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Thursday, May 23, 2024

What Even Is Friction, Anyway?

We can't escape the fact that we live in a world governed by friction. There's friction in your car engine, there's friction between your feet and the ground, and there can even be friction in your relationships—but that's actually a different kind of friction that I won't get into. No, I'm just talking about the frictional force resulting from two surfaces interacting with each other. We often think of friction as a bad thing that we want to reduce—but there are also many cases where we need it.

What the Heck Is Friction?

I'll be honest—friction is pretty complicated. Imagine that I have a block of wood sliding on a table. In some way, the atoms on the surface of the wood block are interacting with the surface atoms on the table. If you want to look at each of these individual atom-atom interactions, you are going to be overwhelmed with the numbers. Even a small block that is 1 cm x 1 cm might have as many as 1016 atoms on the surface. No one has time for that many calculations.

But don't worry. We have a model that works fairly well, (even though it's not perfect). This model says that the frictional force is parallel to the surface and always pointing in the opposite direction as the motion (or possible motion) of the two surfaces. That is to say, the frictional force pushes in a direction to try to prevent sliding.

If the two surfaces are stationary relative to each other, we call this "static friction." The maximum magnitude of the static frictional force depends on how much these two surfaces are pushed together (this is the normal force, N) and the types of materials interaction (wood vs. steel or whatever) characterized by the coefficient of static friction (μs). We can write this as the following mathematical model.

Yes, that "less than or equal" sign is important. Let me show you why it's there with a simple experiment that you can try yourself. Take a book and put it on the table. Put pressure on the book horizontally, but not so much that the book slides. If you drew a force diagram, it might look like this.

If the magnitude of your pushing force was 1 newton, then the frictional force would also have to have a magnitude of 1 newton. The horizontal forces have to add up to zero newtons, since the book is at rest (zero change in velocity). That's just the way forces work. OK, now push a little bit harder—but not so hard that the book slides. Now the diagram might look like this. Notice that the push arrow and the friction arrow are still balanced, but both are bigger (greater force).

Since the book is STILL stationary, the forces must STILL add up to zero. That means the frictional force has to increase the same as the pushing force to make the net force zero. It's the only way to keep the book at rest. If the friction force was less than the pushing force, the book would accelerate in the same direction as the push. If the frictional force was greater than the pushing force, the book would accelerate in the opposite direction as the push—and this would be super weird. Just imagine pushing a book and it accelerates the opposite way. That would be crazy.

The only way to make this work is to have a variable frictional force. If the frictional force didn't exactly match the pushing force, weird stuff happens. That's why the less-than-or-equal sign is there. However, once the book DOES start to move we can use a slightly different model of friction. It looks like this.

Unlike static friction, if the two surfaces are rubbing and sliding, the frictional force is essentially constant. That's just the way the model works (based on actual experimental evidence). Again, it's not a perfect model—but it works fairly well in most cases.

Why Is Friction Bad?

Friction is an interaction between objects in contact with each other. Pretty much everything we see touches something else—so friction is all around us. But it's also not always great. Consider the following situation. I have a smooth bowl, and I place a coin on the inside wall of the bowl near the edge. When I let go of the coin, it slides down toward the center of the bowl and maybe it goes a bit up the opposite side. However, it won't go up as high as it started—because of friction.

If you consider this sliding coin from an energy perspective, it should start off with some gravitational potential energy (which depends on the height of the coin). As the coin moves down the bowl, the gravitational potential energy will decrease, resulting in an increase in kinetic energy (which depends on the speed of the coin). Once it goes back up the other side of the bowl, it will decrease in kinetic energy as it slows down and increase in potential energy as it gets higher.

But it doesn't rise as high on the other side of the bowl. That means that there is some missing energy. Well, it's not REALLY missing—it went somewhere. In the case of friction interactions, there is some energy that goes into increasing the temperature of both the coin and the bowl. We call this thermal energy. If you take an infrared camera, you can see the surfaces heating up as things rub against each other. Check out this gif showing my shoes skidding on the floor (in infrared, the brighter colors represent higher temperatures).

For most situations, we don't want things to warm up—but they do. Check this out: Here is an infrared image showing the axle on a freight train.

If those axles heat up, that means they have an increase in energy. If the axles increase in energy, the train has to decrease in kinetic energy and slow down—even on a flat track. If you didn't have a train engine pulling the cars, it would eventually slow down and stop. This friction interaction also happens inside the internal combustion engine in most cars. As the pistons move up and down, they rub against the engine and increase the temperature of stuff. Yes, for an engine in a car things also get hot from all of the burning gasoline. But it would be better with frictionless internal parts—less energy loss. This is why we try to make machines like this with as little friction as possible. Friction reduces the amount of useful energy we can get out of machines and stuff.

Why Is Friction Good?

I saw this new thing online. It's a way to play a virtual reality game. Yes, you would wear the VR goggles—but in order to allow the human to pretend to run around, there is this low-friction base. That way the gamer can run but not go anywhere. It's cool even though it would probably make me sick.

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Of course, with no (or very little) friction, you couldn't get the ground to exert a horizontal force on your feet. Without this horizontal force, there is no change in horizontal motion. That means if you are at rest, you would stay at rest. Perfect, right? No. There's still a problem.

Humans have been living with friction for so long that we've become accustomed to it as an interaction. Even going through the walking motions on a low-friction surface (think about walking on ice) is pretty tough. Imagine you are taking a step. At some point your front foot is off the ground and your back foot is touching. Normally, this isn't a big deal. I don't know about you, but I can even walk with my eyes closed. Here is a diagram showing the forces on you during a walk on normal ground (with friction).

The red dot represents your center of mass. If you want to pretend like the gravitational force acts at just one point on your body—it would be the center of mass. The other two forces are due to the ground. They are the normal force pushing up and the frictional force pushing forward. But it's not just about forces, it's also about torque. Torque is the rotational equivalent of a force and it depends not only on the magnitude of the force but where that force is applied. A force causes a linear acceleration, but a torque would cause changes in rotational motion. However, for this example we really just need to think about the rotational directions of the torque.

Look at the normal force. Since it's pushing up and to the right of the center of mass, this force would produce a counterclockwise torque, as it would tend to make the human rotate counterclockwise. The frictional force pushes to the left and underneath the center of mass. This force would produce a clockwise torque. Since these two torques are in opposite directions, they at least partially cancel and the human stays mostly upright. Yay for the human.

Oh, but now the person is on ice and there is no friction. If the body position is the same, the only change will be the lack of the frictional force. Like this.

Now there is only the counterclockwise torque from the normal force. The person will start to rotate about the center of mass. If this is you walking on ice, you better be careful. You could wind up with your face on the ground—which is usually bad.

But it's not just walking. What if you want to kneel down on a frictionless surface? Yup, that's going to be a problem too. Actually, let's imagine you're kneeling down and then want to stand up (probably as part of that VR game we are playing). On a normal surface with friction, this is what the forces might look like as you are standing up.

Notice that there is a frictional force pushing backward on your front foot and forward on your back foot? You can use this friction to push your front foot forward on the ground. Since there is friction pushing on your back foot, you don't slide away. But this prevents your front foot from sliding so that you can straighten your leg. Because the two feet don't slide, this results in an upward motion of the whole body. Boom—you are standing.

Now remove the frictional force. Not only do you have to push yourself up, but you have to pull your leg in toward your body. I don't know about you, but my legs don't have much strength for a motion like that. It would be super difficult. It's not the same as standing up on normal-friction ground.

Just to be clear—friction isn't just useful for stuff like walking and kneeling. We use it in other places too. The friction between your car tire and the road allows a frictional force that can increase your speed, decrease your speed, and even turn your car. Of course, you already know the importance of friction while driving if you've ever driven on ice. It's pretty tough, right? So, although friction is sort of bummer when it comes to losing energy—it's sort of a good thing when it comes to moving around. We would be doomed without it.

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