Kinetic friction, air resistance, and effect of velocity

Hi,

So I've read that kinetic friction does not depend upon velocity, but that air resistance does depend upon velocity. I hope those two statements are correct from the get go.

I can see why the force of kinetic friction does not depend upon speed using a simple thought experiment. You have two surfaces that are smooth except for little dome-shaped studs on each. Let's say you only hit one stud at a time. At any instant you are only overcoming the resistance from one stud hitting another. This should not depend upon how quickly studs collide in succession as you only hit one at any instant. So, it makes sense to me that the force remains roughly the same.

Now, with air resistance you have air molecules sliding across the surface and also colliding with it in the direction of movement (we are pulling one surface through air and the surface has depth and this perpendicular edge will slam into air). At anyone intance in time, you would seem to have the same situation as in the previous paragraph and so air resistance would not change with the velocity of the surface moving through the air. However, I believe it does change.

Any intuitive explanation for why? I'm thinking it has something to do with air being able to move along with the surface and also air piling up against the front ledge where impacts are occuring.

rcgldr
Homework Helper
In the case of the air, the air is accelerated in the direction of the object. The rate of acceleration and the amount of air affected is such that at sub sonic speeds below mach 0.4, the drag increases with the speed^2 of the moving object. At higher speeds, it gets more complicated.

In the case of of sliding surfaces, the friction is generating heat as opposed to accelerating some amount of mass. Depending on the surfaces, kinetic friction may decrease somewhat as velocity increases.

As rcgldr said, air gets accelerated in the direction of the object. The faster the object moves, the faster the air gets moved. Since Energy = .5mv^2, the energy needed to accelerate the air rises as a square function of the object’s velocity….and therefore the force needed to accelerate the air rises as a square function of the velocity.

I never actually thought much about this before, so I just kind of pulled this out of my @. Maybe someone can comment on the above line of thinking?

This all makes some sense and I appreciate you taking the time, but what in the following view is incorrect?

A bit of texture on a sliding surface hits a bit of texture on an opposing, non-sliding surface much like something hitting air molecules. Whether the object struck can move or not, it will still strike the sliding object as hard as it is struck, correct? And this should be related to velocity in both cases. I understand that the air actually is accelerated, but with two surfaces, one is attempting to accelerate the other right? If kinetic friction generates heat then it is increasing the average velocity of the molecules involved, which at some scale means acceleration.

I am thinking of surfaces as these simplified structures with jagged teeth, that is likely my conceptual hurdle.

rcgldr
Homework Helper
I am thinking of surfaces as these simplified structures with jagged teeth, that is likely my conceptual hurdle.
Using the jagged teeth model, as speed increases, the surfaces will separate slightly sort of like a boat skipping on wave tops at high speed due to deformation (compression) of the surfaces and/or actual displacement of the objects involved (assuming there isn't some huge force keeping the surfaces together). In this case, the kinectic friction decreases with speed, even in a vacuum where any void formed between surfaces isn't filled with air. It's complicated, and there's a point of diminishing effect at higher speeds.

Thanks.

Still struggling with why one piece of sandpaper accelerating the molecules in another piece it slides past (which raises the temperature by increasing average velocity of molecules) is significantly different from a box hitting air molecules and accelerating them.

Thanks.

Still struggling with why one piece of sandpaper accelerating the molecules in another piece it slides past (which raises the temperature by increasing average velocity of molecules) is significantly different from a box hitting air molecules and accelerating them.

As rcgldr explained, the “jagged teeth” won’t actually be interlocking when there’s relative motion between the surfaces, and so they won’t be ripped out and accelerated. The portion that does get accelerated…perhaps that portion does rise as a square of the speed.

I guess. I don't really know, I'm just discussing because I think I understand friction as much as you do.

But in the end, don’t be surprised if you’re struggling, because ultimately nobody really fully understands friction. I think the latest model states that friction is more due to chemical bonding between atoms, and not due to “jagged teeth”. Nevertheless, “jagged teeth” do play a major role in some materials, such as rubber on road. In the end it’s both these effects and who knows how many others that get rounded off to “friction = normal force x coefficient of friction”.

Thanks for the thoughtful post, Lsos. And it is enjoyable to discuss this.

I'm glad I'm not the only one who sees the difficulty in this seemingly simple concept.

In case I was unclear, I was speaking of the atoms in the jagged teeth. Even if the jagged teeth don't seem to move, for them to get hotter, I believe the atoms in them must be moved. Not sure if that helps out.

It is frustrating because most texts accessible to a non-physicist like myself do not share intuitive insights into how to understand these things. They will be succinct and give a the equations and various laws of regularities, but this always leaves me wanting. Often, the next step up is a full course in the subject, which I don't currently have time for. So, I hope I'm not trying to get "fast food physics", but it is often possible to hear or read a very good analogy that makes it dawn upon you, and that is rewarding.

Hi,

So I've read that kinetic friction does not depend upon velocity, but that air resistance does depend upon velocity. I hope those two statements are correct from the get go.

I can see why the force of kinetic friction does not depend upon speed using a simple thought experiment. You have two surfaces that are smooth except for little dome-shaped studs on each. Let's say you only hit one stud at a time. At any instant you are only overcoming the resistance from one stud hitting another. This should not depend upon how quickly studs collide in succession as you only hit one at any instant. So, it makes sense to me that the force remains roughly the same.

Now, with air resistance you have air molecules sliding across the surface and also colliding with it in the direction of movement (we are pulling one surface through air and the surface has depth and this perpendicular edge will slam into air). At anyone intance in time, you would seem to have the same situation as in the previous paragraph and so air resistance would not change with the velocity of the surface moving through the air. However, I believe it does change.

Any intuitive explanation for why? I'm thinking it has something to do with air being able to move along with the surface and also air piling up against the front ledge where impacts are occuring.

Well, in my opinion, it is just like what you said, impacts are occuring. Air resistance is simply a force, and force is simply change of momentum. When air molecules and plate collides, there would be momentum change and energy change. In the air-plate system, E=p^2/2m, thus object with less mass (air) would have more energy after collision. If the plate is moving faster, the energy gained by molecules increased further, which means momentum change is also greater.

Otherwise, simply thinking about faster moving cars would collide harder with faster speed would solve your problem.