximations, you draw the force diagram. You can solve dynamics problems with sliding and static friction, just as easily as you can solve any other kind of dynamics problems at all.
The Forces of Friction
Understanding the Frictional Force Between Two Surfaces Page [3 of 3]
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