Direction of Kinetic Friction and Static Friction

[jbriggs444]

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.

Edit: Added the clause about the engine above.

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.

 

[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.

 

[IgorIGP]

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."

 

[sophiecentaur]

determined by the phrase "in opposit to the direction of motion."

Yes. That phrase is a good summary. However, the 'direction of motion' refers to the motion between the two friction surfaces - which confuses people because they assume that it must represent the motion of a vehicle.

 

[IgorIGP]

That phrase is a good summary. However, the 'direction of motion' refers to the motion between the two friction surfaces - which confuses people because they assume that it must represent the motion of a vehicle.

You're right. And we must always and everywhere explain it to them.