Static Friction on Cars: Does it Do Positive Work? Explanation and Examples

[Cyrus]

I was reading a post in the homework section about friction being able to do positive work.
Several people provided examples, and one was the case of a car. Doc Al pointed out that static friction did not do any work on the car because the wheel was not slipping and the friction force acted over no distance.
However, I disagree, or more likely I fail to see, his reasoning. Its true that the wheel is not slipping, that's why the friction is static. But I don't agree that it acts over no displacement. At every instant, or snapshot so to speak, on the free body diagram of the car, static friction is acting forwards in the direction of motion of the car. Thus static friction HAS to be doing positive work on the car, no? I am not saying that the static frictional force is giving energy to the car, because its not. I said that it transfers energy, to which Andrew Mason did not like my wording, I believe he called it a mechanical link of energy. Well, I appreciate your help. I have a few more cases about friction I will ask, so please try not to anwser my question with another example of friction doing work on a different body. At this time all I care about in particular is the case of the car.

(Im sorry if I am misquoting Andrew or Doc).

 

[Tide]

You cannot infer that a force does work simply by virtue of it having magnitude and direction. Work requires that there be a displacement (i.e. something has to move!) which is absent in the static case. I'm not sure what you mean by direction of motion when the car is standing still.

 

[Cyrus]

The car is accelerating, which means motion. sorry i was not explicit in that point.

 

[Doc Al]

No work is being done by friction on the car because the point of application of the force--the patch of tire in contact with the ground--does not move. No displacement = no work.

This does not mean that the force of friction does not accelerate the car per Newton's 2nd law. It certainly does! But that does not mean that work is being done by the force. The energy of motion comes from transforming internal energy (fuel + oxygen) into kinetic energy. No energy comes from the earth, even passively (like would happen if the car were on a conveyor belt being accelerated).

Note that Newton's 2nd law implies:
F_{net} \Delta x_{cm} = 1/2 m v_{cm}^2
This is often confusingly call the "work-energy" theorem, but that quantity on the left is only properly equal to work in the special case of a point mass. Some authors call this "pseudo-work" to distinguish it from real work (real work is the work used in conservation of energy). This is a subtlety rarely discussed in elementary classes. It's a pet peeve of mine, so feel free to ask more questions.

(Sorry I didn't see and respond to this thread earlier.)

 

[Cyrus]

So, should I consider the tires to be giving the car a contiuum of impulses?

 

[Doc Al]

I would simply say that the ground exerts a continuous force on the tires, which accelerates the car.

 

[Cyrus]

Correct me if I am wrong, but I thought the car has two possible ways of motion. Work can be done on the car, which in this case friction isint doing, or the force can provide an impulse.
Just as a thought experiement, let's say that the car is moving with constant velocity. And the friction force is needed to overcome the drag and rolling resistance of the tires. In that case, the distance traversed, s=g(t), is linear. And let's assume that the force of static friction needed to overcome the retarding forces is also constant, as the speed of the car is not changing, I think its a pretty good assumption, F =h. Then the car needs a net input of force to maintain its motion, clearly. If the point of contact does not move, as is the case with the point of application of the static frictional force with the tire, then delta(X), clearly has to be zero. Which means Fdelta(X) too is zero, and work can't be passive through the Earth as you state. But because delta(x) is zero, that implies that the amount of time, delta(t), that the wheel is in contact with the ground has to be zero also. If it were not, then delta(x) would have to advance and be nonzero, else the car would not be moving forwards. So this means an impulse is not given to the car either. So now I am really confused! BLA. I see your point, and I agree with it. However, I am failing to see how just a "Force" will cause motion if this force is not doing work nor providing an impulse to the body that is being set into motion.
(I probably have a lot of holes in my logic, so please shine light through them :-) ).

 

[Doc Al]

If a net force is exerted on the car for a given time then, as a consequence of Newton's laws, an impulse will be imposed, leading to a change in momentum. But that's not work! Work (real work, as used in the first law of thermo) is a means by which energy is transferred into the system. You can still apply Newton's law (as I did two posts ago) and integrate the force over the distance that the center of mass moves and calculate the change in KE. Again, that's not work (for a body with internal degrees of freedom, like the car).

In the case of the car moving at constant speed: Is work being done on the system? Yes! Negative work from air resistance. Which means the net energy of the system is decreasing: The car uses fuel to overcome the resistance.

In the case of the accelerating car (no air resistance): Is work being done on the system? No! (The static friction does no work.) That means the net energy of the system does not change. But internal energy is being transformed into KE.

 

[Twukwuw]

when a tyre is rotating at angular speed w, and we put it on the floor with zero translational velocity, the following mechanism will happen:

1st, the fiction force will act to decrease the angular speed of the tyre, since it excerts a negetive torque on the tyre.

2nd, the force will also act to increase the translational speed of the tyre, because at any instant the fiction force is there, it must accelerate the CM of the tyre! ( Maybe you will think this is unreasonable and you may think that a fiction force should always act to deccelerate the CM. This is not the case, however. I try to make it clear to you regarding how it works. Initially, the contact point (the lowest point) of the tyre is moving BACKWARDS and horizontally at velocity = wR, R = radius of tyre. That means, the contact point is PUSHING the floor, hence it will thus being accelerate to the front, just like what is happening when you try to jump!
And, at any instant, the CM moves in +x direction but the contact point moves in -x direction. Thus, the CM's velocity will increase until it is EQUAL to the velocity of the contact point!
When this happen, the tyre is in rolling, wthout slipping! Equilibrium, no more change in both the CM's speed and the angular speed!

In fact, the floor has done a NEGATIVE work on the tyre. But, at the same time, the tyre also did a POSITIVE work on the floor (the Earth is being pushed a little bit and its velocity will increase a little bit also!)
Hence, the total energy for the whole system is CONSERVED.
To understand the NEGATIVE work done, I would say, some energy is ECTRACTED from the tyres to the floor, hence it is negative.

Now, let's try to understand how does a car move.
The fuel in a car will release energy (by chemical reaction!), and this energy will be converted to the rotational energy of the tyres! That means, initially the tyre have angular speed, but NO CM's speed!
After that, everything will follow what is mentioned above!
That is, the total energy of the car will DECREASE but at the same time we get what we want--> the tyres move to the front!

Hope this will help,
Twukwuw.

 

[Doc Al]

when a tyre is rotating at angular speed w, and we put it on the floor with zero translational velocity, the following mechanism will happen:

1st, the fiction force will act to decrease the angular speed of the tyre, since it excerts a negetive torque on the tyre.

2nd, the force will also act to increase the translational speed of the tyre, because at any instant the fiction force is there, it must accelerate the CM of the tyre! ( Maybe you will think this is unreasonable and you may think that a fiction force should always act to deccelerate the CM. This is not the case, however. I try to make it clear to you regarding how it works. Initially, the contact point (the lowest point) of the tyre is moving BACKWARDS and horizontally at velocity = wR, R = radius of tyre. That means, the contact point is PUSHING the floor, hence it will thus being accelerate to the front, just like what is happening when you try to jump!
And, at any instant, the CM moves in +x direction but the contact point moves in -x direction. Thus, the CM's velocity will increase until it is EQUAL to the velocity of the contact point!
When this happen, the tyre is in rolling, wthout slipping! Equilibrium, no more change in both the CM's speed and the angular speed!

I hope you realize that this is not the situation that cyrusabdollahi is describing. But, if you drop an already rotating tire onto the road you are correct: The friction does negative work on the tire until it meets the condition for rolling without slipping.

In fact, the floor has done a NEGATIVE work on the tyre. But, at the same time, the tyre also did a POSITIVE work on the floor (the Earth is being pushed a little bit and its velocity will increase a little bit also!)
Hence, the total energy for the whole system is CONSERVED.

Mechanical energy is certainly not conserved! The amount that the Earth moves is certainly negligible, and the work done on it equally so. The negative work done by friction becomes thermal energy. (Of course, total energy is conserved.)

To understand the NEGATIVE work done, I would say, some energy is ECTRACTED from the tyres to the floor, hence it is negative.

The mechanical energy of the tire decreases due to the friction; that energy lost becomes thermal energy.

Now, let's try to understand how does a car move.
The fuel in a car will release energy (by chemical reaction!), and this energy will be converted to the rotational energy of the tyres! That means, initially the tyre have angular speed, but NO CM's speed!
After that, everything will follow what is mentioned above!
That is, the total energy of the car will DECREASE but at the same time we get what we want--> the tyres move to the front!

In the case of the car, if we assume that the tires don't slip then no work is done by the static friction on the tires and the total energy of the car (chemical plus KE) remains constant (ignoring air resistance, etc.).

 

[Cyrus]

That is helpful, thank you.

I will have to think a little more, and let this brew in my head. Then Ill ask some more questions when I have had more time to think things through.