B The work done by two objects on each other

[Herman Trivilino]

I think that generalized work (a transfer of mechanical energy without a transfer of mass) is the same thing as thermodynamic work, but am still awaiting your definition.

I think that such a definition is beyond what I can put in a forum post. It wouldn't do justice to the question asked, and would just result in an extended back and forth discussion. It is instead something to be found in a textbook or a published article. You can find good definitions in many of the college-level introductory physics textbooks written in the last 15-20 years.

I refer you to, and strongly recommend, the paper by Arnold B. Arons that starts on page 1063 of the American Journal of Physics [Am. J. Phys. 67 (12), December 1999]. If you can't get access to the article let me know and I can send you the PDF via private message.

Here is an excerpt from that paper that may answer your question:

How must work be calculated? Experience shows
that the useful operational definition of work must be developed
along the lines discussed by P. W. Bridgman in his
careful, insightful, and thorough analysis in The Nature of
Thermodynamics:

Turn now to an examination of the W of the First Law.
This W means the total mechanical work received by the
region inside the boundary from the region outside [or
delivered to the region outside from the region inside]. As
in the case of [heat transfer] Q, this work is done across
the boundary, and the evaluation of W demands the posting
of sentries at all points of the boundary, and the summing
of their contributions. In the simple cases usually
considered in elementary discussions, the work received
by the inside from the outside is of the simple sort typified
by the motion of stretched cords or of simple linear piston
rods. Our sentry can adequately report this sort of thing in
terms of finite forces acting at points and finite displacements.
In general, however, there will be contact of the
material outside over finite regions of the boundary, and
we become involved in the stresses and strains of elasticity
theory.

[Bridgman goes on to mention the ‘‘infelicities" that result
when we apply the notion of work to the sliding of two
bodies on each other with friction.]

To emerge as a conserved quantity, work must be calculated
by summing the product of forces and their corresponding
displacements over the periphery or boundary of the system
which has been defined. For example, for a compressed
spring, we must calculate the integral over the displacement
of the end of the spring and not over the displacement of its
center of mass.

 

[sophiecentaur]

But if a student comes to us and asks why the work done by the road on the car

Yes; a problem. However, that sort of question will mostly, only be asked when previous teaching has made the student thing that it's essential to consider the work situation. We all know that this Work thing is harder than one would think so why use it when not absolutely necessary, or at least point out that there are many situations in which it really doesn't help. It's having a tool that introduces more confusion than doing a job another way.

I guess there are parallels with Photons and Electrons being used far too early by students who somehow feel those two concepts are necessary to explain basic macroscopic phenomena. Nonsense like "Why did they get the sign of the current wrong?" is an understandable quandary and pointless hurdle for many students to deal with.

The problem with trying to resolve frequently held misconceptions with students can result in their leaving with the wrong lesson being learned. (They woke up up half way through the lesson)

 

[jbriggs444]

Yes; a problem. However, that sort of question will mostly, only be asked when previous teaching has made the student thing that it's essential to consider the work situation. We all know that this Work thing is harder than one would think so why use it when not absolutely necessary, or at least point out that there are many situations in which it really doesn't help. It's having a tool that introduces more confusion than doing a job another way.

That sounds plausible in the abstract. Can you make it concrete?

For instance, we have a car on a road. The car starts with some velocity and is subject to a constant force. We are asked for the final velocity. We could apply the concept of work, multiply force by distance to get the change in the car's kinetic energy. Add the change to the car's original kinetic energy, get the final kinetic energy and extract the final velocity.

Your alternative, I suppose, would be to find the right SUVAT equation: $v^2 = u^2 + 2as$. That is the one SUVAT equation that I never bothered to memorize because I prefer the notion of "work".

So far, you seem to have a viable proposal. But what if have a large reservoir of compressed gas that is used to slowly push a piston across a known displacement in a small cylinder. The piston is further connected to a crankshaft, the details of which are irrelevant. We are asked for the energy supplied to the piston by the gas.

Now the SUVAT equations are no longer applicable. The most convenient way to proceed is through the notion of mechanical (or thermodynamic) work.

 

[sophiecentaur]

For instance, we have a car on a road. The car starts with some velocity and is subject to a constant force. We are asked for the final velocity. We could apply the concept of work, multiply force by distance to get the change in the car's kinetic energy. Add the change to the car's original kinetic energy, get the final kinetic energy and extract the final velocity.

I challenge you to find many A level students who would avoid Suvat and use work for that.Any problem involving vehicles is full of unstated extra effects. I remember that nagging feeling about 'constant accleration' in any car question and that was even before I had learned to drive.

That is the one SUVAT equation that I never bothered to memorize because I prefer the notion of "work".

Really? SUVAT is just one of those things that are taught very early on. Did you already have an understanding of mechanical work? I can understand you having a preference and I prefer it too. But that's another issue.

But what if have a large reservoir of compressed gas that is used to slowly push a piston across a known displacement in a small cylinder.

What indeed? Where would that sort of problem sit on the timeline of learning mechanics, though?

That sounds plausible in the abstract.

Yes; it is abstract because it's about how easily (or not) people can learn this stuff. If you acknowledge that you are aware of (other) people's problems with all the questions I have quoted above then you would need to address them and not give the 'right answers'. Those right answers assume familiarity with a whole lot of other stuff which (asleep in class etc.) they don't keep in their heads.

Logically, the only way to respond to the sort of naive question that's often posted on PF would be to start with a health warning: "Unless you actually understand a whole lot of mechanics already, then don't attempt to understand the following:".
PS "and don't you come back no more no more"

 

[jbriggs444]

Any problem involving vehicles is full of unstated extra effects. I remember that nagging feeling about 'constant accleration' in any car question and that was even before I had learned to drive.

Of course you are right. First year physics is full of idealizations and simplifications. We usually ignore air resistance. We assume frictionless surfaces, rails and axles. We are dealing with students who have not been exposed to calculus, so we avoid non-constant forces.

Really? SUVAT is just one of those things that are taught very early on.

Almost all of the SUVAT equations are intuitively obvious. Nothing to really memorize. You just write them down when needed. For me, the only one that does not immediately flow from the pen is $v^2 = u^2 + 2as$. But that equation obviously the same thing as the work energy theorem: $E_f = E_i + F \cdot s$ with a factor of $\frac{2}{m}$ thrown in. One less thing to memorize.

For me, understanding is fun while memorization is hard. I have a decent memory, but an ample supply of laziness.

Did you already have an understanding of mechanical work?

It is hard now for me to recall what my understanding was like back then. I certainly understood the "center of mass" work that was being taught. That was enough to get 100% on all of the tests.

But the understanding felt flawed. What we were taught did not include the possibility of external forces exerted on moving parts within non-rigid bodies. It was obviously not accounting for the complete energy flow. I had the private idea of mechanical work, but no formal coursework to provide confirmation or a name to go with the notion.

That was frustrating and uncomfortable for me. It made me want more detail from my physics instructors. Not less.

 

[sophiecentaur]

It made me want more detail from my physics instructors.

I was always too lazy to perform well in tests but my retention has always been a lot better than people who always got better exam grades; many of them went 'high flying ' and promptly forgot all that interesting g Physics.
But my comments in this thread were not aimed at 100%'ers. I suspect we are a bit in quadrature about this issue.

For me, understanding is fun but memorization is hard.

Yeah well . . . your memorisation was clearly subconscious (you lucky man).