Understanding Work: Defining the Price of Electron Redistribution in Electricity

[Beanyboy]

The definition referred to by @zanick is actually my preferred definition of work. It comes from thermodynamics. The way I usually hear it expressed is: work is the transfer of energy from one system to another by any means other than heat.

Of course, that definition in turn relies on definitions of energy and heat and so forth, and it all has to be related to experimental measurements.

Thanks. Nice of you to pitch in. May I ask, do you find that nuance, word order, analogy, etc, make a significant difference to you when you're trying to understand something new in Physics? I guess, what I'm saying is,can you define why you might find A's definition is 'better' than B's?

Here's a personal simple example: F=ma. When I was told "Force is equal to mass times acceleration", frankly this did not really 'sink in'. One day, someone said, "The acceleration of a mass, is its force, and by 'of', I mean multiplied by." Cue light bulb going off. This to me made sense: the more you accelerate a massive object, the more force comes with it. Bingo. Finally.

Here, word order was critical for the explanation. The "teacher" read the expression from right to left, left to right.

So, what do you look for when looking for "a good definition?"

 

[Beanyboy]

I don't think this was fully addressed:

Being an English teacher, your natural way of thinking is that definitions of words are put together with other words. Physics doesn't work that way. In physics, the language is math and definitions are made of math. At best, the words are just an imprecise translation of the math. So the only way to really learn this concept is to accept that English is the wrong language for describing it and instead use the right one.

 

[Beanyboy]

Thanks, I really like this explanation. I do speak three other language fluently, so the idea that what's needed here is another language really resonates with me. I am going back to my Math, working from the ground up. Today, Mr. Descartes told me: You just keep pushing. You just keep pushing. I made every mistake that could be made. But I just kept pushing.

For me, it's like Physics is "a joke" - one that I don't get. But, I want to be in on the joke. I want to understand what happens when I turn the lightswitch on in my room. I want to be able to tell my daughter why the sky is blue.

People like you help. So thanks.

 

[Beanyboy]

It may not be very helpful but it is a natural reaction to someone who is way out of his depth. Physics (real Physics) is a very self consistent (working) structure and can't be bent to a personal model. If you want to work with your own rules then they have to be as self consistent as what you can read in textbooks. How much cross checking have you done with your model?

First, thanks for taking time out to reply. This helps, really. Yes, I'm "out of my depth". My dilemma is to try to figure out what I need to know, in order to understand. This is not always easy, because I don't know what the rungs on the ladder are. I'm the novice. If I've given "a definition", then I assure you, it's not mine! I haven't had an original thought since I was five years old and I thought the sun and moon were brother and sister. A "learned man" said "We manipulate electrons to do our bidding. They don't always want to be where they are ..." I won't bore you with the details here. His definition resonated with me. But then, of course it would, perhaps because, it was "a lie".

I'm giving him the benefit of the doubt here, but I do find, as a teacher, that sometimes we have to simplify, "to lie" in order to "engage the learner". Remember, the Bohr model of the atom? A "lie", of course. But, it got you started. Later, you were smart enough to figure out how to unpack it, then re-tool yourself with the more advanced version. You were able to take off the "training wheels" and you were on your way.

Incidentally, I'm not a Science teacher. I have no background in Science whatsoever. I've been taking AP Physics and Chemistry online, with Khan Academy, purely for personal amusement for about 6 weeks. So, I'm sorry if I've wasted your time, but again, I really appreciate you taking time out to try to explain this tricky concept to me.

 

[Beanyboy]

If you are really interested in learning basic physics, I recommend finding a used physics textbook and working through it. https://www.amazon.com/dp/0201603225/?tag=pfamazon01-20 to the 2004 edition of the textbook I use. It's for sale on amazon for $3.19 right now (click on "Other Sellers").

I appreciate the offer of help. Thanks. I 'took up Physics' a 6 weeks ago, and it's become "a beautiful obsession". I have no background whatsoever in Science, but I'm learning a lot. Since the book is so cheap, I think I'll go ahead and order it. There might be a half-dozen sentences in that book that could help me. But hey, at that price, it'd be worth it. So thanks. I appreciate you pitching in.

 

[Beanyboy]

@Beanyboy
You used this fiction line about CERN before, haven't you?

Eh, no. I was just trying to, well , you know...

My work at CERN does keep me busy though. Being a lavatory attendant aint just about changing toilet rolls let me tell you. Boy, oh boy, those Physicists! Why, half of them can't even pee straight standing up. All over the GD floor! And who's going to clean it up? And they're always to darn busy to answer my questions. Which is what brought me to PF!

 

[sophiecentaur]

Being a lavatory attendant aint just about changing toilet rolls

I imagine there are particles on the floor that need to be removed sometimes. Do you charge your users? I bet they come in all colours. and some of them would be very strange.

 

[sophiecentaur]

Thanks. I 'took up Physics' a 6 weeks ago, and it's become "a beautiful obsession".

Enjoy it; it can be really "beautiful"! I would advise you to try to get a good base of conventional / elementary Physics before being tempted too far into QM and Relativety, though. Hardly a day goes by for me when I don't refer back to the classical Physics I learned in my schooldays. (This was before they had sorted out Quarks, the Big Bang or Plate Tektonics - hard to believe but true and I wasn't taught in Latin)
Popular Science Broadcasting and Writing can be dangerously glib about modern ideas and it should all be treated with healthy skepticism until you can read the same things in Nature or The New Scientist.

 

[Beanyboy]

Enjoy it; it can be really "beautiful"! I would advise you to try to get a good base of conventional / elementary Physics before being tempted too far into QM and Relativety, though. Hardly a day goes by for me when I don't refer back to the classical Physics I learned in my schooldays. (This was before they had sorted out Quarks, the Big Bang or Plate Tektonics - hard to believe but true and I wasn't taught in Latin)
Popular Science Broadcasting and Writing can be dangerously glib about modern ideas and it should all be treated with healthy skepticism until you can read the same things in Nature or The New Scientist.

Thanks for the advice. Very helpful and very reassuring. Ciao for niao.

 

[Dale]

May I ask, do you find that nuance, word order, analogy, etc, make a significant difference to you when you're trying to understand something new in Physics?

No. That is essentially the purpose of using math. All of the English is just a loose translation from the math, and is subject to all of the deficiencies of translations.

The definition I mentioned above was a translation from $W=Q-\Delta U$

Of course, a particular student may "get it" based on their personal learning style, but that is more about the teaching and learning styles than about the definitions themselves.

 

[Beanyboy]

No. That is essentially the purpose of using math. All of the English is just a loose translation from the math, and is subject to all of the deficiencies of translations.

The definition I mentioned above was a translation from $W=Q-\Delta U$

But isn't using English the means by which you extract meaning from the symbols? Or using French, or Italian for that matter. How can it make sense if there are no words to express it? And of course, I'm not being glib here.

 

[Dale]

But isn't using English the means by which you extract meaning from the symbols? Or using French, or Italian for that matter. How can it make sense if there are no words to express it? And of course, I'm not being glib here.

Ask yourself, does Italian require translation into English as the means by which you extract meaning from Italian words?

 

[Beanyboy]

It is the integral of a force over the distance. What this means is it tells you how much energy is being put into a system, regardless of time, which makes it useful to express a system as a state function such as energy. When you talk about a conservative force, it is the potential energy, which helps us explain why orbits work. In orbits and other oscillatory motions in classical mechanics governed by conservative forces, it is as if the potential energy and the kinetic energy (a measure of 'how fast you are' [squared times half the mass]) are playing ball, constantly moving energy back and forth between states, as energy is a state function. Again useful when you aren't worried about time.

As for electronics and electrical engineering, we have a conservative force, however, the source does not have an infinite amount of energy, i.e. the battery drains out. The work generated by a battery is regarded as a potential, a bucket with a certain amount of water. It is more useful to use the electric fields, which can be thought of as odors, rather than the force.
Protons: emit positive odors, hate positive odors, like negative odors.
Electrons: emit negative odors, hate negative odors, like positive odors.
The further away the particle is from a the source of an odor, it senses that said odor as less potent.
If the particle likes the odor, it will move closer, if it hates it, it will move away.
Also they can't smell themselves, so we are golden with those rules.

So we need to use a different quantity, electric tension, the integral of the electric field over distance. This is not however a measure of energy, but this quantity is constant to every power source (in theory) and does not care whether you have 1 meter wire or 10 meters of the same wire, the tension is the same. With that we can conclude the electric field decreases if it is a longer wire, in a sense the longer wire has more resistance, how hard it is for the battery to generate a field with the given tension.
The real method of proving resistance though involves more math and vector analysis, but at the end of the day V=IR, ohm's law, will pop in your notebook.

We know resistance is how hard it is to generate a field, and know what is Voltage (electric tension), what is I? Well, within the real proof you will find that I is the current, how much charge is being transferred at a given time. I know you have requested no maths, but it is virtually impossible for me to base my explanations on anything but. Then again the language of physics IS math so please bare with me as I wave my hands with math that would surely make mathematicians scream at me.
If we apply just a little calculus:
F=qE
∫F⋅ds=∫qE⋅ds
because our charge q is of a point charge, we can take it outside of the integral and thus:
U=qV
where U is energy, and V is the voltage
but wait we have current not charge, and current is the change of charge over time:
(d/dt)U=(d/dt)qV
For the purposes of demonstration we shall assume constant voltage (DC) so V remains as is:
dU/dt=V(dq/dt)
Now we got Power, change of energy for a given time, we shall denote that as P.
P=VI [from ohm's law: P=IV=I²R=V²/R]

So now finally after all this math we can summarize:
Each battery has a certain capacity, the amount of energy it holds, it is your bank account in circuits. When a circuit is connected, it will allow a current to flow, like a service company, however no service is free, it needs food, so it will require you to pay money, but unlike a service which will want money in regular intervals, the circuit will require you to apply power constantly. If you run out of energy, the circuit will stop giving you service.

Physically, work is the difference between an extreme state to a state of equilibrium for non-conservative forces. Charges will happily move to where they want to be, state of equilibrium, but for that they lose energy. Although the electric force is conservative for the purposes of most circuits, you have some form of friction, which isn't conservative, which is why electrons don't flow forever in an oscillatory motion. In regard to the salmon analogy, they are not flowing upstream, they flow downstream, they just hit rocks on the way. A clumsy fish that is I should say.

I should stress though, analogies are okay to get you started, but as you progress you need to treat the electric circuit as it is, an electric circuit. It'll help you understand the basics of ohm's law but once you start to look at RC circuits, semiconductor circuits, electro-mechanical machinery etc., you are getting into the realms of differential equations, and analogies will not solve you those equations, they can only get you as far as to express the circuit in terms of its components in a differential equation. At that point and on work is the amount you pay for the circuit to keep working. That is from an engineering point of view.

Congratulations, you've blown the top of my head off. First, a confession. I'm not "making up" definitions, I'm just repeating what other "experts" have said and trying to make sense of it. I'm a total novice at this game too, ignorant but not stupid. Let's try to go through your reply, bit by bit, and I'll give you my honest feedback on each paragraph.
1. Paragraph 1: Love it. Love the "baseline tennis" analogy of potential and kinetic energy passing the ball back and forth.
2. Paragraph 2. Again, wonderful use of language by resorting to metaphor of smell. Mmmm.
3. Paragraph 3. Mr Ohm raises his "ugly" head. He and I have met, very very briefly and although he did try to speak to me, I couldn't really understand him that well. I'm assured however it's essential I get to know him, and I shall.
4. Paragraph 4. I know I requested no Math, but look, you've explained so much so far without it. That said, I realize a deeper, more meaningful appreciation of the "joke" does require me to be more mathematically adept. I'm working on it, daily. Incidentally, what was it about your math style that would have pissed off the mathematicians? Anyway, suffice to mention, this was the most challenging part of your reply for me, but I'll attack it again later.
5 Paragraph 5. Now that's some good writing there my boy; the battery and the bank account. That's the sort of writing that has me copying out what you've written word for word, by hand. The type of paragraph I like to have in my car, in the bathroom, on fridge. Bravo sir.

Finally, the poor auld salmon. You know there was something that told me that the "upstream" motion in the original quote didn't quite fit. And yes, I understand why he's clumsy.

So thank you sir, thank you very much indeed. It's been a pleasure listening to you.

 

[Beanyboy]

Ask yourself, does Italian require translation into English as the means by which you extract meaning from Italian words?

Funny you should ask, I speak Italian, and French and Irish too, fluently. So, the honest answer is yes, sometimes for the sake of brevity for example, a translation can be very practical. However, some things are harder to translate, Take the French word "aperitif", in Italian "aperitivo". Put simply, the drink you have before a meal. However, there's more, much much more to it than just the consumption of a drink. One would have had to live in these countries to fully appreciate what it means to have this pre-dinner drink, and, although it's a similar phenomenon in France and Italy, it's not the same. However, the short answer to your question is, yes, I can understand a lot of Italian if I translate it into English, and personally, I often require the translation, just to get me started.

 

[Beanyboy]

Congratulations, you've blown the top of my head off. First, a confession. I'm not "making up" definitions, I'm just repeating what other "experts" have said and trying to make sense of it. I'm a total novice at this game too, ignorant but not stupid. Let's try to go through your reply, bit by bit, and I'll give you my honest feedback on each paragraph.
1. Paragraph 1: Love it. Love the "baseline tennis" analogy of potential and kinetic energy passing the ball back and forth.
2. Paragraph 2. Again, wonderful use of language by resorting to metaphor of smell. Mmmm.
3. Paragraph 3. Mr Ohm raises his "ugly" head. He and I have met, very very briefly and although he did try to speak to me, I couldn't really understand him that well. I'm assured however it's essential I get to know him, and I shall.
4. Paragraph 4. I know I requested no Math, but look, you've explained so much so far without it. That said, I realize a deeper, more meaningful appreciation of the "joke" does require me to be more mathematically adept. I'm working on it, daily. Incidentally, what was it about your math style that would have pissed off the mathematicians? Anyway, suffice to mention, this was the most challenging part of your reply for me, but I'll attack it again later.
5 Paragraph 5. Now that's some good writing there my boy; the battery and the bank account. That's the sort of writing that has me copying out what you've written word for word, by hand. The type of paragraph I like to have in my car, in the bathroom, on fridge. Bravo sir.

Finally, the poor auld salmon. You know there was something that told me that the "upstream" motion in the original quote didn't quite fit. And yes, I understand why he's clumsy.

So thank you sir, thank you very much indeed. It's been a pleasure listening to you.

Oh, and I forgot to add, NO, I won't bare (sic) with you! Now that, that made me smile.

 

[Dale]

So, the honest answer is yes,

No, the honest answer is no. Italian words have meaning even without translation into English. If such a translstion were required then Italian bambinos would not be able to extract meaning from their parent's speech until after they learned English.

That is what I get for asking a rhetorical question instead of just making the point as a statement.

for the sake of brevity for example, a translation can be very practical

Yes, this is correct. As a practical matter it is faster to communicate and learn using translations. But do not mistake convenience for a fundamental limitation on the ability of mathematical symbols to convey meaning.

 

[Beanyboy]

We were at crossed purposes since I didn't assume you were speaking of a uniquely mono-lingual environment. If we assume then, a uniquely monolingual environment, then the Italian bambino that hears, say Pythagorus' theorem in Italian, but does not understand it, would be none the wiser if it were translated into English.

Physics and Math are like foreign languages to me. The speakers of those languages also speak my language, English. Sometimes they can help me with explanations, and I really should ask them for their help, since many of them like to help. However, sometimes I need to discover it for myself. I need to see for myself, that if you draw a square, 1cm by 1cm, and if you calculate the magnitude of the diagonal, you'll never really find that number on the number line. But the process of drawing the square, the process of figuring it out for myself the wonder of it all, is "untranslateable". No one can explain this to me. I have to live for myself. These moments, in Physics as in Math, are like being in the Dorgdogne, playing boules, eating pate, speaking in French to French people, and drinking a Pernod, all at the same time. Calling this, "an aperitif", a "pre-meal drink", does not equate to having experienced what it really means.

For me then, it's a process of finding the people who can tell me, what can be explained, and what must be experienced to be really understood.

I don't know if I've explained myself clearly. But, thanks for taking time out to help me.

 

[Dale]

We were at crossed purposes since I didn't assume you were speaking of a uniquely mono-lingual environment.

It doesn't matter if the environment is monolingual or not. The symbols in any language (natural, math, computer) have meaning on their own. The meaning is not acquired by virtue of the translation into some other language, although such translations are often convenient. This is in response to your previous post that English is the means by which meaning is extracted from math.

Physics and Math are like foreign languages to me. The speakers of those languages also speak my language, English. Sometimes they can help me with explanations, and I really should ask them for their help, since many of them like to help.

Yes, and the point is that you should be aware that these people are translating the concepts for your convenience. If you stick exclusively with English then you need to recognize that you are getting a loose translation. You will therefore need to be a little tolerant of things like word ordering and nuance, recognizing that such subtleties are often beyond the capability of any translation.

 

[Beanyboy]

It doesn't matter if the environment is monolingual or not. The symbols in any language (natural, math, computer) have meaning on their own. The meaning is not acquired by virtue of the translation into some other language, although such translations are often convenient. This is in response to your previous post that English is the means by which meaning is extracted from math.

Yes, and the point is that you should be aware that these people are translating the concepts for your convenience. If you stick exclusively with English then you need to recognize that you are getting a loose translation. You will therefore need to be a little tolerant of things like word ordering and nuance recognizing that such subtleties are often beyond the capability of any translation.

This is good. I like the way you've pointed this out to me. Thanks.

 

[DarkBabylon]

His definition is also standard, for thermodynamics.

Which d? The surfaces are sliding past each other, so the d for one is different than the d for the other. This specific example is actually one where the definition is advantageous.

I don't see why would the distance d be different from body to body. One being rougher does not justify it, so at hindsight it doesn't seem to make sense. Care to back that up?

 

[Mark44]

Here's a personal simple example: F=ma. When I was told "Force is equal to mass times acceleration", frankly this did not really 'sink in'.

What you were told was a direct translation of the formula into English.
Force --- F
is equal to -- =
mass -- m
times -- X (can be omitted; symbols that are adjacent are assumed to be multiplied)
acceleration -- a

When I was an undergrad, I took a year-long engineering physics sequence. The equation F = ma came up so much that my housemate and I decided that if we didn't know this formula, the alternative was "F = your grade."

One day, someone said, "The acceleration of a mass, is its force, and by 'of', I mean multiplied by." Cue light bulb going off. This to me made sense: the more you accelerate a massive object, the more force comes with it. Bingo. Finally.

That's really a backwards perspective. It's the force that causes the object to accelerate.

Here, word order was critical for the explanation.

I don't see how changing the word order in "Force is equal to mass times acceleration" leads to greater understanding.

The formula F = ma is derived from the second of Newton's three laws of motion. See https://en.wikipedia.org/wiki/Newton's_laws_of_motion under "Newton's second law".

 

[Dale]

I don't see why would the distance d be different from body to body.

Consider an automobile skidding to a stop with locked brakes. The tires moved perhaps 50 m, the ground moved 0 m.

 

[bsheikho]

OP, don't fret over the formulas. Watch a Richard Feynman on electricity and you'll get what your looking for. A way to visualise the concept.

 

[DarkBabylon]

Consider an automobile skidding to a stop with locked brakes. The tires moved perhaps 50 m, the ground moved 0 m.

Now put the automobile at rest and the ground has moved 50 meters and the car 0 :)
They skidded on one another a distance d, of course there was some work done on the car and it lost energy, but where did that energy go? Initially to the ground, you'd find that while one lost energy, the other gained it if you keep the axis the same but change point of origin's placement, that is a frame of reference.

 

[ZapperZ]

OP, don't fret over the formulas. Watch a Richard Feynman on electricity and you'll get what your looking for. A way to visualise the concept.

That's rather ironic, considering the video ends with Feynman exulting the remarkable accomplishment of "Maxwell equations". I also don't see how this has any relevant with the concept of "work" that has been the central question here.

Here's the thing: you can learn about physics superficially by reading pop-science books, watching YouTube video like this, and not wanting to learn about these equations. But you'll never go beyond that level without the mathematics, and understanding the mathematics. There is just no way around this, and Mother Nature has made this non-negotiable.

As I've said a million times, physics doesn't just say "what goes up, must come down". It must also say "when and where it comes down"!

Zz.

 

[jbriggs444]

Now put the automobile at rest and the ground has moved 50 meters and the car 0 :)
They skidded on one another a distance d, of course there was some work done on the car and it lost energy, but where did that energy go? Initially to the ground, you'd find that while one lost energy, the other gained it if you keep the axis the same but change point of origin's placement, that is a frame of reference.

The rest frame of the car is not inertial. That complicates the analysis. Can you pick an inertial frame and re-cast the problem using it?

 

[Beanyboy]

What you were told was a direct translation of the formula into English.
Force --- F
is equal to -- =
mass -- m
times -- X (can be omitted; symbols that are adjacent are assumed to be multiplied)
acceleration -- a

When I was an undergrad, I took a year-long engineering physics sequence. The equation F = ma came up so much that my housemate and I decided that if we didn't know this formula, the alternative was "F = your grade."
That's really a backwards perspective. It's the force that causes the object to accelerate.

I don't see how changing the word order in "Force is equal to mass times acceleration" leads to greater understanding.

The formula F = ma is derived from the second of Newton's three laws of motion. See https://en.wikipedia.org/wiki/Newton's_laws_of_motion under "Newton's second law".

That's really got me thinking now. Very interesting indeed. You do know I'm a complete novice here, so feel free to just ignore my ignorance. But, if you're in the mood for explaining ... you're saying "Force causes the object to move". Haven't you altered the expression "Force is equal to mass times acceleration"? Are you altering it for "your convenience"?

So, let me ask you this, are you saying I could/should read the equation as "Force causes mass times acceleration". Looks like I may have some "unlearning" to do! As the great Mark Twain once said: It aint what you know that gets you into trouble. It's what you know for sure, that just aint so."

 

[DarkBabylon]

what was it about your math style that would have pissed off the mathematicians?

Physicists and mathematicians tackle mathematical problems differently. Physicists generally avoid certain mathematical formalism being too obvious or too redundant for certain purposes, or that we like to apply logic and physics to solve a certain equation without needing half a white board worth of formalism, sometimes however we resort to that formalism if we need to. Mathematicians, at least first year undergrads, would be annoyed by just you treating dv/dt as a fraction rather than a derivative, but the annoyance is innocent most of the time.
There probably is nothing wrong mathematically in what I wrote and mathematicians would be fine with it.

Also I do understand that I kinda lost you with the math, but kinda did expect that. However I should point out, the math itself uses algebra and just a tiny amount of calculus. The rest is just physics. All of these are not too complicated to learn, heck sometimes you don't even need the integral and derivatives in certain cases and just solve it with pure algebra. Sure pure algebra wouldn't get you a PhD, but the basic understanding as a layman it is sometimes enough.

 

[Beanyboy]

That's rather ironic, considering the video ends with Feynman exulting the remarkable accomplishment of "Maxwell equations". I also don't see how this has any relevant with the concept of "work" that has been the central question here.

Here's the thing: you can learn about physics superficially by reading pop-science books, watching YouTube video like this, and not wanting to learn about these equations. But you'll never go beyond that level without the mathematics, and understanding the mathematics. There is just no way around this, and Mother Nature has made this non-negotiable.

As I've said a million times, physics doesn't just say "what goes up, must come down". It must also say "when and where it comes down"!

Zz.

I couldn't agree more with you. "Philosophy is written in that great book, which ever lies before our eyes, by which I mean, the Universe. But, we cannot understand it, if we do not first learn the language and grasp the symbols in which it is written. This book is written in the mathematical language... without which one wanders in vain through a dark labyrinth."

 

[Mark44]

That's really got me thinking now. Very interesting indeed. You do know I'm a complete novice here, so feel free to just ignore my ignorance. But, if you're in the mood for explaining ... you're saying "Force causes the object to move". Haven't you altered the expression "Force is equal to mass times acceleration"? Are you altering it for "your convenience"?

No, I'm not altering anything. I was attempting to correct what seems to be a misconception on your part in post #36:

the more you accelerate a massive object, the more force comes with it

The force doesn't "come with it" - the force is what causes the acceleration of the object.

So, let me ask you this, are you saying I could/should read the equation as "Force causes mass times acceleration".

No, read it as "force equals mass times acceleration", exactly like the formula F = ma.

Looks like I may have some "unlearning" to do! As the great Mark Twain once said: It aint what you know that gets you into trouble. It's what you know for sure, that just aint so."

 

[berkeman]

"Force causes mass times acceleration".

No. The force causes the mass to accelerate, and the amount acceleration depends on the values of the force F and the mass m, according to the equation F=ma..

 

[DarkBabylon]

Due to a disagreement with F=ma, let me point out that it is only a derivation and a rule of thumb, not the law itself.
The law itself states that for every body you can assign a quantity of momentum which is equal to its mass times the velocity of the object, which ends up being a vector because of this. Such quantity can be altered, and if we would like to know how much it changes over time we just take the derivative with respect to time. In a sense, we want to know how much momentum does a body get over a certain amount of time. That rate of change, THAT's the force, so in general:
F=dp/dt
Which means now you can talk about a system with a changing mass, such as a rocket.

 

[Beanyboy]

No, I'm not altering anything. I was attempting to correct what seems to be a misconception on your part in post #36:
The force doesn't "come with it" - the force is what causes the acceleration of the object.
No, read it as "force equals mass times acceleration", exactly like the formula F = ma.

12 = 4 times 3. Therefore, if I have 3 repeated, 4 times, then I'd have 12. Here, I've explained the equation without using the word "equals". To my knowledge, I haven't altered the essence, even if I've altered the words. Now it's your turn. Explain F = ma without using the word "equals".

 

[Mark44]

12 = 4 times 3. Therefore, if I have 3 repeated, 4 times, then I'd have 12. Here, I've explained the equation without using the word "equals". To my knowledge, I haven't altered the essence, even if I've altered the words. Now it's your turn. Explain F = ma without using the word "equals".

Why?
The formula uses the symbol '='. My explanation uses the equivalent word in English.
What's your point?

 

[berkeman]

Explain F = ma without using the word "equals".

I just did!

The force causes the mass to accelerate