Is holding something in a gravitational field doing work ?

[Dale]

Fair enough I suppose. Although if I was the son I would counter this with "could the situation of a man holding a ball physically exist in the conditions needed for the latter?"

Yes, of course it could physically exist. Reference frames are just coordinate systems. Changing reference frames is just a way of looking at the same problem differently. So, although it is silly, there is no physical reason that would prevent you from using a free-falling reference frame for this problem.

And if I was the father I would counter this by grounding him (because I could).

 

[russ_watters]

Yes, of course it could physically exist.

So, although it is silly, there is no physical reason that would prevent you from using a free-falling reference frame for this problem.

Could it? How? Describe this reference frame to me.

 

[bunburryist]

Believe it or not, I've never had to ground my son! But seriously folks . . .

What I'm going to take away from this is what my son and I were going back and forth about in the first place - that he was talking about a local frame "guy holding a ball in his hand" and I was talking about something relativistic (accelerating rockets, etc.).

Thanks for all of your responses.

 

[russ_watters]

Were you really? Or are you changing the scenario now because you don't want to be beaten by your son?

I always hated it when people would do that when I was a kid. No one ever wants to be wrong in front of a kid.

I once won a bet with my 7th grade math teacher. He wouldn't actually admit he was wrong, but he bought me the soda anyway.

 

[Renge Ishyo]

Were you really? Or are you changing the scenario now because you don't want to be beaten by your son?

This thread is another great example of how to apply the relativity defense:

Person 1: "Here, measure the length of this bookshelf for me. It should be 14 inches."

Person 2: "It's 14 and 1/2 inches."

Person 1: "No it's not! Let me see that."

(Person 1 measures it out..."crap, it's 14 and 1/2 inches. What to do? I need relativity!")

Person 1: "Well I can see how you may have been led to believe that this bookshelf is 14 and 1/2 inches long, but in actual fact if you account for relativistic effects it is just as true that this bookshelf is 14 inches long. You are just failing to account for its length as it approaches the speed of light."

("Phew, good ole relativity to the rescue again!)

 

[Phrak]

My son and I are on opposite sides of this question - if I am holding something in my hand in a gravitational field, am I doing work? My position is this - if I constantly accelerate a ball in space I am doing work. Since acceleration is equivalent to being in a gravitational field, and since holding a ball on Earth is in a gravitational field, I am doing work when I hold it. My son's position is that since the thing I am holding is not moving (there is a net acceleration of zero) I am doing no work. Is it simply that we are disagreeing about what is the relevant frame of reference - mine being the Earth's gravitational field, his being my body?

There are two different contexts at work here. One is Newtonian physics, which I presume your son is speaking with, the other is General Relativity.

I bring this up because you say "acceleration is equivalent to being [stationary] in a gravitational field." This is true in Relativity, but not generally true in Newtonian physics.

As you may have gathered from previous posts, work is defined as force acting over a distance.

Your son is operating under the assumption (I presume) that the force of gravity is balanced by the opposite force applied by your hand. So with no net force there can be no work done.

On the other hand, in your case, without a gravtiational force, forces are not balanced, so there's at least some chance of work being done.

 

[Renge Ishyo]

Whether or not you use Relativity or Newtonian physics you still end up with the problem that experimentally the ball releases the same amount of energy when it is dropped to the ground whether you hold it for 2 seconds before dropping it or 2 minutes. If this is true it implies that no work is done on the ball by simply holding it for a period of time regardless of which model you use to study it. But of course, this is the beauty of taking the relativistic approach. Even faced with such a situation as coming dangerously close to violating the law of conservation of energy, you can still use the theory to "distort" time and make 2 seconds the same thing as 2 minutes and dodge the issue entirely...

 

[atyy]

OK, since this has been going on and on, let me chip in with another scenario for you guys to play with. There is nothing special or general relativistic about all this. It all makes sense within Newtonian theory. Let's pretend the Earth is flat, and the gravitational field of the Earth uniform. There is a man standing on the surface holding a ball. In Newton's theory, the free falling observer (she) is not an inertial observer - she is an accelerated observer. She will therefore feel an "inertial" force due to her acceleration that exactly cancels the "real" gravitational force on her due to the attraction of the earth. She will see the ball being accelerated towards her, and conclude that there is a net force on the ball. The downward force on the ball is the attraction of real gravity. The first upward force on the ball is the reaction (3rd law) provided by the man's hand against the ball's weight on the man's hand. The second upward force on the ball is the "inertial force" due to her acceleration. Since the reaction provided by the man's hand on the ball is equal and opposite to the attraction of gravity on the ball, she will conclude that the ball is accelerating towards her due to the "inertial" force. Therefore, she will conclude that neither gravity nor the man is doing any work, but that the "inertial" force is doing work. So maybe although work is being done, it is not necessarily being done by the man holding the ball.

 

[Dale]

Could it? How? Describe this reference frame to me.

Reference frame 1: Standard reference frame at rest wrt the surface of the earth. Origin at the ball at t=0, x north, y west, z up.

Position of the ball: r(t) = (0,0,0)
Displacement of the ball: d(t) = r(t)-r(0) = (0,0,0)
Velocity of the ball: v(t) = dr/dt = (0,0,0)
Acceleration of the ball: a(t) = dv/dt = (0,0,0)
Net force: f(t) = ma = (0,0,0)
KE of the ball: KE(t) = mv²/2 = 0
Work done on ball: f.d = (0,0,0).(0,0,0) = 0
Son wins

Reference frame 2: Free falling frame. Axes coincident with unprimed frame at t=0.

x' = x
y' = y
z' = gt²/2 + z

Position of the ball: r'(t) = (0,0,gt²/2)
Displacement of ball: d'(t) = r'(t)-r'(0) = (0,0,gt²/2)
Velocity of the ball: v'(t) = dr'/dt = (0,0,gt)
Acceleration of the ball: a'(t) = dv'/dt = (0,0,g)
Force on ball: f'(t) = ma' = (0,0,mg)
KE of the ball: KE'(t) = mv'²/2 = mg²t²/2
Work done on ball: f'.d' = (0,0,mg).(0,0,gt²/2) = mg²t²/2
Dad weasels out a draw

But of course, this is the beauty of taking the relativistic approach. Even faced with such a situation as coming dangerously close to violating the law of conservation of energy, you can still use the theory to "distort" time and make 2 seconds the same thing as 2 minutes and dodge the issue entirely...

Please note that I did not use special relativity above. Even with classical Newtonian physics energy is clearly frame variant and energy is clearly conserved in both cases. I think you misunderstand the idea of reference frames even in Galilean relativity.

 

[atyy]

Reference frame 2: Free falling frame. Axes coincident with unprimed frame at t=0.

x' = x
y' = y
z' = gt²/2 + z

Position of the ball: r'(t) = (0,0,gt²/2)
Velocity of the ball: v'(t) = dr'/dt = (0,0,gt)
Acceleration of the ball: a'(t) = dv'/dt = (0,0,g) -> net force, normal force not canceled out
KE of the ball: KE'(t) = mv'²/2 = mg²t²/2
Work done on ball: KE'(t) - KE'(0) = mg²t²/2 - 0 = mg²t²/2
Dad weasels out a draw

But the work is done not by dad (mum?) holding the ball. It is done by the "inertial" force of the accelerated frame.

 

[Renge Ishyo]

The greatness of relativity as a theory lies not in its power to contradict objective reality. Einstein was very careful when he formulated it to stipulate that it must agree completely with observed classical phenomena for it to be of any use. It is indeed useful when it is (correctly) applied in that it can account for extreme phenomena that lie beyond the boundries of classical mechanics (and indeed our common experiences) while still reducing down to the exact classical rules mathematically so that our observable facts which we can rely on are not betrayed. Using relativity to describe classical phenomena doesn't make a person's interpretation "more true" here on Earth anymore than using a lot of extra digits for pi makes a mathematicians calculation "more true." The approximations should agree to a very close degree in either case if the mathematician has done his job right. So should the classical physicist and the relativist.

That is not what is happening here. Here we have a clear cut question with a simple answer as far as classical physics is concerned. No, the man is not doing any work by holding up the ball. What is trying to be argued here is that in certain reference frames or at certain speeds, relativity says that classical physics is wrong and the man is doing work in such frames. So "O.K., maybe so." But at least as far as Einstein is concerned the two answers should have agreed. Furthermore, nobody has addressed my query that if work is being done on the ball in *any* reference frame, why it releases the same amount of energy classically when it is dropped regardless of how long you hold it there. But I suppose it doesn't matter, because I cannot say whether the relativistic concepts are incorrect because I can't test them or experience such frames of reference.

 

[Phrak]

...
Reference frame 2: Free falling frame. Axes coincident with unprimed frame at t=0.

x' = x
y' = y
z' = gt²/2 + z

Position of the ball: r'(t) = (0,0,gt²/2)
Displacement of ball: d'(t) = r'(t)-r'(0) = (0,0,gt²/2)
Velocity of the ball: v'(t) = dr'/dt = (0,0,gt)
Acceleration of the ball: a'(t) = dv'/dt = (0,0,g)
Force on ball: f'(t) = ma' = (0,0,mg)
KE of the ball: KE'(t) = mv'²/2 = mg²t²/2
Work done on ball: f'.d' = (0,0,mg).(0,0,gt²/2) = mg²t²/2
Dad weasels out a draw
...

Dale,

I think what you have done is to demonstrate that Newtonian mechanics is generally valid only in Galilean reference frame, haven't you?

 

[Renge Ishyo]

Actually, I think I have found a non-relativistic way for the father to weasel his way into a tie on this bet.

O.k., suppose a man is holding a ball static in a gravitational field. Further suppose that the ball is at a lower temperature than the man's hand. In such a situation net work *would* be performed by the man's hand on the ball at the molecular level even if both objects were held "perfectly still". At the molecular level, the hot vibrating molecules in the man's hand would do work on the colder molecules in the ball increasing their vibration. The work done on the ball can be verified experimentally as the temperature increase of the surface of the ball. At equilibrium no net work would be done, but so long as the temperatures were different you can have net work in this system. This isn't quite what the original bet inferred, but it wasn't specific enough to remove this interpretation either...

 

[Dale]

But the work is done not by dad (mum?) holding the ball. It is done by the "inertial" force of the accelerated frame.

Technically work is always done by the net force, but you could make a reasonable case for that view since the difference between the primed and unprimed frames (in terms of forces) is the inertial force. In general, inertial forces can do work in their reference frame and can even be associated with a potential.

The greatness of relativity as a theory lies not in its power to contradict objective reality. Einstein was very careful when he formulated it to stipulate that it must agree completely with observed classical phenomena for it to be of any use. It is indeed useful when it is (correctly) applied in that it can account for extreme phenomena that lie beyond the boundries of classical mechanics (and indeed our common experiences) while still reducing down to the exact classical rules mathematically so that our observable facts which we can rely on are not betrayed. Using relativity to describe classical phenomena doesn't make a person's interpretation "more true" here on Earth anymore than using a lot of extra digits for pi makes a mathematicians calculation "more true." The approximations should agree to a very close degree in either case if the mathematician has done his job right. So should the classical physicist and the relativist.

That is not what is happening here. Here we have a clear cut question with a simple answer as far as classical physics is concerned. No, the man is not doing any work by holding up the ball. What is trying to be argued here is that in certain reference frames or at certain speeds, relativity says that classical physics is wrong and the man is doing work in such frames. So "O.K., maybe so." But at least as far as Einstein is concerned the two answers should have agreed. Furthermore, nobody has addressed my query that if work is being done on the ball in *any* reference frame, why it releases the same amount of energy classically when it is dropped regardless of how long you hold it there. But I suppose it doesn't matter, because I cannot say whether the relativistic concepts are incorrect because I can't test them or experience such frames of reference.

I don't see the relevance of any of these comments since I didn't use any special relativity in my recent calculations. I even went out of my way to explicitly point out the fact that I didn't use any SR. I used strictly classical mechanics and implicitly assumed v<<c, so as you say, any relativistic corrections would be negligible.

What I showed is that even in classical physics energy and work are frame variant. This really has nothing to do with SR. This is purely classical mechanics (aka Galilean relativity) and you "experience such frames of reference" every day.

Btw, regarding your query, in the other reference frames the remainder of the energy goes into changing the energy of the earth.

I think what you have done is to demonstrate that Newtonian mechanics is generally valid only in Galilean reference frame, haven't you?

It is not demonstrated by what I did above, but yes you are correct. Newton's third law is violated in non-inertial reference frames since the inertial forces do not form 3rd-law pairs. But otherwise classical mechanics works fine in non-inertial reference frames and these analysis techniques are well understood.

 

[ValenceE]

Hello to all,

Earth’s reference frame is accelerating as it rotates around itself and the sun.

Anything that is on Earth’s ground or attached to it is accelerated accordingly.

Dad is holding a ball, sitting in a comfortable chair, itself sitting on the living room floor which, through the house’s construction, sits on Earth’s ground.

The ball that dad’s holding, all the way down to Earth’s surface, is accelerated accordingly.

If the Earth is doing work, keeping anything inert on it’s surface, then so is dad.


We can certainly use Earth’s reference frame as a free fall frame. I mean it’s big enough so some of us can get their thrills doing free fall jumps. So, no need to go too far in the explanations…


Regards,

VE

 

[atyy]

Earth’s reference frame is accelerating as it rotates around itself and the sun.

As pointed out by several people earlier in this thread, although an object undergoing circular motion is accelerating, no work is done by the centripetal force, because the direction of the force is perpendicular to the direction of motion.

Dad or mum's best bet is to settle for an linearly accelerated observer, such as an observer free falling in a uniform gravitational field. But even then, it is not evident that the person holding the ball is doing the work, as DaleSpam and I discussed.

 

[Phrak]

Consider the man fired out of a cannon, in a freely falling inertial frame.

On his trip up, the ball does work on the man. On the trip down, the man does work on the ball.

 

[Dale]

No, in a freely falling inertial frame the man and ball fired out of the cannon are at rest. Since d=0 then f.d=0 and there is no work done on or by the ball either going up or down. Also, since both are in free fall there is no force required to keep the ball with the man (think of an astronaut in orbit).

 

[ohadohad2]

My son and I are on opposite sides of this question - if I am holding something in my hand in a gravitational field, am I doing work? My position is this - if I constantly accelerate a ball in space I am doing work. Since acceleration is equivalent to being in a gravitational field, and since holding a ball on Earth is in a gravitational field, I am doing work when I hold it. My son's position is that since the thing I am holding is not moving (there is a net acceleration of zero) I am doing no work. Is it simply that we are disagreeing about what is the relevant frame of reference - mine being the Earth's gravitational field, his being my body?

I didn't read all the thread so excuse me if I repeat something someone else said.

By holding the ball you DON'T DO WORK BUT you DO "SPEND" ENERGY.

Its exactly like an car with automatic gear on a slop, it standstill but the engine is still running and create torque on the wheels but there is no movement although fuel is burnt and energy is being used.

This whole debate is just wording since physics defintion of work and everyday definition are a little different.

 

[russ_watters]

Reference frame 2: Free falling frame. Axes coincident with unprimed frame at t=0.

That's what I thought. You prove my point: in the example in the OP, that frame is not physically possible. Or, perhaps I should say, it is only physically possible for about half a second. It also doesn't exist (it wasn't described in the OP). In the OP, you have a person, an object, and the earth. That's it. To make your accelerating frame happen, you have to introduce another object (perhaps being dropped from his other hand).

And that's even if we let atyy's objection slide: the work done on the ball doesn't come from dad's arm, it comes from the ground pushing up on dad's feet. Or put another way, a table pushing up on a book is not expending energy in order to avoid freefall - the Earth is pushing up on it. Only in the case of a hovering rocket or helicopter can we say that the energy to hold up the object is physically real (as opposed to existing on paper and only wrt an imaginary reference frame).

The OP compares this example to a rocket, but IMO, you can't do that because the rocket provides its own force to counteract gravity. The person is only relaying the force provided by the ground.

Inventing a frame that doesn't physically exist (if there is no observer there to measure the motion against, it isn't physically real) doesn't, imo, avoid losing the bet.

 

[russ_watters]

Actually, the more I think about it, the simpler this issue gets: I think the "correct" frame of reference is made clear by the question.

Let me give a counterexample. A person is pushing a large box across a room. Is the person doing work? Again, we have three objects from which we can choose our reference frames: the person, the box, and the room. But in this example, the person and box are moving wrt the earth. So there can be only one answer: the input work comes from the person, the output work comes from the box sliding on the floor against friction.

No reasonable person would conclude anything else from this example.

 

[Dale]

Inventing a frame that doesn't physically exist (if there is no observer there to measure the motion against, it isn't physically real) doesn't, imo, avoid losing the bet.

I don't understand your objection. Reference frames are mathematical abstractions that never have any physical existence. They are nothing more than coordinate systems. There is no requirement that a reference frame have a physical object at rest in the system.

In any case, your objection can be easily overcome by beginning with a free-fall observer at a sufficient height that he doesn't hit the ground until the experiment is over.

No reasonable person would conclude anything else from this example.

I agree, the free-fall reference frame is silly and unreasonable, which is why I always say that if he uses it he only "weasels out a draw". However, the free-fall reference frame is a valid (but silly) reference frame and in that frame work is done.

 

[russ_watters]

I don't understand your objection. Reference never have any physical existence. They are nothing more than coordinate systems. There is no requirement that a reference frame have a physical object at rest in the system.

In a real-world problem, there is. For two reasons:

-You can't physically measure motion wrt something that doesn't exist.
-If what you are saying is allowed, you could assume literally anything and get any answer you wish. Why not assume there is a rocket somewhere accelerating up and calculate the energy wrt it? That would be equally valid, right?

This is not a question of math, it is a question of reading comprehension.

Further, I think allowing this weaseling does a real disservice to his son. His son might take this lesson to school with him and start applying it to problems he does in school - producing wrong answers. One of the most critical things to know about answering questions is how to read them. Don't read something that isn't there.

 

[Dale]

In a real-world problem, there is. For two reasons:

-You can't physically measure motion wrt something that doesn't exist.
-If what you are saying is allowed, you could assume literally anything and get any answer you wish. Why not assume there is a rocket somewhere accelerating up and calculate the energy wrt it? That would be equally valid, right?

Certainly an upward-accelerating reference frame would be equally valid, and yes you can get any finite value for the energy by judicious choice of reference frame.

The whole point is that energy and work are not intrinsic quantities, they are frame-variant quantites (even in Newtonian mechanics). In other words, talking about energy without specifying a reference frame is essentially meaningless. Once you have specified the reference frame, then all of the usual conservation laws apply, although different frames will disagree on the details.

This is not a question of math, it is a question of reading comprehension.

I agree 100%, and from a pedantic standpoint the free-fall reference frame is terrible.

In the OP the usual reference frame is clearly implied by the son's statement that "the thing I am holding is not moving". But the free-fall frame is also implied by the parent's reference to the equivalence principle. This thread, IMO, must be addressed in terms of the frame-variant nature of energy and specifically wrt the usual frame and the free-fall frame.

 

[Phrak]

No, in a freely falling inertial frame the man and ball fired out of the cannon are at rest. Since d=0 then f.d=0 and there is no work done on or by the ball either going up or down. Also, since both are in free fall there is no force required to keep the ball with the man (think of an astronaut in orbit).

I should have been better written. The man holding the ball is standing on the ground. An observer is shot ot of a cannon.

In this case, even the direction in which work is done changes.

 

[atyy]

And that's even if we let atyy's objection slide: the work done on the ball doesn't come from dad's arm, it comes from the ground pushing up on dad's feet.

That's not my objection. The direct contact comes on the ball comes from the hand that is holding it, so we can assign the force to that, rather than working in 3rd law pairs all the way to the ground.

I agree with DaleSpam that it is the net force that does work, and that if we wish to assign work done to various force components, then it is reasonable to assign the work done to the "inertial force", and not to the man. The "inertial force" is distinguishable because it is not part of a 3rd law pair. This becomes especially clear if we use an accelerated frame that is not a free-falling frame, eg. the upward accelerating frame Phrak suggests. (Minor point: DaleSpam and I use different terms for the free-falling frame - I call it an accelerated frame, working within Newtonian theory, DaleSpam calls it an inertial frame, working from GR - not quite true since Newton knew the Principle of Equivalence - anyway, that's just nomenclature.)

I think the weasling is great! Just like school kids should learn that velocity is meaningless without the specification of a reference frame, they should learn the same for work and energy. Furthermore, I think the weasel is adequately punished since it can't even win the bet if we concede to its terms (The claim was not "Work is being done", but "I am doing work").

Of course, kids should also be taught to give the "right" answers on exams - that's life - the boss is always right (unless you're being asked to do something morally wrong).

 

[sp1408]

Think about it this way...the person is holding something in air by applying some force on it...If there was no gravity,and he would still apply the same force,the body would accelerate and you would be doing work on it...of course this is a bit difficult to visualize in the sense that you wouldn't need to hold anything if there was no gravity...

 

[Topher925]

Wow, way to take a simple problem and make it 100x times more complicated than it needs to be. This is why I am an engineering and not a physicist. Anyways...

..If there was no gravity,and he would still apply the same force,the body would accelerate and you would be doing work on it...

So your saying that all mass is constantly doing work regardless of what state or properties it might have? I'm not sure but I think there's something wrong with that logic.

 

[ValenceE]

Post # 59, Dalespam writes "The whole point is that energy and work are not intrinsic quantities, "

are you saying that any and every reference frame doesn't have a minimal energy quantity ?

VE

 

[Dale]

What is "a minimal energy quantity"?

 

[ValenceE]

DaleSpam,

I guess I’m referring to zero-point energy. I do believe that space-time is permeated with energy and that there is a minimal energy quantity or density that must be above zero.

In this view, isn’t energy intrinsic to space-time, whatever the coordinates, whichever reference frame is selected?


Regards,

VE

 

[Dale]

I don't know much about zero-point energy. But my understanding is that it is a prediction of the standard model and the standard model is compatible with SR, so I would be surprised if it weren't properly frame-variant.

Do you have some reason to think that it isn't?

 

[atyy]

In this view, isn’t energy intrinsic to space-time, whatever the coordinates, whichever reference frame is selected?

I don't know much about zero-point energy. But my understanding is that it is a prediction of the standard model and the standard model is compatible with SR, so I would be surprised if it weren't properly frame-variant.

I suppose VE's point is that a cosmological constant or vacuum energy would not only be properly frame-variant, but would also be frame-invariant, unlike Newtonian kinetic energy and work. I'm a bit confused this when we go out of Newtonian physics, but it seems we don't even have to go to GR to make sense of VE's point. In SR, E²=p²c²+m_o²c⁴ is the squared length of a four-vector, so it is frame-invariant, although p is frame-variant. In Newtonian physics, work and kinetic energy are useful because of the work energy theorem, and because KE+PE is conserved for curl free force fields. In SR, E is defined differently from Newtonian physics, because physicists can't bear the thought that energy is not conserved, and by demanding conservation, one also obtains invariance.