Is holding something in a gravitational field doing work ?

[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.