About the total work done loading and unloading (setting down) an object

[llober]

The other day I saw this question:

"A man carries a suitcase weighing 50kg over his head, and travels a distance of 15m along a horizontal direction. What would be the work done?"

My answer was:

"Suposse the height of the man is 1.8m. Then, the work done by the man, considering the load/unload phase aswell, will be more or less 2*M*g*h = 2*50*9.8*1.8 = 1764 J"

Afterwards, I got a lot of comments saying something like: "Hey, you missed a sign, because obviously, when loading the suitcase the force you do is in the same direction as the displacement, and when you download is in the opposite direction, so the Work cancels out, and is zero".

So I replied:

"Imagine the following case:

John lifts 10 50Kg potato sacks from the ground to the platform of a truck, which is at a height of 1.5m. Does he get tired? Yes, of course … obvious, isn’t it?. What is the work done by John? More or less, you could say that 10x50x9.8x1.5 Joules (mgh).

They drive to the destination, and there Peter downloads the 10 potato sacks, very carefully and gently putting them on the ground … he doesn’t want to spoil the potatos … Does he get tired? Yes, of course … obvious, isn’t it? What is the work done by Peter? Again, more or less, you could say that 10x50x9.8.1.5 Joules.

But, as one of them is uploading and the other is downloading … then the net work done is zero? That's what the John and Peter's boss said, pretending not to pay anything!"

Ok, you see the problem ... who's right?

 

[BvU]

When unloading, you could use the force to generate energy (work) -- just as much as you used to lift them on the truck. So yes, the work is zero.

'Getting tired from it' is not a criterion for work:
Holding a book in front of you with a stretched arm is tiring, but it doesn't do any work. A bookshelf doesn't need an energy supply to keep a book in place.

 

[llober]

When unloading, you could use the force to generate energy (work) -- just as much as you used to lift them on the truck. So yes, the work is zero.

'Getting tired from it' is not a criterion for work:
Holding a book in front of you with a stretched arm is tiring, but it doesn't do any work. A bookshelf doesn't need an energy supply to keep a book in place.

Yeah, when unloading I could have used such "force" to generate energy ... and indeed I did, because I had to "dissipate" that energy in order to place the suitcase at the ground level at zero speed ... didn't I? My muscles got very hot!

 

[Dale]

Afterwards, I got a lot of comments saying something like: "Hey, you missed a sign, because obviously, when loading the suitcase the force you do is in the same direction as the displacement, and when you download is in the opposite direction, so the Work cancels out, and is zero".

These comments are correct.

Considering whether or not a human would get tired doing a task is never a good way to analyze work done. Humans are very complicated machines and often horrendously inefficient.

Instead, you should consider very simple ideal machines, like a spring. You can place a weight on an ideal spring and it will bounce up and down, loading and unloading repeatedly, without further energy input. No net work is done over each full load-unload cycle.

 

[llober]

Obviously, the example given is just a "joke", and the meaning of "getting tired" is just to pinpoint that you're actually doing a "work". I could have said that I sweated a lot, got my muscles very hot, burned a lot of calories, and so on...

We could consider simple machines and so on, but we're not ... we a considering a human, lifting up a suitcase to a certain height (over his head, to be more precise), using only its muscular brute force.

What makes the difference is that we, as a machine, are not reversible ... we transform chemical energy into mechanical, but not the other way round, nor we can store that energy inside an "internal spring" (at least, not very much), like we were a clock-work robot.

For the evidence given as far, I continue considering that the work done by the man is not zero, and basically it`s due to the man not being able to store somehow the energy in the download phase, that he put in the upload phase. From the point of view of the human-system, there's a work done, gone and lost by heat.

From the point of view of the suitcase ... who cares!

 

[Ibix]

@llober - If you want to know the work done on the suitcase, your calculation is wrong because you have the signs wrong.

If you want to know the energy expended by the man your calculations aren't even in the right ballpark because, as Dale says, humans aren't really the kind of simple system that you can model with simple physics. Taking the initial problem, you got 1764J. Increase the distance the man walks from 15m to 20m. Your method gives 1764J. Increase the distance to 20km. Your method gives 1764J. At some point the man will die of exhaustion, according to your method having burnt only the energy he could get from a chocolate bar.

Clearly your method isn't measuring the man's energy expenditure, nor is it measuring the work done on the suitcase.

 

[Dale]

the meaning of "getting tired" is just to pinpoint that you're actually doing a "work".

But you are not actually doing work. Work has a precise definition, and it is 0 in this case. You are getting tired because you are expending energy. Energy expended only equals work performed if your machine is 100% efficient. A human is not a 100% efficient machine. So the fact that a human expends energy does not imply that they did work.

I continue considering that the work done by the man is not zero,

Well, it is your grade. You are wrong and if you like to be wrong despite being taught correctly then your grade will reflect that.

 

[A.T.]

"getting tired" is just to pinpoint that you're actually doing a "work".

This is not how "work" is defined in physics.

 

[llober]

But you are not actually doing work. Work has a precise definition, and it is 0 in this case. You are getting tired because you are expending energy. Energy expended only equals work performed if your machine is 100% efficient. A human is not a 100% efficient machine. So the fact that a human expends energy does not imply that they did work.
Well, it is your grade. You are wrong and if you like to be wrong despite being taught correctly then your grade will reflect that.

Okay, but considering again the example I wrote about the potato sacks ... Did John make any work lifting the 10 potato sacks to the truck platform? I mean now in the physical sense. I hope you agree with me that the magnitude of the work done by John is more or less (without going into the efficiency of the "human machine" and other complicated details) 10*50*9.8*1.5 J.

About Peter, the man who settles down the potato sacks from the truck ... seems to me that the potential energy of the sacks gets somehow transferred to Peter, and as this energy cannot be stored in form of mechanical energy by Peter's body, has to be (mostly) converted into heat ... of course, such heat must be dissipated by the body's mechanisms (sweting ...). So, at the end, this amount of energy is lost by Peter.

For me to say that the total work done is zero, in this case, is like saying that the area of the curve represented by Cos(φ) between 0 and 2π is zero. And so for the example of the suitcase.

I think is the same situation as a man cyclically lifting and setting down a weight in a gym machine ... if he was a "mechanical clockwork" machine, he would do only the work needed to compensate for the "inefficiency" (friction, ...), not more ... but this is not the case.

About the grade, ... all is relative.

 

[llober]

@llober - If you want to know the work done on the suitcase, your calculation is wrong because you have the signs wrong.

If you want to know the energy expended by the man your calculations aren't even in the right ballpark because, as Dale says, humans aren't really the kind of simple system that you can model with simple physics. Taking the initial problem, you got 1764J. Increase the distance the man walks from 15m to 20m. Your method gives 1764J. Increase the distance to 20km. Your method gives 1764J. At some point the man will die of exhaustion, according to your method having burnt only the energy he could get from a chocolate bar.

Clearly your method isn't measuring the man's energy expenditure, nor is it measuring the work done on the suitcase.

My "method" is only trying to measure the work done by the man, from his point of view, with the actions of lifting and setting down the suitcase. Nobody discussed the work done to the suitcase, which is zero.

 

[Ibix]

My "method" is only trying to measure the work done by the man, from his point of view, with the actions of lifting and setting down the suitcase.

Either the answer is zero (because you mean work in the physicist's sense of the word) or your answer is hopelessly wrong (because you use work to mean "energy expended by the man" and you are ignoring that the human body isn't remotely like the kind of simple machine you assume when you use mgh to model its energy use).

 

[llober]

Either the answer is zero (because you mean work in the physicist's sense of the word) or your answer is hopelessly wrong (because you use work to mean "energy expended by the man" and you are ignoring that the human body isn't remotely like the kind of simple machine you assume when you use mgh to model its energy use).

Okay, but then if we consider only the man lifting the suitcase? Even if the human body is such a complicated machine (which it is), I hope that you'll agree with me that the work done would be, more or less, mgh, isn't it? So, if we neglect the "inefficiency" of the human body mechanics, we can give a very accurate estimation of the work done, even when the system is such a complicated machinery.

What I'll realized is that from the point of view of the man, the total work done is mgh (plus the internal "inefficiencys"), and not 2*mgh as I said initially. The mechanical energy given to the suitcase, in form of potential energy, will be back transferred to the man, but the human body can't store mechanical energy (perhaps some in form of the elasticity of the muscles), so that energy will get converted into heat, and at the end dissipated from the man's body (sweting, radiation ...).

 

[256bits]

more or less, mgh, isn't it

the suitcase.

he man's work is -- well is he lifting from the knees, bending at the waist to pick the suitcase up.
the man is lifting parts of his body, upper torso, arms -- none of which we know the mass.
there is no definitive answer that takes into account all occasions of lifting the suitcase.

 

[Ibix]

You need to be very careful about what you mean, basically.

When lifting the suitcase, the man burns some quantity of his energy reserves. That energy ends up in three places. First, the suitcase gains mgh from the height change. Second, the man was probably bent down when he started lifting the suitcase and straight when he finished (at the very least his arm has risen), so his gravitational potential energy has increased - possibly significantly more than the suitcase depending on its contents. Third, a lot of heat gets dumped to the environment.

On the way down, we start with energy in the man's reserves, and gravitational potential energy in the man's body and the suitcase. This all ends up dumped into the environment as heat. What the man's miscles are doing is (inefficiently) dissipating the gravitational potential as heat.

So what do you want to know? The suitcase has the same energy it started with. This is what physicists call work (or useful work). When the suitcase was on the truck we could have tied a rope to it and pushed it off and used the fall to turn a generator or something. But once you've lowered it to the floor we can't do that.

Or you can ask how much energy the man expended. This is related to the m, the g, and the h, but depends critically on many factors like how fast the man lifts and how well he uses his body.

I think your basic problem is analogous to you handing me a £10 note and me handing it back. How much money changed hands? It would be really odd to claim £20, since neither of us is richer or poorer than when we started - the net change is zero. And the chaps at the Serious Fraud Office will eventually want a word if you try to claim otherwise. The only reason that the man lifting example seems more complicated is that he doesn't get to keep the energy equivalent of the tenner. He metaphorically drops it down a drain because he doesn't have regenerative braking built into his muscles.

 

[llober]

the suitcase.

he man's work is -- well is he lifting from the knees, bending at the waist to pick the suitcase up.
the man is lifting parts of his body, upper torso, arms -- none of which we know the mass.
there is no definitive answer that takes into account all occasions of lifting the suitcase.

Okay, then for the lifting the Work would be M_s·g·h + M_b·g·Δh_bcm, where Δh_bcm is the vertical displacement of the center of mass of the body.

 

[llober]

I think your basic problem is analogous to you handing me a £10 note and me handing it back. How much money changed hands? It would be really odd to claim £20, since neither of us is richer or poorer than when we started - the net change is zero. And the chaps at the Serious Fraud Office will eventually want a word if you try to claim otherwise. The only reason that the man lifting example seems more complicated is that he doesn't get to keep the energy equivalent of the tenner. He metaphorically drops it down a drain because he doesn't have regenerative braking built into his muscles.

Nope, the anology is: I hand you a bank note of 10 pounds, you return to me, but just as the bank note lands in my hand, a bird passes flying and picks the bank note, flying away with it!

From you point of view, you returned the money. From my perspective, I spent 10 pounds by handing to you the money in the first place. I obviously poorer at the end. And worst, because the tax office will tell me that I've to pay taxes for the money transfer!

The moral of all this story is that the initial question about "which is the work done ... blah, blah ...", is an stupid question if you want to teach how physics work ... or not?

 

[A.T.]

The moral of all this story is that the initial question about "which is the work done ... blah, blah ...", is an stupid question if you want to teach how physics work.

It's stupid to ask about work done, when you are actually interested in something else, like energy dissipated.

 

[llober]

It's stupid to ask about work done, when you are actually interested in something else, like energy dissipated.

But the energy dissipated comes from a work done, at least in this case!

 

[Dale]

seems to me that the potential energy of the sacks gets somehow transferred to Peter,

Yes, the “somehow” is by the negative work Peter does on the sacks.

Nothing further can be accomplished here. We have taught correct physics, and @llober is not misunderstanding the physics but simply choosing to be wrong anyway.

Thread closed.