Is there any work done by static friction when accelerating a car?

[rcgldr]

Still, the only force external to the car is the contact patch static friction force, and the point of application of that force advances forwards as the car moves forwards over time (and at the same speed if on a flat road). The remaining forward forces that are transmitted from the tire to components of the vehicle are internal to the vehicle, so the argument here is that internal forces are responsible for the power that accelerates a car?

 

[jbriggs444]

Still, the only force external to the car is the contact patch static friction force, and the point of application of that force advances forwards as the car moves forwards over time (and at the same speed if on a flat road). The remaining forward forces that are transmitted from the tire to components of the vehicle are internal to the vehicle, so the argument here is that internal forces are responsible for the power that accelerates a car?

Well yeah. Fred's legs. The car's engine. Significantly, neither is rigid. If you focus in even more tightly, the non-rigidity in the muscles in Fred's legs and in the combustion gasses in the engine cylinders makes it possible for those entities to act as mechanical energy sources.

Flogging the horse a bit more, the motion of the contact patch has nothing to do with anything.

 

[A.T.]

Still, the only force external to the car is the contact patch static friction force, and the point of application of that force advances forwards as the car moves forwards over time (and at the same speed if on a flat road).

That it happens to work out right only in special cases (flat road), should give you the hint that it's a red herring.

 

[A.T.]

Here a simple example to see that for work & power calculations the velocity of the physical material at the point of force application is relevant, not the advance of the geometrical contact point:

A wheel is turned by a motor, while its axis is held in place. If you place the wheel on a board which lies on ice, it will accelerate the board, by doing work on it. But the geometrical contact point is static, so it's obviously irrelevant to the work done.

 

[jbriggs444]

A wheel is turned by a motor, while its axis is held in place. If you place the wheel on a board which lies on ice, it will accelerate the board, by doing work on it. But the geometrical contact point is static, so it's obviously irrelevant to the work done.

Oh nice, I see what you did there. Instead of looking at work done on the car, you looked at work done on the road. And even though the red herring happens to works out nicely for the car (since the car is more or less stationary relative to the point of contact), it works out poorly for the road (since the road is not).

 

[rcgldr]

Here a simple example to see that for work & power calculations the velocity of the physical material at the point of force application is relevant, not the advance of the geometrical contact point

A wheel is turned by a motor, while its axis is held in place. If you place the wheel on a board which lies on ice, it will accelerate the board, by doing work on it. But the geometrical contact point is static, so it's obviously irrelevant to the work done.

In this case, the force has a velocity (other than the initial state where t=0, v=0). It's still my opinion that the work done can be calculated in the normal way for both cases. Where the surface distance of the work done equation is based on the point of application. Either the force is moving or the surface is moving, or in the case of my small moon + car example, both.

$$ \int F(s) \cdot ds $$

 

[Dale]

the "contact patch" can be moving with respect to the ground (even though the tread isn't, since it's moves backwards through the contact patch), and power = force · speed. The contact patch static friction force from the ground times the speed of the contact patch equals the power that accelerates the car.

This just doesn’t work. Yes, the speed of the contact patch has units of speed, so if you multiply it by the force at the contact patch you do get a quantity that has units of power. But what does this quantity mean?

One possibility is that it is the rate of energy transfer across the contact patch, this is the most physically important quantity since it is the one related to the conservation of energy. However, that quantity is 0, so your quantity is the wrong value.

Ok, so maybe your quantity is the power output of the engine. For the original scenario that coincidentally works, but if the tire is spinning in place (peeling out) then the power output can be quite high while your quantity is zero. So it doesn’t work that way either.

Ok, so maybe your quantity represents the increase in KE. Again, for the original scenario this works coincidentally, but consider a runner accelerating. In that case your quantity is zero while the KE is increasing. So it doesn’t work for that either.

I cannot think of any meaning that you can consistently give to your quantity. Yes, it has units of power, but it does not represent the power transferred at the contact patch, nor the power produced by the engine, nor the rate of increase of the KE. As far as I can tell it has no physical significance. It is simply a quantity with units of power.

It's still my opinion that the work done can be calculated in the normal way for both cases. Where the surface distance of the work done equation is based on the point of application.

How many times in how many different ways does this need to be proven wrong before your opinion on the matter will change? If you don’t have an exact number a ballpark estimate would be fine.

Look, I completely understand where you are coming from. The human mind is excellent at generalizing. You have a concept that in this one scenario works pretty well. So it is easy to believe that it is a general approach. It is not. It works for a car on level road with no slipping. It doesn’t work for many non-cars, it doesn’t work for some non-roads, it doesn’t work for hills, it doesn’t work during slipping. Your opinion here is simply an over generalization.

In contrast to the force times the velocity of the contact patch, the force times the velocity of the material at the contact patch has a well defined and consistent physical meaning. It is the power transferred to or from the object through the contact patch. That definition works regardless of if the surface is stationary or moving and regardless of if there is slipping or not. It works for tires or feet, roads or boards, hills or level road, slipping or not.

 

[rcgldr]

In contrast to the force times the velocity of the contact patch, the force times the velocity of the material at the contact patch has a well defined and consistent physical meaning. It is the power transferred to or from the object through the contact patch. That definition works regardless of if the surface is stationary or moving and regardless of if there is slipping or not. It works for tires or feet, roads or boards, hills or level road, slipping or not.

All chassis dynamometers measure driven wheel power using static friction force times speed at the contact patch of the driven tires, and yet there's no relative motion at the contact patch between the moving tires tread and the drum(s). Typically the force is calculated by sensing the angular acceleration of the drum(s), knowing the drum(s) radius and angular inertia. How does this significantly differ from the case where a car is accelerating on a road?

Note that there are no sensors in the straps that hold a car in place. The measurement of power is solely based on the force at the contact patch times the speed.

It wouldn't take much to change the software to calculate force times distance moved by the surface of the drum(s), in order to measure the work performed on the drum(s), and compare it to the increase in angular kinetic energy of the drum(s).

 

[A.T.]

It's still my opinion that the work done can be calculated in the normal way for both cases.

What is the "normal way"? What "both cases"? What is the work done on the board by the wheel in post #75, according to your method based on contact patch advance speed?

 

[jbriggs444]

speed at the contact patch of the driven tires

Bingo. They are using the speed of the material at the contact patch, not the speed of the contact patch.

 

[Dale]

All chassis dynamometers measure driven wheel power using force times speed at the contact patch ... How does this significantly differ from the case where a car is accelerating on a road?

It differs pretty substantially and shows another way that your approach fails.

In this case the speed of the contact patch is 0, so according to your method the power is also 0. This is incorrect.

In contrast, the speed of the material at the contact patch is nonzero as is the force, correctly giving a nonzero power transferred at the contact patch. This correctly indicates that energy is leaving the car since the battery or fuel is being depleted without increase in KE.

So now that you are providing examples where the “velocity of the contact patch” method fails do I correctly understand that you now recognize that it doesn’t work?

 

[rcgldr]

They are using the speed of the material at the contact patch, not the speed of the contact patch.

I thought the issue in prior posts was that the force being used to determine power or work done is a static friction force, where the surface of the tire and the surface of the road travel at the same speed (which could be 0) at the contact patch.

For the dynamometer, the drum surface is moving, for the original case, the car and what I refer to as contact patch are moving. In both cases, you have a static friction force and a speed, which can be multiplied to calculate the power. There have been dynamometer comparisons versus "real world", comparing what the dynamometer shows as power, versus the power calculated from video and/or radar capture of a car's acceleration and speed, where the car's acceleration · car's mass is used to calculate the static friction force. If the dynamometer is accurate (and the conditions similar), the resulting power calculations via the two methods are the same (within reasonable tolerance).

 

[A.T.]

For the dynamometer, the drum surface is moving, for the original case, the car and what I refer to as contact patch are moving.

There is no consistency in your approach. In one case you use the contact material speed, in the other the geometric contact point speed.

Your error, as explained many times, is replacing the car's CoM with contact patch in the original case. It happens to work out numerically in special cases, but has no physical meaning and is pure obfuscation.

 

[jbriggs444]

I thought the issue in prior posts was that the force being used to determine power or work done is a static friction force, where the surface of the tire and the surface of the road travel at the same speed (which could be 0) at the contact patch.

The force being discussed throughout this post has been static friction. It is static because there is no relative motion between tire and road. Both the surface of the tire and the surface of the road move at the same speed. No one has disputed that. There is no confusion on that point.

The problem is with the speed that is used to determine power. Which speed is to be used?

1. The speed of the contact patch?
2a. The speed of the tire material at the contact patch?
2b. Equivalently, the speed of the road material at the contact patch?
3. The speed of the car's center of mass?

It appears that your approach is "whatever speed gives a calculated result that matches the engine power it is supposed to match". This leads you to pick the single incorrect choice from the list: the speed of the contact patch.

All of the other choices can be used to compute results that reflect physically meaningful power measurements.

2a: Rate at which energy is being delivered by road to tire surface.
2b: Rate at which energy is being delivered by tire to road surface.
3: Rate at which bulk kinetic energy of car is increasing due to external force from road.

 

[hutchphd]

I ask @rcgldr to explain the motion of an "inchworm" using this theory.

 

[Dale]

I thought the issue in prior posts was that the force being used to determine power or work done is a static friction force, where the surface of the tire and the surface of the road travel at the same speed (which could be 0) at the contact patch.

Nobody disagrees about the force. The issue is the speed. You want to use the contact patch speed which is incorrect in many cases, including the dynamometer.

Note that with the use of the speed of the material at the contact patch it is possible to handle both static friction and sliding friction.

 

[rcgldr]

The force being discussed throughout this post has been static friction. It is static because there is no relative motion between tire and road. Both the surface of the tire and the surface of the road move at the same speed. No one has disputed that. There is no confusion on that point.

I apparently mistakenly thought that the issue was with a static friction force being able to perform work, since that is the question being asked in the title of this thread: "Is there any work done by static friction when accelerating a car?"

1. The speed of the contact patch?
...
3. The speed of the car's center of mass?

On a flat road, 1 and 3 are the same. For a car on a hill situation, I could change my small moon + car example to use a car on stilts that raises the cars center of mass above the contact patch so that the car's center of mass is located 25% further away from the center of the moon than the contact patch. So what speed (1 or 3) should I use to calculate the power based on static friction force time speed?

 

[Dale]

So what speed (1 or 3) should I use to calculate the power based on static friction force time speed?

IMO, neither. You should use the speed of the material at the contact patch. That gives the correct answer that the static friction force does no work on the car meaning no power is transferred from the ground to the car.

The net force on the whole car times the speed of the center of mass of the whole car can be used to calculate the rate of change of the KE. You cannot attribute that to work done by any force or even by the combination of forces. It has units of power, but it does not represent a transfer of energy (work) to or from the system.

 

[Dale]

Which speed is to be used? ...

2a. The speed of the tire material at the contact patch?
2b. Equivalently, the speed of the road material at the contact patch?

... reflect physically meaningful power measurements.

2a: Rate at which energy is being delivered by road to tire surface.
2b: Rate at which energy is being delivered by tire to road surface.

I am glad that you separated out 2a and 2b. This distinction is particularly useful in cases of slipping where you are using dynamic friction and the speed of the road material is different from the speed of the tire material. In that case the forces are equal and opposite (per Newton's 3rd law) but since the velocities are not the same the power is different. The difference in power is the amount of power that remains at the interface as thermal energy. It is a good exercise to calculate this in different reference frames. The work done by each force depends strongly on the reference frame, but the power dissipated is a (Galilean) invariant.

 

[rcgldr]

You should use the speed of the material at the contact patch. That gives the correct answer that the static friction force does no work on the car meaning no power is transferred from the ground to the car.

So what about chassis dynamometers? The only force they use to calculate power is static friction force (times the speed of the tire/drum(s) surfaces at the contact patch). in this case, the static friction force is performing work on the drum(s), increasing their angular kinetic energy.

 

[Dale]

So what about chassis dynamometers? The only force they use to calculate power is static friction force (times the speed of the tire/drum(s) surfaces at the contact patch). in this case, the static friction force is performing work on the drum(s), increasing their angular kinetic energy.

I already addressed this explicitly above in post 82. The “velocity of the material at the contact patch” correctly calculates the power for a dynamometer. The “contact patch velocity” does not.

 

[rcgldr]

The “velocity of the material at the contact patch” correctly calculates the power for a dynamometer. The “contact patch velocity” does not.

Just to be clear, static friction force can perform work on the drum(s) in a dynamometer, but not on car on a road?

 

[jbriggs444]

Just to be clear, static friction force can perform work on the drum(s) in a dynamometer, but not on car on a road?

Static friction can perform work on a box of car parts in the bed of your pickup truck when you accelerate after a stop.

Static friction from the highway can perform "center of mass" work on a car on the highway.

 

[Dale]

Just to be clear, static friction force can perform work on the drum(s) in a dynamometer, but not on car on a road?

Yes. On the drums the velocity of the material is non-zero so the work is non-zero. On the road the velocity of the material is zero so the work is zero.

 

[rcgldr]

Static friction from the highway can perform "center of mass" work on a car on the highway.

On the road the velocity of the material is zero so the work is zero.

This seems like a conflict, what am I missing here?

The only external force acting on a car on the road is the static friction force from the road, created as part of a Newton 3rd law pair of forces that originates with the car's engine or motor. If that is not the external force that performs work on an accelerating car, then what force is responsible for the increase in mechanical kinetic energy that was converted from potential energy of fuel or battery by the car's engine? Internal forces can't increase linear kinetic energy.

 

[jbriggs444]

This seems like a conflict, what am I missing here?

The need to be clear on what definition of "work" one is using. Which means the need to be clear about which velocity (or displacement) is being used.

 

[Dale]

This seems like a conflict, what am I missing here?

The "center of mass work" is not work since it can occur without any transfer of energy. It is a somewhat common misuse of language. I prefer $\Delta KE$.

 

[Doc Al]

This seems like a conflict, what am I missing here?

"Center of mass" work is just an application of Newton's 2nd law; the actual "real" work done (as in the first law of thermodynamics) is zero. As @jbriggs444 says, be careful what version of "work" you're using. (I would prefer that center of mass "work" not be called work at all.)

The only external force acting on a car on the road is the static friction force from the road, created as part of a Newton 3rd law pair of forces that originates with the car's engine or motor. If that is not the external force that performs work on an accelerating car, then what force is responsible for the increase in mechanical kinetic energy that was converted from potential energy of fuel or battery by the car's engine? Internal forces can't increase linear kinetic energy.

Sure, an external force is needed to convert internal energy into mechanical kinetic energy. Yet no work is done by that force.

 

[jbriggs444]

I agree with @Dale on this. Center of mass work is as much about momentum as about energy. You just apply the SUVAT equations and get something that looks like energy.

Note that when you apply it to the case of a car cresting a hill where the center of mass and the contact patch have significant differences in speed, you will find that the normal force on front and back tires have a significant discrepancy in magnitude and angle. That combines to produce a retarding horizontal force. Fail to account for that force and your measure of center-of-mass work will be off.

That is a case where using contact patch force times contact patch speed leads to a simple computation and a correct answer.

 

[Dale]

The only external force acting on a car on the road is the static friction force from the road, created as part of a Newton 3rd law pair of forces

Yes.

If that is not the external force that performs work on an accelerating car

There is no work on the car (under the usual assumptions). Note, I consistently use work meaning an actual transfer of energy, not fictitious “center of mass work”.

what force is responsible for the increase in mechanical kinetic energy

Forces are the rate of change of momentum, not energy. Power is the rate of change of energy. So this question is wrong. It incorrectly assumes that forces do something that power actually does.

The power that is responsible for the increase in KE is the engine/motor power.

Internal forces can't increase linear kinetic energy.

There is no such thing as linear KE, and internal forces most certainly can increase KE.

Force is the rate of change of momentum. The external force provides the momentum, not the kinetic energy. Both increase but they have different sources.

 

[A.T.]

...what force is responsible for the increase in mechanical kinetic energy ...

Depends on what "is responsible for" exactly means. If you want to gain clarity, you should try to avoid ambiguous terms.

Consider a simpler case:

A stick falls over from while the bottom end doesn't slide due to static friction.

- The gain in horizontal momentum comes from the impulse of the static friction.

- The gain in kinetic energy comes from energy the stick initially has, not from work by static friction.

There is no contradiction between these two statements, and they both also apply to the accelerating car. The changing contact location in the car case is irrelevant for the energy calculations.

 

[jbriggs444]

There is a sense in which one can attach useful meaning to the motion of the contact patch. If one views the contact patch as a "handle" which is rigidly attached to the car and through which the ground "grips" the car and if one ignores the motion of the tire surface entirely then the work done on this "handle" by the ground is identical to the bulk kinetic kinetic energy imparted to the [pretended-to-be] rigid car by the ground.

This includes the bulk rotational kinetic energy of the car as it rotates forward in the top-of-the-hill case or backward in a bottom of a valley case. It does not include any kinetic energy in the car-relative motion of the tires or drive train.

 

[Dale]

- The gain in horizontal momentum comes from the impulse of the static friction.

- The gain in kinetic energy comes from energy the stick initially has, not from work by static friction.

This is a very clear and simple example. Also, if you repeat the experiment but on a frictionless surface then you see that the KE is the same as with friction and only the momentum is changed.

 

[rcgldr]

There is no such thing as linear KE, and internal forces most certainly can increase KE.

Then restate this as energy related to change in linear movement. Internal forces can't change the center of mass, linear speed, or linear momentum of a closed system, while internal forces can can change angular velocity and angular energy, while angular momentum is conserved, of a closed system.

Although the accelerating car is converting potential energy into mechanical energy (so no "real" work is done), what I was getting at that for the static friction force and distance the force is applied, then

$$\int F \cdot ds = \Delta KE$$

 

[jbriggs444]

what I was getting at that for the static friction force and distance the force is applied, then

$$\int F \cdot ds = \Delta KE$$

Of course, that equation holds for point-like objects where there is little ambiguity about $ds$ or $\Delta \text{KE}$. Invoking it for non-rigid or rotating objects or where the point of application may otherwise not have a fixed position relative to the center of mass introduces ambiguity.