# Direction of Kinetic Friction and Static Friction

sophiecentaur
Gold Member
static friction force tends to accelerate the braking wheels rather than slow them down.
In a complicated system like the drive to car wheels, at every point of contact between the parts, N3 applies and you can choose a force in either direction. The effect on the car is to slow it down (of course) and it is fruitless to spend too much time looking for a paradox; there is not one. More than 20 posts on this thread is evidence that this approach just generates confusion.
I made the point much earlier that everything can be resolved with a diagram (and I haven't seen one on this thread) which includes all the forces with and without slipping. Rather than demanding a resolution to this question, people who have a problem should really sit on their own with a paper and pencil and figure it out independently. Intuition can easily fail you in a case like this
This is not strictly right. But it's really a matter of how you are defining things. Are you referring to acceleration of the CM of the wheel, or to its rotational motion? If there were no friction, the wheels would be travelling forward (rotating or not; that's irrelevant). Friction contact with the ground would, of course, tend to cause peripheral speed (relative to the axle) of the wheel to approach the translational speed of the car. Assume that the wheel is massless. The only forces will be due to the force on the mass of the car, acting through the axle. Take an instantaneous fulcrum, half way between the contact point and the axle and you have equivalent forces slowing the car and forcing the wheel to rotate.
If the wheel has mass (moment of inertia, actually) and not rotating, but moving forward, when dropped onto a surface with finite friction, there will be a backwards force on the contact point until its rotation speed reaches the linear speed. But there will be a transfer of linear KE to rotational KE, which will slow up the wheel. You could say that you have 'sped up' the wheel by making it rotate - but have you?

You could say that you have 'sped up' the wheel by making it rotate - but have you?
If it in context of the TC question, - yes I have. Because this:
. Are you referring to acceleration of the CM of the wheel, or
is out of context as far as I understand. I have asked TC to describe the professor's example with two bodies more detail, but without an answer. So as I have understood the speech goes about the point of contact moving. Otherwise it can be built arbitrarily complex schemes of arbitrarily complex conjugate bodies and constructive discussion on the verge of it will completely lose the constructivity. I have no to add something and I do not know if it needs because TC keeps silence. Let we wait to him reaction.

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A.T.
My point was that, if the (dynamic) friction force is in the same direction as the motion, this would involve getting energy out of the system (Work being force dot displacement).
Work is frame dependent, and of course you can have inertial frames, where dynamic friction on an object is in the same direction as the motion of that object, thus doing positive work on that object. This doesn't violate energy conservation, because the equal but opposite friction force on the other object is doing more negative work on the other object.

sophiecentaur
Gold Member
Work is frame dependent,
That's true, in principle but my point is that, if the brakes and the tyres get hot, the procedure cannot be looked upon as reversible. This is what happens with anything other than operating above the limit of static friction. The operation of wheels on the ground can only result in loss of energy, which determines the relevant choice of direction. Hot brakes won't supply Kinetic Energy to either the car or the road.
Does it help to look at a system in a more complicated way (as long as the simple way is not neglecting to include something relevant)?
I see where you're coming from, though.

A.T.
That's true, in principle but my point is that, if the brakes and the tyres get hot, the procedure cannot be looked upon as reversible.
Its not reversible becuse of entropy, not because of energy conservation.

Hot brakes won't supply Kinetic Energy to either the car or the road.
The force of dynamic friction can supply kinetic energy to them.

sophiecentaur
Gold Member
The force of dynamic friction can supply kinetic energy to them.
Yes but it doesn't work the other way round, does it? I don't understand why you don't seem to understand.??
Would you say that it is relevant whether the wheels do work on the road or the road does work on the wheels? Either way, there's no work resulting from the heating up effect of the tyres or brakes.

Its not reversible becuse of entropy, not because of energy conservation.
I didn't think I said it was. But the energy deficit, due to the effect of friction only applies ' one way round' and the heating comes from whichever side of the contact is supplying the energy. If you choose the instantaneous point of contact on the turning wheel as your reference frame, it strikes me that you are just making your life more difficult for yourself. It is a pretty established principle to choose the (vastly) more massive body as the reference for this sort of problem. There could be an alternative scenario involving a conveyor belt and an unpowered vehicle but afaics, the assumption was of the more familiar situation.
If the car is accelerating and there is slipping, the heating power is coming from the engine and if it's braking, the heating power is coming from the KE of the car. The friction force (on the road) will be in different directions in the two cases and so will the reaction force (on the contact point of the wheel).

A.T.
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The force of dynamic friction can supply kinetic energy to them.
Yes but it doesn't work the other way round, does it?
It does. Dynamic friction can add or remove kinetic energy from an object, by doing positve or negative work on it. It depends on the reference frame.

Would you say that it is relevant whether the wheels do work on the road or the road does work on the wheels?
It's frame dependent.

It`s not reversible becuse of entropy, not because of energy conservation.
I didn't think I said it was.
You originally wrote the reversal would manufacture energy out of nowwhere. It wouldn't. But it would decrease entropy.

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sophiecentaur
Gold Member
You originally wrote the reversal would manufacture energy out of nowwhere. It wouldn't. But it would decrease entropy.
I see what you are getting at now and, of course, I could have stated things better. The reversal I am referring to is not 'that' one. I am talking in terms of Energy flow.
I started writing here because people seemed to be claiming that there was some confusion about the 'direction' to assign the friction force. For some reason, there is an opinion that the directions of Dynamic and Static friction forces could, somehow be different. That has to be either nonsense or due to choosing a different force in each case. The only point I am making is that to resolve this question, it is only necessary to consider that mechanical energy will always be lost due to friction. This principle takes you just one way and will always tell you how to choose a suitable direction to assign the force. There is less work done in accelerating the car, when there is slippage, than the engine is actually doing. I don't think that statement is controversial. is it?
The choice of frame is not relevant here - but I still say that, in the simple case of a car on a road, it would only add further confusion to work in terms of the car's frame - and particularly to work with the lowest point on the tyre. For someone struggling with this stuff, the possibility of using an alternative frame can only be confusing.

jbriggs444
Homework Helper
2019 Award
There is less work done in accelerating the car, when there is slippage, than the engine is actually doing.
I don't think that statement is controversial. is it?
Possibly not controversial. But not unambiguously correct.

Consider a car accelerating eastward at a red light on the streets of Chicago. It spins its tires briefly and a small cloud of smoke forms. The engine is doing a good amount of work on the drive shaft. But if we adopt an earth-centered inertial frame, the power being applied to the surface of the spinning tires by the pavement during this event is even larger than the power being supplied by the engine. That is because the surfaces of the tires are actually moving eastward at 600 to 700 of [earth-centered-inertial] miles per hour despite the engine's best efforts to get them moving westward at, perhaps, 30 [car-relative] miles per hour.

It would be more correct to say that the work done by the pavement on the surface of the tires plus the work done by the surface of the tires on the pavement adds up to a negative total.

sophiecentaur
Gold Member
Possibly not controversial. But not unambiguously correct.

Consider a car accelerating eastward at a red light on the streets of Chicago. It spins its tires briefly and a small cloud of smoke forms. The engine is doing a good amount of work on the drive shaft. But if we adopt an earth-centered inertial frame, the power being applied to the surface of the spinning tires by the pavement during this event is even larger than the power being supplied by the engine. That is because the surfaces of the tires are actually moving eastward at 600 to 700 of [earth-centered-inertial] miles per hour despite the engine's best efforts to get them moving westward at, perhaps, 30 [car-relative] miles per hour.

It would be more correct to say that the work done by the pavement on the surface of the tires plus the work done by the surface of the tires on the pavement adds up to a negative total.
This is all a bit disingenuous, I think. The source of the Power that we are discussing is the fuel in the tank in the car. You can hardly be suggesting that the fuel in the tank is somehow being 'used' by the Earth, in order to accelerate the car (not an inertial frame, because there is acceleration). That is, afaiac, a very relevant point in this discussion. There will, of course, be a finite but very small, increase in the KE of the Earth during the interaction. The source of the energy to achieve this is also in the fuel tank. Do you mean the total power developed by the engine?
But you need to remember that the periphery of the tyres is changing its velocity, constantly and the top of the tyre is actually moving eastwards at 600 - 60 mph. There is no possible reason to use the earth centre unless you think that the centripetal force involved in the rotation of the Earth is relevant. Could you measure it in practice (in the sort of experiment we are discussing)? We both know that a flat, stationary earth surface is by far the most sensible frame to be working with.
I would say that is wrong, or at least, unclear. There is a region of tyre and grit upon which the wheel is expending a lot of energy but the effective work done " by the pavement", (being the Reaction Force times the velocity along the road ) is the same as the Work done by the engine, (effective drive force times velocity). Any left over power will be stirring up the grit and the tyre surface - abrading it and getting it hot. If you consider the earth to me of infinite mass then there is no change in the Earth's KE so it can not be 'supplying' any power (or it would be changing). Momentum remains the same and the velocity change is zero for the earth.

Here's another thing. When the brakes are applied and there is no slippage of the tyres (just on the pad surfaces), is there anything different about the power flow situation compared with the situation where the brakes lock and the slippage is all on the tyre surface (arranged so thet the acceleration is the same in each case)? Again, because the KE of the infinite Earth is not changing, all the energy comes from the KE of the car; where it happens to be dissipated is not relevant.

jbriggs444
Homework Helper
2019 Award
This is all a bit disingenuous, I think. The source of the Power that we are discussing is the fuel in the tank in the car. You can hardly be suggesting that the fuel in the tank is somehow being 'used' by the Earth, in order to accelerate the car (not an inertial frame, because there is acceleration).
I am not suggesting anything at all about the fuel in the tank of the car. I am concentrating on the work done by the surface of its tires on the pavement. In my opinion, if we are discussing kinetic friction then we ought not be discussing fuel, engines or drive trains. We should be discussing kinetic friction. If one insists on phrasing things in terms of energy and if one insists on concentrating only on the energy of the car and ignoring the energy of the pavement then the fact that the resulting statements about energy are not frame invariant is to be expected. Energy is not invariant with respect to choice of inertial reference frame.

Can you explain your parenthetical about acceleration and inertial frames. Surely the fact that the car has non-zero acceleration (proper or coordinate, take your pick) does not preclude one from using an inertial frame to analyze the situation?

There will, of course, be a finite but very small, increase in the KE of the Earth during the interaction.
This is not unambiguously true. In the ECI frame, the decrease in the Earth's rotational KE will be roughly equal to the gain in KE of the accelerating car. The discrepancy between the gain and loss will be equal to the total work done in both directions across the pavement/tire interface plus the work done by the engine.

If one chooses a more exotic frame from which to analyze the situation, the change in the Earth's KE would become monstrous.

We both know that a flat, stationary earth surface is by far the most sensible frame to be working with.
Yes, if one of the surfaces in question is motionless relative to the Earth, we do agree that it simplifies matters to only have to worry about the work being done in one direction. However, not all surfaces subject to kinetic friction are at rest on a [notionally] static earth.

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A.T.
Again, because the KE of the infinite Earth is not changing, all the energy comes from the KE of the car
Where kinetic energy is coming from, and where it is going to, is frame dependent. There are inertial frames where the car gains speed during braking, so it cannot be the source of energy for the heat in the brakes.

sophiecentaur, they are right when say that the energy is the frame dependent or not invariant and so on. But it seems to me I understand what you tried to say. Watching that battle I have desided to equalize the forces acted on your side))
All answers to TC are present in that topic and it can be spent a bit of time to the sacred cause of the establishment of world harmony :D
In general, energy considerations in defining the direction of the force of friction is worse than the example of a professor with the two bodies.
However, you can try to not identify and but explain the algorithm determining the direction of dynamic friction force from the energy point of view. Although it is easier to make the analysis of the mechanism of interaction friction surface microroughness.
In terms of energy it can be said the following.
Problem:
Location - away from the bodies in space.
Let there be two smooth and flat bodies which are in contact with each other on one of the planes.
Suppose that one is moving relative to each other uniformly in a straight line and let no pressing force is present.
Then, the friction ( and other interactions) is zero, and the movement could go on forever. Any conversion of energy is absent.
Suppose there is a pressing force directed along the normal to the contact surface is appeared. This force is perpendicular to the movement and it does not perform the work. It was established experimentally that it generates a force directed along the contact surface.
Question - to find the direction of such a force.
Solution:
If this force is directed along the motion, it would lead to unlimited acceleration interacting bodies. The world in which this is possible is likely unstable. Anyway this world is not like ours.
It is clear that if this force is perpendicular or had component perpendicular to the motion, it would lead to a violation of the law of conservation of angular momentum. In addition such a force could not work, which contradicts experiment, as established experimentally that the friction generates heat.
So by elimination we come to the fact that such a force can be directed only in opposit to the movement. Then, sooner or later, the relative motion of two bodies fade away, and its energy will be transformed into heat.
Truth be told, this is the wildest proof of algorithm for determining the direction of force dynamic friction that determined by the phrase "in opposit to the direction of motion."

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sophiecentaur