Talk:Work (physics)/Archives/2011/October

Change of the lead and some other modifications

Prompted by the above comment, I decided to rewrite the lead, introducing (stepwise) a definition independent of energy. Actually, this general definition is just the well known integral formula expressed in words. Why should it be anything else?

Feel free to improve my English (if you do not have more serious objections).

I felt compelled to do this because I have already contributed to acurateness of the article. While at it, I also removed repetitive/unnecessary sections of the article. On the whole, it now looks to me as a reasonably correct text: "it is not all that bad".

Nontheless, it is far from a well-balanced, comprehensive and properly illustrated article. In that respect, however, it does not differ much from other articles on elementary/basic physical concepts; and it might even be better than some. Consider, for instance, how definition of torque depends on some fictitious particle, how the (praised) article on force does not even mention the model of point force (or application point, or resultant force distinction from the net force), how the article on energy contains a meaningless section on virtual work, etc. Hopefully, one day...Ilevanat (talk) 00:14, 30 September 2011 (UTC)

I would like to make some minor modifications to the introduction using the concept of power. I think this can simplify some of what is needed for a correct presentation of Work. Prof McCarthy (talk) 17:53, 4 October 2011 (UTC)

I agree with your general idea that the concept of power could be helpful here, but you do not seem to mention the word itself ("power") in the article. In the sentence "At any instant, this is the scalar product of the force with the velocity vector of the point of application" it is not really clear what the word "this" stands for. And when you add the time integral of power to the formula (2) (which I fully support), there is again no reference to the term "power". Besides, there remains the question of whether we want to keep the lead as "light" as possible...

Regarding your other interventions, I certainly welcome my English and style improvements, e.g. your version of the numerical example is more likeable. But elsewhere, I would tend to be more careful: The sentence "This equates work and energy." is quite unnecessary (in addition to being generally incorrect). (And do we really need thermodynamics in the lead... perhaps it could be discussed later in the text.)

Besides, work can be defined based on energy transition, if the energy is defined in abstract terms only (e.g. starting with "the quantity conserved due to time..."). So perhaps some reference to alternative work definitions should be kept in the lead.

And finally, it seems to me that "changes in the trajectory" are a bit "heavy stuff" for the first paragraph of the lead. Perhaps after the formula (2), and there with a reference/link to virtual work (by the way, I find your notation there more likable than what has been used in the Work article).

In any case, I have no intention to re-edit your edits. I leave to you to reconsider, or to further discussion.--Ilevanat (talk) 00:10, 6 October 2011 (UTC)

I always look at the leading paragraphs to see how readily they can be understood by a young person or someone new to the field. With some articles on scientific topics there is a tendency to launch immediately into calculus even though it isn't necessary. (See WP:MTAA) The two leading paragraphs of Work (physics) are almost satisfactory from this perspective.

However, I think the following information appears too early:

At any instant, this is the scalar product of the force with the velocity vector of the point of application. Because changes in the trajectory of the point of application will change the calculation of work, work is said to be path dependent.

I think these two sentences would be better placed after the comment about Coriolis and before the comment about the first law of thermodynamics. Dolphin (t) 02:55, 6 October 2011 (UTC)

I appreciate and approve your overall opinion about the appropriate content of the lead. However (no offense intended) you might have overlooked some technical issues involved in particular statements.

I hoped for some response by Prof McCarthy, who accomplished his edits of the Work article in about half an hour (whereas I usually spend much more than that in mere reading of an article claimig to be an encyclopedia entry). As my primary concerns are elsewhere, I give up further attempts to modify en.wiki contents of this article.--Ilevanat (talk) 00:19, 8 October 2011 (UTC)

Sorry to be slow getting back to this. I can adjust my edits to the lead paragraph if they move too quickly. I can find better wording for changes in trajectory and point of application, but I cannot change work equals energy. I can drop the reference to thermodynamics but that is where the relationship between work and energy is discussed in its most general form, which is what I thought was the goal. The work-energy principle is a derived result from Newtons laws. I understand that this may not be best for the lead, but I was trying to work with what was there. In fact, it would be nice to have the derivation of the work-energy principle in this article.Prof McCarthy (talk) 15:44, 8 October 2011 (UTC)

I am glad you are back! As it now seems that this may lead to the first really interactive editing of a wiki article I have been involved in, I would like to stay involved a bit longer (contrary to my previous hasty decision to give up).

For the beginning, I have tried to reorder the lead paragraphs into what looks to me as a more appropriate sequence. In the process, I have also introduced minor changes to 2 paragraphs. In the first sentence, I believe that "defined" should be substituted by something like "roughly described" (please feel free to improve my style); not only because the correct definition is given two paragraphs below, but also because people will try to improve this sentence (if it says "defined"): see an attempt in the recent changes. The other modification was in the paragraph on power; I hope you find it acceptable.

The lead now looks to me much better than before we began its editing. There remains only one issue I would still like to discuss. I assume we agree that work is “transfer” of energy from one system to another (mediated by forces/interactions), so it is not the energy “contained” in the system; and most of the energy in universe may never appear as work. Therefore, I do not understand why you "cannot change work equals energy". I appreciate the need to strongly stress the aspect of equivalence, but could it not be re-worded to accomodate full truth? (And then perhaps, although I would not insist on that one, the "popular" alternative definition of work as "the energy transfered by force..." may be mentioned in passing, without my previous discussion you rightly described as unnecessary.)

And let me leave a few minor thoughts on the work and kinetic energy section for a day or two later.--Ilevanat (talk) 00:17, 10 October 2011 (UTC)

I edited Ilevanat's latest text for a couple of reasons:

• I changed "roughly described" to "described". The sentence loses none of its meaning when "roughly" is removed, therefore "roughly" is redundant. "Roughly" might be appropriate in a conversation, or in students' notes, but not in an encyclopedia.
• I removed "More precisely" for the same reason given above for removing "roughly".
• I changed "generates work" to "does work". A force does work on a body but I see no grounds for saying a force generates work. Dolphin (t) 04:51, 10 October 2011 (UTC)

Thank you both for your patient efforts on this article. I believe all of this has lead to improvements for this article. Regarding work as the transfer of energy, I hate to be a stickler on this, but transfer generally implies a rate at which something happens, and in this case energy transfer would be power not work. I am not sure that there is a more full truth than that work is equivalent to energy. I have never heard that work is energy transferred by a force, but if you interpret energy transfer as power, then a force acting on a moving particle generates power and power over a period of time is work. At this point, may I propose that the last paragraph of the introduction on work-energy be moved to the beginning of the section on work and kinetic energy? Prof McCarthy (talk) 07:19, 10 October 2011 (UTC)

The article is clearly improving, but there is still some way to go. First, let me approve of the changes Dolphin made, thanks. Second, I welcome the proof of the work-energy theorem, but let me discuss some details. It is (of course) stated correctly, but I would strongly prefer a brief derivation based on more "physical" arguments. For example, after the introductory sentence on the second law, I would propose the following arguments:

In the non-relativistic case, the law can be interpreted as the statement that a net force F acting on a particle of mass m gives the particle an acceleration a according to the equation F=ma. However, only the tangential component of the force does work, and the acceleration it gives to the particle is tangential acceleration, which is equal to the time derivative of the particle speed. Therefore, in order to calculate work done by the net force F, only the scalar tangential component of the equation F=ma is needed:

$F_{t}=ma_{t}=m{dv \over dt}$

Starting from the last integral of the formula (2), the work done from the instant $\scriptstyle t_{1}$ (when the particle speed is $\scriptstyle v_{1}$) untill the instant $\scriptstyle t_{2}$ (speed $\scriptstyle v_{2}$) is:

$W=\int _{t_{1}}^{t_{2}}\mathbf {F} \cdot \mathbf {v} dt=\int _{t_{1}}^{t_{2}}F_{t}\,vdt=m\int _{t_{1}}^{t_{2}}v\,{dv \over dt}\,dt=m\int _{v_{1}}^{v_{2}}v\,dv={\tfrac {1}{2}}m(v_{2}^{2}-v_{1}^{2})$

Since kinetic energy of the particle equals $\scriptstyle {\tfrac {1}{2}}mv^{2}$ and is usually denoted by $\scriptstyle E_{k}$ (or by $\scriptstyle K$), the result can be summarized as:

$W=\Delta E_{k}=E_{k_{2}}-E_{k_{1}}$

This is the work-energy theorem. Although here derived for a particle, in the above brief form it is also valid for rigid bodies. In words: Net work done by all forces acting on a rigid body equals the change in the kinetic energy of the body.

When forces act on a particle, the work of the net force is same as the net work of all forces, because they all have the same point of application so the work integrals are calculated along the same path (net work is obtained by addition of all works done by individual forces, taking into account the sign of each work).

When forces act on a body, however, net force can be used only when it is possible to determine its line of application in such a way that its torque is equal to the net torque. This is clearly not the case when forces form a couple (vanishing net force but non-vanishing torque). Therefore, the term "net work" must be used in the general formulation of the work-energy theorem. Also, the change in kinetic energy cannot be described as simply as in the case of a particle. But the instantaneous value of the rigid body kinetic energy can be described as the sum of the translational part $\scriptstyle {\tfrac {1}{2}}mv^{2}$ (using speed of the center of mass) and the rotational part $\scriptstyle {\tfrac {1}{2}}I\omega ^{2}$ (where the moment of inertia $\scriptstyle I$ is calculated around the axis set through the center of mass and parallel to the angular velocity vector $\scriptstyle {\vec {\omega }}$). Work done on the body generally changes both kinetic energy components.

For relativistic particles, work-energy theorem is described in the kinetic energy subsection of the special relativity article.

Let me know what you think about the proposal. Then we can resume discussion of the article in general.--Ilevanat (talk) 00:40, 13 October 2011 (UTC)

Work and Kinetic Energy

This derivation of the work energy principle is as correct and concise as I can make it. It is my understanding that the dot product of the resultant force on a particle with its velocity vector is how the component of the force that does work is separated from the component that does not do work. Perhaps there is notation that makes this more clear. However, I do not think that introducing a reference frame aligned with the velocity so the force can be decomposed into tangential and normal components only to obtain the same result is a simpler approach. Prof McCarthy (talk) 14:33, 13 October 2011 (UTC)

Regarding the similar derivation for rigid bodies, there is no special challenge because one computes the dot product of the resultant torque with the angular velocity vector. This is true for pure couples as well. Prof McCarthy (talk) 14:40, 13 October 2011 (UTC)

I made no implication the rigid body derivation could qualify as a remaining challenge of classical mechanics (though it would require a few more lines than the work-energy theorem for a particle). I only noted that "the change in kinetic energy cannot be described as simply as in the case of a particle", and proceeded with a note on translational and rotational kinetic energy. This was all intended to draw attention to the contribution of work to the rotational energy of unconstrained body, and to underline the incorrectness of the phrase "the work of the net force" appearing in the lead paragraph you moved into this section. However, such "notes in passing" might be insufficient; in the Croatian (Hrvatski) Work article I drew an illustration for the work done by the force acting on a body off the center of mass.

Regarding derivation of the theorem for a particle, I cannot agree with any argument that the concept of tangential force component is too difficult to grasp, simply because without it there is no understanding of the concept of work done by the force. Nor can there be any understanding of how the force changes the speed of an object (nor how it changes direction of its velocity). Your phrase "introducing a reference frame aligned with the velocity so the force can be decomposed into tangential and normal components" does sound discouraging (and pompous); however, it is my experience that even the least capable students can easily understand a simple explanation such as:

Tangential and normal component of force

"If a force acts generally forward (not necessarily exactly in the direction of velocity, there may be an angle of say 30 or 60 degrees), it increases the speed of the object. If it acts generally backward, it decreases the speed. But if it is perpendicular to velocity, than it is neither forward nor backward, so it cannot affect the speed: therefore such force only changes direction of velocity. For that reason, it is very useful to decompose any force into two components. One component is perpendicular to the velocity ($\scriptstyle {\vec {F}}_{n}$ , called normal, radial or centripetal) and changes its direction. The other component lies along the line defined by the velocity (the line of motion or tangent line); it is called the tangential component $\scriptstyle {\vec {F}}_{t}$ . This component changes the speed, and only this component does work."

So, why do not we introduce something like this in the lead, if it is needed to understand the concept of tangential component. Otherwise, we should remove the reference to "tangetial component" from the lead.

Besides, using dot product of the force and velocity, under assumption that readers do not understand it equals the product of the scalar tangential component and speed, is something I would not want to be any part of (would it not be hiding behind dot product simbols assumed meaningles?). Since we went this far, I hope we shall do better.

Eventually, the structure of the entire article should be reassessed. E.g. "Units" go to the end; "Zero work" certainly not before the formula (2) (and most of it does not deserve to remain); if "the line integral of its scalar tangential component along the path of its application point" should remain, then formula (2) should somehow reflect that (e.g. by including $W=\scriptstyle \int _{A}^{B}F\cos \alpha \,\mathrm {d} s$).

Finally, let me return to the statement "I am not sure that there is a more full truth than that work is equivalent to energy". I could live with that, but not with "This equates work and energy". Though I do not really understand what "stickler" means, I am old enough (over 60) to be an ever bigger one (whatever it menas, it sounds right). Work is a process, while energy is a state. Equivalent they may be, but not equated. And (though I hate to do this) let me quote the Resnick reference of the Work article "It is important to note that work is an energy transfer; if energy is transferred to the system (object), W is positive; if energy is transferred from the system, W is negative." Although I am not too fond of the textbook, let me also quote its lead statement on work: "Work is done by a force acting on an object when the point of application of that force moves through some distance and the force has a component along the line of motion". Not bad, but I prefer our present approach.--Ilevanat (talk) 02:25, 15 October 2011 (UTC)

I do not disagree with anything you have presented here. I try to keep my edits of others work focussed on moving the article in the right direction. Please make the changes you want. I do not like introducing a line integral into the lead of this article, but to say that it is simply the scalar tangential component of a force is misleading. I added "times the velocity" but only consider this to be correct, not enlightening. Prof McCarthy (talk) 00:37, 31 October 2011 (UTC)

Edits to the lead

I would propose moving this entire paragraph to a later section in the article:

Calculating the work as "force times straight path segment" can only be done in the simple circumstances described above. If the force is changing, if the body is moving along a curved path, possibly rotating and not necessarily rigid, then only the path of the application point of the force is relevant for the work done, and only the component of the force parallel to the application point velocity is doing work (positive work when in the same direction, and negative when in the opposite direction of the velocity). This component of the force can be described by the scalar quantity called scalar tangential component ($\scriptstyle F\cos \theta$, where $\scriptstyle \theta$ is the angle between the force and the velocity). And then the most general definition of work can be formulated as follows:

Work of a force is the line integral of its scalar tangential component times the velocity along the path of its application point.

Simpler (intermediate) formulas for work and the transition to the general definition are described in the text below.

It would fit well as the lead to the section "Mathematical calculation." Prof McCarthy (talk) 00:57, 31 October 2011 (UTC)

Good idea. Work is not a complex concept and it can be explained to readers who aren't familiar with calculus, dot products etc. I agree that the nominated text should be re-located to the section "Mathematical calculation." Dolphin (t) 01:55, 31 October 2011 (UTC)