Are Photons Tangible Entities or Merely Energy Manifestations?

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The discussion centers on the nature of photons and energy, questioning whether photons are tangible entities or merely energy manifestations. Participants express confusion about the concept of energy, particularly its definition as the capacity to do work, and how it relates to matter and photons. The conversation highlights the distinction between energy as a measurable quantity in physics and its more abstract interpretations in popular culture. There is also debate over the conservation of energy, especially in the context of systems and the universe's expansion, with some suggesting that energy may seem to "disappear" as it spreads out. Ultimately, the discussion emphasizes the complexity of understanding energy and its implications in both theoretical and practical contexts.
  • #51
chroot said:
Photons do not have rest mass. They do have energy, which is "equivalent" to mass, but they do not have mass.

- Warren
Photons are always moving relative to everything, aren't they? It isn't really possible to find an inertial frame relative to which any photons are at rest, is it?
 
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  • #52
Well I think Gravity is defined by time. What do you think of this

If electron A exists only in probability to be found 50% of the time on the left of a line and 50% on the right of a line. Then just like everything in our universe time is relative, so if time is running at a higher frame rate on the right of the line it may actually have spent more than 50% of the time on the right of the line. Therefor the energy it exerts on the rest of the atom is shifted to the right, and the whole atom shifts in such a method.

Ok now what if you put a photon in a box of perfect mirrors and there was only one Planck length of space to bounce around in.
 
  • #53
zoobyshoe said:
Photons are always moving relative to everything, aren't they? It isn't really possible to find an inertial frame relative to which any photons are at rest, is it?
Quite right, zoob.

- Warren
 
  • #54
PRyckman said:
Well I think Gravity is defined by time. What do you think of this
I think this is third time I've told you not to post your personal theories in the general physics forums. I really don't want to have to restrict your posting; please just follow our rules.

- Warren
 
  • #55
Isn't this the theory development one? sorry I'm getting tired. I think I'll just stick to talking in my own thread
 
  • #56
It's okay -- just please help us keep the place in order.

- Warren
 
  • #57
zoobyshoe said:
However, I don't see that the term motion is attached to velocity in a completely exclusive way. We don't say motion is velocity. I think it would be possible to arrive at a way to accurately describe all the forms of energy such that the relative motion in each is viewed as the unifying concept.

To refresh my memory, I did a search in my old dynamics books for the word "motion". It turns out that the term is actually identified not with the velocity, but with the position as a function of time. "Find the motion of particle P under the given forces" really means "Find r(t) for particle P under the given forces."

This would be a big help to those people who get hung up on grasping the concept. It explains a lot about the interconvertability of the different forms, and hence about the conservation of energy. The motion of one thing gets transferred to another and to another: the kinetic motion of a coil relative to a conductor causes the motion of electrons that cause the motion of their electric fields which results in the motion of photons.

Hmmm...Something seems to be lost in this equivocation though. When a mass is raised from a height y1 to a height y2, there particle is not in motion with respect to the Earth in either state. But it's energy most definitely has changed.

I don't think we can accurately say that energy is motion when there is an instance in which the motion of a body experiences no net change, while the energy does.

Is it not safe to say that all things which are in motion have energy, and that all things that have energy are in motion? (Potential energy = potential motion, of course.)

Yes, but here's the kicker: It's also safe to say that all things which are in motion have momentum, and that all things that have momentum are in motion.

Equating motion and energy not only blurs the distinction between those two concepts, but it also blurs the distinction between energy and momentum.
 
  • #58
I appologize for the lateness of my response. (For some reason, my notification setting had been changed to weekly update.)

LW Sleeth,
I apologize if I seemed obsesively contrary. It was not my intention. I basically agree with everything you said and that you gave a good explanation.




LW Sleeth said:
I can't say I fully understand why you find a contradiction between E = mc2 and what I said. Was it me describing energy in terms of "movement power,"
Yes.




LW Sleeth said:
how do we know work is done? Isn't it only when we observe movement?
That is my understanding.




LW Sleeth said:
Matter may contain a lot of energy, but the only way we know that is when we release it and observe how it moves things.
This characterizes my objection (which I admit was picky) precisely.




Tom Mattson said:
That's quite a nitpick there, Turin.
Yes, I agree. I guess I should emphasize that I basically agree with everything LW said. I just wanted to point out that the definition was not a general one.




Tom Mattson said:
It would be true enough for any mechanical engineer.
I would ask, how does a mechanical engineer define the initial amount of energy? It is this definition with which I contend.
 
  • #59
Tom Mattson said:
The problem with Moonrat's identification is that the term "motion" is already attached to a very different concept, namely that of velocity. Energy is not the same as velocity. The two have different units, and are described by different dynamical laws.

so correct me if I am mistaken, you cannot have velocity WITHOUT motion, correct, velocity without energy?
Velocity is motion *n* mass in combination and in harmony, am I mistaken with this understanding?
 
  • #60
Moonrat said:
so correct me if I am mistaken, you cannot have velocity WITHOUT motion, correct, velocity without energy?
Velocity is motion *n* mass in combination and in harmony, am I mistaken with this understanding?

No, what you have written here is not mistaken, but the problem is that it does not imply that "motion is energy".

Yes, motion implies that a body has energy. But to make the identification "motion is energy", it has to work both ways. That is, it must be true that having energy implies being in motion, and it doesn't.

Also, if you see my post to zoobyshoe, the identification "energy is motion" is too loose, because the reasons for applying it could just as easily apply to the statement "momentum is motion". Indeed, the latter statement would be more accurate, because you truly cannot have momentum without motion, and vice versa.
 
  • #61
Moonrat said:
so correct me if I am mistaken, you cannot have velocity WITHOUT motion, correct, velocity without energy?
Velocity is motion *n* mass in combination and in harmony, am I mistaken with this understanding?

well, let's see... I can be sitting here completely still but you can still come up to me and calculate my velocity. It's zero. So I do have a velocity. But to have positive or negative velocity there would have to be some motion involved. I have to move in a direction.
If I sit in the chair and do nothing I still have energy, because I have the ability to do some work.
rats - I can't remember where I was going with this! :confused:
 
  • #62
Math Is Hard said:
well, let's see... I can be sitting here completely still but you can still come up to me and calculate my velocity. It's zero. So I do have a velocity. But to have positive or negative velocity there would have to be some motion involved. I have to move in a direction.

And this brings up another problem with the identify "motion is energy". Motion is directed, and energy is not. You can have two people moving in opposite directions with the same mass and the same speed. They have the same energy, but not the same motion.
 
  • #63
Tom Mattson said:
And this brings up another problem with the identify "motion is energy". Motion is directed, and energy is not. You can have two people moving in opposite directions with the same mass and the same speed. They have the same energy, but not the same motion.

That makes sense - it will always be a scalar quantity. I tried to look up the units that energy is expressed in and I came back with several:

joules - the official energy unit of the International System of Units
watt-hours or kilowatt hours ( one kilowatt hours = 1000 watt hours)
BTUs - British Thermal Units
Therms (100 Therms = 1 BTU)

from http://www.uccs.edu/~energy/courses/energy_units.html

The one about Joules bugs me because I think of Joules as a measure of Work. If Joules are units of energy, then are Foot-Lbs units of energy also?
 
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  • #64
Math Is Hard said:
The one about Joules bugs me because I think of Joules as a measure of Work. If Joules are units of energy, then are Foot-Lbs units of energy also?

Energy has the same units as work by definition. When solving problems involving nonconservative forces using energy methods, you add the nonconservative work directly to the energy, which means they must have the same units.

The really annoying thing is not that energy and work have the same dimensions (indeed, they must), but that torque has the same dimensions as both energy and work (but we don't report torque in Joules, we report it in Newton-meters).
 
  • #65
Tom Mattson said:
Hmmm...Something seems to be lost in this equivocation though.
I have spent about an hour scouring what I said to see why you got the impression I was equivocating. I suppose it was this:"Yes, I see the problem. It isn't exactly accurate to say energy is motion." To avoid the impression of equivocation I should perhaps have been more definite, and said: "Yes, I see the problem: it isn't accurate to say energy is motion.

Ans so, when I said: "I think it would be possible to arrive at a way to accurately describe all the forms of energy such that the relative motion in each is viewed as the unifying concept," I was saying I thought such a description was possible, and not that it had already been accomplished. (Certainly not by saying "energy is motion". I agree with you that this can't be used.)

When a mass is raised from a height y1 to a height y2, there particle is not in motion with respect to the Earth in either state. But it's energy most definitely has changed.

I don't think we can accurately say that energy is motion when there is an instance in which the motion of a body experiences no net change, while the energy does.
I agree that we can't say "energy is motion."

However, I can use your example of a change in potential energy to demonstrate how following the trail of motion helps to understand the conservation of energy: in changing from the state of lower potential energy y1 to the state of higher potential energy y2 the particle had to be moved by an outside agent which had to transfer some part of its own kinetic energy to the particle to move it. If you subtract motion from the situation the particle will never change position. There will never be a higher position y2 and, consequently, no net change in energy.
Yes, but here's the kicker: It's also safe to say that all things which are in motion have momentum, and that all things that have momentum are in motion.
I think you have an excellent point here, because if my goal is to clarify things by describing energy with respect to motion, there is the momentum/kinetic energy confusion that seems to crop up quite often in the very same people who ask "What is energy?"

Everything you have said in this thread has been quite helpful in helping me to sharpen up the edges of my concept of energy. Every time this question comes up I am thrown back to remembering the massive Gale17 "What is Energy?" threads, and I am just realizing now that she may have been completely thrown off by the preconception you pointed out that some people have, that energy is some kind of substance or perhaps fluid. I am glad you thought to specify that it isn't. That kind of science fiction notion of "pure energy" as a substance or fluid may be the preconception that most needs to be eliminated when people are confused by the concept of energy.

Zooby
 
  • #66
Tom Mattson said:
No, what you have written here is not mistaken, but the problem is that it does not imply that "motion is energy".

Yes, motion implies that a body has energy. But to make the identification "motion is energy", it has to work both ways. That is, it must be true that having energy implies being in motion, and it doesn't.

.

cannot something have internal motion? as a cheeky example, me. I can sit complelty motionless and still, even in a coma. Yet I still have internal motion, organ systems and what not.

So even an object, say a asteroid. It is composed of elements that too are 'motioning' against one or the other..

am I mistaken in this?

thank you for your time
 
  • #67
zoobyshoe said:
I have spent about an hour scouring what I said to see why you got the impression I was equivocating. I suppose it was this:"Yes, I see the problem. It isn't exactly accurate to say energy is motion." To avoid the impression of equivocation I should perhaps have been more definite, and said: "Yes, I see the problem: it isn't accurate to say energy is motion.

Sorry, I saw where you had approved of Moonrat's equivocation "energy=motion", and I read something into your post that wasn't there. Sorry you wasted an hour on it!
 
  • #68
Moonrat said:
cannot something have internal motion? as a cheeky example, me. I can sit complelty motionless and still, even in a coma. Yet I still have internal motion, organ systems and what not.

Yes, there is always internal motion, but there's no apparent motion that can account for the difference between particles in different positions in a gravitational field. Also, there is the problem of direction that I mentioned.

So even an object, say a asteroid. It is composed of elements that too are 'motioning' against one or the other..

am I mistaken in this?

No, you're not mistaken, it's just that what you have presented is not enough to justify the identification "motion is energy".
 
  • #69
Tom Mattson said:
Sorry, I saw where you had approved of Moonrat's equivocation "energy=motion", and I read something into your post that wasn't there. Sorry you wasted an hour on it!
Now I think there is a different problem here. I see you referring to "energy=motion" as an "equivocation". My impression is that you think the word "equivocation" means "to relate by equasion" .

However "equivocation" is from the verb "equivocate" which means: to use equivocal language, esp with intent to decieve 2: to avoid committing oneself in what one says syn see LIE-equivocation.

In other words, by using the word "equivocation" you are either calling something a deception, or calling it non-committal.

I hope you can see why I was somewhat distressed.
 
  • #70
zoobyshoe said:
Now I think there is a different problem here. I see you referring to "energy=motion" as an "equivocation". My impression is that you think the word "equivocation" means "to relate by equasion" .

However "equivocation" is from the verb "equivocate" which means: to use equivocal language, esp with intent to decieve 2: to avoid committing oneself in what one says syn see LIE-equivocation.

In other words, by using the word "equivocation" you are either calling something a deception, or calling it non-committal.

I hope you can see why I was somewhat distressed.

Ach, no, that's not what I meant. I was using the word "equivocation" in the specialzed sense of logic. A "fallacy of equivocation" for example is the use of words that are not univocal in such a way as to make an unsound argument appear sound. It is done by equating two things that are not in fact equivalent.

No malintent is assumed in a fallacy of equivocation. Indeed, the "trickster" is not the person forwarding the argument, but language itself.

From Fallacy Files:

Of course, most words are ambiguous, but context usually makes a univocal meaning clear. Also, equivocation alone is not fallacious, though it is a linguistic boobytrap which can trip people into committing a fallacy.[/color] The Fallacy of Equivocation occurs when an equivocal word or phrase makes an unsound argument appear sound. Consider the following example:

All banks are beside rivers.
Therefore, the financial institution where I deposit my money is beside a river.

And that's what I meant. So you can think of my use of "equivocation" as "mis-identification".

Sorry for the misunderstanding. :smile:
 
  • #71
Tom Mattson said:
Yes, there is always internal motion, but there's no apparent motion that can account for the difference between particles in different positions in a gravitational field. Also, there is the problem of direction that I mentioned.



No, you're not mistaken, it's just that what you have presented is not enough to justify the identification "motion is energy".

My friend, help me here then because I cannot find one distinction where there is 'motion' and no 'energy'

Motion may be 'non-directional' so therefore, it does not create direction but rather the direction is created by mass, and in relation to other mass..

motion by itself may be unpredictable, as such when we enter the quantum realm, which is, if I am not mistaked, pure energy quantified.

motion by the way I see it is motion, big or small, and all things at their essence being composed of matter and motion, mass and energy, order and choas.

perhaps as we break things down into the quantum realm the distinctions become more blurred, but where can we have energy without motion? Motion, movement, vibration...zzzzzzzzzzzzzzzz.! Even my DNA 'vibrates'.

Velocity is only then relative to the relationship to the speed of light and mass, then, a vector or map of the motion, not the motion in and of itself?

Thank you again, you must being getting tired with all of this?
 
  • #72
Tom Mattson said:
Ach, no, that's not what I meant. I was using the word "equivocation" in the specialzed sense of logic...
...Sorry for the misunderstanding. :smile:
Thanks for clearing that up.
 
  • #73
Moonrat said:
Thank you again, you must being getting tired with all of this?

I also thank you, Tom. It is a great service what you do here.
:smile:
 
  • #74
Moonrat said:
My friend, help me here then because I cannot find one distinction where there is 'motion' and no 'energy'
See if this helps:

When we consider motion we are considering the phenomenon of change of location. Change of location is our focus and concern when we consider motion. The word "motion" was invented (or arrived at) to describe the phenomenon of change of location.

When we consider energy, we are considering the ability to do work, or, more broadly, to effect change. When we look at a thing in physics with respect to its ability to effect change, or work, then we are looking at it in terms of its energy. We aren't, in this case, focusing on the phenomenon of change in location, even if that is also happening.

The difference is one of our perspective: each word desgnates a different human concern about the matter, and they refer to two separate concerns. They really can't be used interchangably.

While it is true that all things that are in motion have energy, the terms "motion" and "energy" are referring to quite separate aspects of the situation. You can say "Where there's motion, there's energy" but not "Motion is energy". As Tom pointed out you can also say "Where there's momentum, there's energy." But not "Momentum is energy", because momentum means something different than energy, just as motion means something different than energy. Being found together does not make them the same thing.

Hope that helps, and hope I haven't misstated anything.
 
  • #75
zoobyshoe said:
See if this helps:

When we consider motion we are considering the phenomenon of change of location. Change of location is our focus and concern when we consider motion. The word "motion" was invented (or arrived at) to describe the phenomenon of change of location.

hmm, so it is more semantical, based on my subjective understanding of the word 'motion'..I see, my understanding of motion does not = the objective usage of the word motion, so I can now see that, as a formulae, motion does not = energy..

BUT! energy can be understood easier by understanding motion, since the two seem to be flip sides of the coin...they are distinguishable aspects of the same thing, quantified and separated for mathematical simplicity...

I don't define motion as 'velocity' I define motion, to myself, as non-directional energy, work, or movement...

as an example, and this may explain my perspective, I study a few of the chinese arts, you know, tai chi and that sort of thing..I noticed in the chinese movements, there is internal 'energy' which is also 'internal motion'. THe energy in the movements is not directed by the energy or the motion, but by the mind (yi in chinese) moving the 'center' or center mass. the 'energy' is just the wave or motion that is directed.

I was startled to discover these princaples of physics inside of this ancient chinese art, who developed these uncanny movements over thousands of yeas, anyway, it gives one a good laboratory to study the motion and mass of things, the human body..

so human beings have our internal motion or energy, feelings and the like..I like to keep things 'human' for myself and other laypeople, but still keep the objectivity of the science intact..

thanks all, I sure do appreciate this forum! Yikes, who needs college with you guys!

Moonrat
 
  • #76
Moonrat said:
hmm, so it is more semantical, based on my subjective understanding of the word 'motion'..I see, my understanding of motion does not = the objective usage of the word motion, so I can now see that, as a formulae, motion does not = energy.
I think you are starting to understand the problem. It is actually not that your understanding of "motion" is different than the "objective" usage. It is different than the physics usage.

In order to be able to speak of things and understand each other, physisists have had to deliberately define many, many terms in very specific ways. A "particle" in physics isn't the same as the everyday use nor does it just refer to elementary particles like electrons, protons, neutrons, and photons. In the right sitution, the Earth itself can be called a "particle" in physics.

Alot of terms have both an everyday use and meaning, and a different, much more specific, physics definition. This can trip people up if they're not aware of the specific physics terminology.
 
  • #77
Moonrat said:
My friend, help me here then because I cannot find one distinction where there is 'motion' and no 'energy'

There is the example I already cited: Gravitational potential energy. What is moving there? Also, rest mass energy does not seem to be connected to any motion.

Motion may be 'non-directional' so therefore, it does not create direction but rather the direction is created by mass, and in relation to other mass..

Don't understand this part.

motion by itself may be unpredictable, as such when we enter the quantum realm, which is, if I am not mistaked, pure energy quantified.

What is "pure energy quantified"?

motion by the way I see it is motion, big or small, and all things at their essence being composed of matter and motion, mass and energy, order and choas.

OK, but that still doesn't establish the identity "energy is motion". Have you not understood my reasons for saying that?

perhaps as we break things down into the quantum realm the distinctions become more blurred, but where can we have energy without motion? Motion, movement, vibration...zzzzzzzzzzzzzzzz.! Even my DNA 'vibrates'.

Right, but I have already cited examples of energy that are not connected to motion. The fact that everything moves is not sufficient to establish that "energy is motion".

Velocity is only then relative to the relationship to the speed of light and mass, then, a vector or map of the motion, not the motion in and of itself?

I'm confused.

*Velocity has no relation to mass.
*A vector is not the same thing as a map, but you seem to be treating them as though they are.
 
  • #78
Tom Mattson said:
There is the example I already cited: Gravitational potential energy. What is moving there? Also, rest mass energy does not seem to be connected to any motion.
Excuse me for stepping in on this point. If you cite "potential" energy then you must ask where is the "potential" motion. Where the "potential" motion is in the case of Gravitational potential energy and rest mass energy is therefore clear. The coexistence of the concepts of energy and motion remains intact.
 
  • #79
zoobyshoe said:
If you cite "potential" energy then you must ask where is the "potential" motion.

The point is that the particle in the gravitational field has nonzero energy, even when it is not moving. Sure, motion and energy can "coexist". Indeed, they must! But this is a clear cut case in which an energy form is not associated with motion.

Yes, there is the potential for motion, but the fact is that there is no motion until the energy changes form to kinetic energy (which is explicitly the energy of motion).
 
  • #80
Tom Mattson said:
The point is that the particle in the gravitational field has nonzero energy, even when it is not moving.
This concept of non-zero energy may be over my head. I haven't run into this term before. You may need to explain.

This is the way I understand it, correctly or incorrectly: if we speak of a particle at rest on top of a skyscraper on the verge of being blown off the edge by the wind so it can fall to the ground, then we can calculate its gravitational potential energy. This is a potential only. It doesn't actually acquire this energy till it falls. We can use it to do no work whatever, nor will it effect any changes, until it falls. As long as it is at rest, it has no real energy. There is the potential for energy by virtue of its height and the acceleration of gravity which will kick in as soon as the skyscraper is no longer blocking its path.
Yes, there is the potential for motion, but the fact is that there is no motion until the energy changes form to kinetic energy (which is explicitly the energy of motion).
My reasoning is that there is also no energy until kinetic energy kicks in. Prior to that it remains only a potential.

Now, when you speak of "non-zero" energy, you may be into a concept that is different than potential energy that is above my head at this point.
 
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  • #81
zoobyshoe said:
This is the way I understand it, correctly or incorrectly: if we speak of a particle at rest on top of a skyscraper on the verge of being blown off the edge by the wind so it can fall to the ground, then we can calculate its gravitational potential energy. This is a potential only. It doesn't actually acquire this energy till it falls. We can use it to do no work whatever, nor will it effect any changes, until it falls. As long as it is at rest, it has no real energy.

No, that's not right. It really does have the energy. If it didn't, then we couldn't say that energy is conserved.

The gravitational potential energy before the drop is equal to the kinetic energy just before it hits the ground.

There is the potential for energy by virtue of its height and the acceleration of gravity which will kick in as soon as the skyscraper is no longer blocking its path.

Potential energy is not "the potential for energy". It is an energy form in its own right.
 
  • #82
zoobyshoe said:
This concept of non-zero energy may be over my head. I haven't run into this term before. You may need to explain.
He's simply saying that if you hold a brick in the air, it has potential energy. If you drop it on your toe, you'll discover how much. It doesn't matter if you're holding the brick still or not.

- Warren
 
  • #83
I have a some what related question, and I hope it's not too far off topic. We were talking about freefall in class and my teacher said that before freefall begins (from whatever height) at time=0 an object's acceleration is = 9.8 m/sec^2, even though velocity =0 and distance = 0.
If I were to graph the acceleration of freefall of an object on Earth as a function of time, at t =0 I would be tempted to draw an open circle at the beginning of a horizontal line of y = 9.8, and thereby specify that acceleration > 0 only at the the fraction of a second that the object begins to move. What is the flaw in my reasoning? Thank you.
 
  • #84
Math Is Hard said:
If I were to graph the acceleration of freefall of an object on Earth as a function of time, at t =0 I would be tempted to draw an open circle at the beginning of a horizontal line of y = 9.8, and thereby specify that acceleration > 0 only at the the fraction of a second that the object begins to move. What is the flaw in my reasoning? Thank you.
...and so you say if you were to throw a stone up in the air, it would have a constant acceleration of 9.8m/s^2 everywhere in its trajectory, except at its highest point where v=0? Why? Doesn't make any sense to me. Just because v=0 does not mean the rate of change of v is zero. Or think of a pendulum: at the extreme point of the swing, v=0 but a= a maximum; right when it passes through centre, v= a maximum, but a=0.
 
  • #85
chroot said:
He's simply saying that if you hold a brick in the air, it has potential energy. If you drop it on your toe, you'll discover how much. It doesn't matter if you're holding the brick still or not.
OK. Just checking to make sure "non-zero energy" wasn't a specialized term.
 
  • #86
zoobyshoe said:
OK. Just checking to make sure "non-zero energy" wasn't a specialized term.

Nope, I just meant that the value of the energy is something other than zero. Of course, one could argue that the zero of energy could be set at any point, which is of course true. But, if you put two identical particles at two different heights, both motionless, then they will certainly have different potential energies (they can't both be zero!), then we have an example of two particles with the same motion (that is, *no* motion, relative to the Earth) and two different energies.
 
  • #87
I have a question which may help (certainly for me) to clear up any confusion regarding potential energy and it's relation to conservation of energy. Consider the following example:

Two planets in space, both have an attraction to one another, and are slowly moving together. They have a certain quantifiable potential energy (correct?) If we were to suddenly move one of the planets as quickly as physically possible, to another part of the universe, would that potential energy then be removed also? Or just shifted so that other objects now closer by would be in receipt of this energy?

I say to move the planet quickly as I have a feeling that if it was done slowly the potential energy would be converted to kinetic by 'tugging' the other planet with it, but it's really an unsubstantiated assumption on my part that the speed of movement in this case is related to the amount of effect it has on the other object.

thanks,
Martin
 
  • #88
krab said:
...and so you say if you were to throw a stone up in the air, it would have a constant acceleration of 9.8m/s^2 everywhere in its trajectory, except at its highest point where v=0? Why? Doesn't make any sense to me. Just because v=0 does not mean the rate of change of v is zero. Or think of a pendulum: at the extreme point of the swing, v=0 but a= a maximum; right when it passes through centre, v= a maximum, but a=0.

Thank you, dear Krab. Excellent example. That helped a lot!
 

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