Should I persue in telling a professor of physics that part of his book is wrong?

Question

An online physics text after several editions consists of a page of erroneous facts regarding the kinetic energy theorem. These errors where discussed on this site and were resolved in the authors disfavor.

In summary He asserts
1. In kinetic energy theorem K=1/2mv^2, the 1/2 is an arbitrary constant whose value is dependent on the unit system used. Under the metric system the constant is 1/2. The metric system was used to make the kinetic energy equation more managable at
the expense of other formulas.
2. the equation cannot be derived from principle but must be experimently determined.

RESOVLED-The THEOREM is mathematically derived. The 1/2 constant is independent of units.

I emailed him and unprosumptiously pointed out the error. However, he still asserts he is correct using arguments that rely on his initial error.

I want to give up because I don't think he will listen, but it bugs me that other students will be learning incorrect information.Should I pursue it further?

Yes I am pretty certain he is wrong. A THEOREM by definition is mathematically dervied. I cannot believe there has been a misnomer for the last hundred or so years for the kinetic energy theorem..Moreover, as discussed on this site the kinetic energy theorem can be derived in a number of ways, one way is through integration of netwons second law F=MA. Therefore it is not experimently or empirically determined but is a consequence of definition and mathematical formalism. If it is mathematically derived, then 1/2 constant is independent of the unit system.

Tto PASCAL

I like your thoroughness. And I do agree with at least part of it. However, I still have trouble accepting some of your propositions and in turn the authors. Here is the part that I do agree!

I gather from what you are saying is that the concept of energy could have been formulated in different ways.HistoricalIly, it cannot be derived from first principle since energy was not defined yet initself! Experimentally, a relationship was discovered between "energy" as defined and the motion of a mass. Again historically the first proposed formulation of energy was mv^2

However, once it was accepted that energy was conserved, then energy must be consistent with Newtons laws of action reaction pairs. mv^2 could not be directly derived from F=ma and was reformulated to 1/2mv^2 to be consistent. The Irony is that the conservation of energy is a more fundamental principle than newtons laws! Where conservation of energy is obeyed always, newtons laws are not at speeds near light.

Here is the part where I am still in disagreement.

Assuming F=ma is true by AXIOM. And through integration KE=1/2mv^2 by THEOREM. Then it appears that the constant 1/2 is independent of any unit system.

By anology, if C=2* pi *r is assumed to true in of itelf by definition, and through integration A= pi* r^2. The circumference and area formula for a circle is true regardless of unit. The constant 2 for circumference and the constant 1 for area do not change regardless if were to use inches or feet or meters etc. Only the final units of our measurement would change, but not the multiplicative constant.

This is in contrast to the gravitational constant found in the unverisal law of gravitation. The gravitiational constant must be discovered by experiment and it's value and associated units are entirely dependent on the choice of units for distance and mass because rather than a multiplicative constant which is unitless it is a proportionality constant bridging one concept to another.

To pascal

I agree that whether a constant is one that unitless and whether it is not unitless depends on the constants selected. As you pointed out under a heat definition you require some type of units constant. However, the authors can no longer assert that the constant is
arbitrary once he includes the work concept of energy into the equation. Simply when he writes KE=1/2mv^2, it is incorrect to assert that the 1/2 is an arbitrary constant.

You analysis of the area and circumference of a cirlce proves to much. While I do agree with you that the circumference formula would be different if it did not assume a unit radius. If a unit radius is assumed, then the area constant is no longer arbitrary but was dependent on AXIOM.

Perhaps we have a difference of semantics. Under your position and the authors, all constants would be arbitrary, either because its a proportionality or because at somepoint some definition was arbitrarily selected.

As Steve and Pascal mentioned,as long as the units are consistent then no new constants are required.Yes,the heat definition of energy requires a unit dependent proportionality constant.

Tthe author assertion that 1/2 constant is entirely dependent on the units And that metric system makes the caculation easier at the expense of others Is entirely inaccurate by way of his presentation and how most people interpret him. .

Another assertion that the kinetic energy theorem cannot be derived from first principle is also misleading. I think he meant that the concept of energy cannot be derived from axiom.Netwon never wrote about energy as far as I know in his Principia.However, once the energy concept was formulated using work rather than heat, then it is deriviable from principle.

our differences for the most part is one of semantics.However, as Pascal mentioned, the author's understanding might not be complete, and thus his arguments are a littlle muddled which lead to this discussion

As Steve and Pascal mentioned,as long as the units are consistent then no new constants are required.Yes,the heat definition of energy requires a unit dependent proportionality constant.

Tthe author assertion that 1/2 constant is entirely dependent on the units And that metric system makes the caculation easier at the expense of others Is entirely inaccurate by way of his presentation and how most people interpret him. .

Another assertion that the kinetic energy theorem cannot be derived from first principle is also misleading. I think he meant that the concept of energy cannot be derived from axiom.Netwon never wrote about energy as far as I know in his Principia.However, once the energy concept was formulated using work rather than heat, then it is deriviable from principle.

our differences for the most part is one of semantics.However, as Pascal mentioned, the author's understanding might not be complete, and thus his arguments are a littlle muddled which lead to this discussion

Id like thank you guys, especially Pascal, for your serious and critical analysis. you guys forced me to think more critically and I learned alot. However, I do believe that our differences is a matter of semantics for the most part . And because of that I have concluded that there is no point writing to author anymore. Thanks!

Answer 1

once out of his class and upon completing all the classes required by the dept,, forward to the dean of the dept to review. don't do it before or those upcoming classes will be tuff!!! likely you won't get anywhere, specially if he has been there awhile as teachers are hard to come by.

Answer 2

You have to look at the statement in context. You could define a unit of energy to fit mv². It just happens that ½mv² makes sense since if it weren't that, then potential energy would be 2mgh. The term "arbitrary" is a bit strong. Although you could make a system work with any constant, ½ makes the simplest system. Certainly ½ is consistent with acceleration where the ½ comes from the integration of t dt.

In a quick nonrigorous derivation:

KE = F s
KE = m a s
KE = m a ½at² ; s = ½at²
KE = ½ma²t²
KE = ½ m (v/t)² t²; a = v/t
KE = ½mv²

Not knowing his reasoning, I would not venture a stronger statement than the ½ is mathematically convenient, not "arbitrary".

Answer 3

You are in a tough spot. A professor or teacher will be loath to admit that he made an error. And his colleagues will back him up, without even thinking about it.

In a undergraduate senior level course in electricity and magnetism my professor asserted that if you connected a battery across two electrodes (constant voltage) that the electrodes would repel each other. (Of course they do not; being oppositely charged they will attract each other.) He then "proved" his conclusion by showing that the energy in the field between the electrodes decreased as the electrodes moved away from each other. He was dead wrong. He ignored the work done by the battery in transferring additional charge to the electrodes in order to maintain a constant voltage (as many E&M texts explain).

When I pointed out the error to him his answer was that he "chose" to ignore the battery - which of course you cannot do. Other professors backed him up with comments like "I'm sure if professor so-and-so says it, it must be true"

So good luck. And by the way, you're going to experience a lot of this in your career.

Answer 4

It is pretty obvious, that he is wrong, 'cause using other units will give as correct result as using metric system. Numbers will differ of course, because that won't be Joules any more.

So yes, you should "fight" for this, as that is pretty big mistake, that can result in even bigger misunderstanding and erroneous education of future students. It is more than vital to understand not only what formulas says, but also how and why. (Even sole bloody derivation of formula for kinetic energy shows, that 1/2 comes from derivatives, not some normalizing constants...)

Answer 5

Yes, by all means draft a short, but clear synopsis of your findings and 'data' and submit that to the author.

I remember your question; the original one about the "1/2". I saw that you had sufficient answers and that most were valid ones, so I opted not to tack on my 2 cents worth.

As far as I know most authors respect and appreciate corrections to their text. I have actually hand-written such letters to authors and I've never had one not respond, or respond in an unappreciative manner.

However

I think what you are submitting isn't necessarily a typo, but a correction to an assertion that he/she made within the body of the text. Those are valid as well, but I'm just letting you know the difference as I see it.

:)

Answer 6

Don't mess with him if you have any more courses to take that he might be teaching. He's obviously crazy and crazy people can do very unexpected things......

MY text derives ½mv² with blistering simplicity:

W = ∫Fdx
F = ma, where a = v*(dv/dx); ergo,

W = ∫mv(dv/dx)dx = ∫mvdv

W = ½mv²

This is totally independent of the units and requires only that they are CONSISTENTunits. The man drags out BTUs as an example of an English system unit of energy, (and there are a few others he could have chosen!) but the ONLY one used in the scientific commuity is the consistent one where mass is expressed in slugs and velocity in ft/sec. The energy comes out in units of F*x, or foot*pound.

Answer 7

Be very very sure of what your saying.
Sciences were not my one of my degrees so,,,,
I cannot follow math it gives me a headache
but my second degree I thought was a first but ended up at 77 because I challenged perceived authority.
But then all that said if we do not argue cases
how would we all learn.

Answer 8

Wow, that's a pretty serious error. It's hard to believe that somebody who teaches physics would even believe this.

It sounds like you are talking to a brick wall, however. Good luck!

Answer 9

Its worth the try, but only if you are sure its wrong. Keep bugging the guy for a little, he might get it and learn something.

Answer 10

If you are sure about it - definitely. Let the truth prevail!

"Think not those faithful who praise all thy words and actions; but those who kindly reprove thy faults." - Socrates