Waiters don't do work

[ma1ic3]

I have a few questions about work.

1st: When reading about work, it is usually said that a waiter carrying a tray across a room or someone carrying weights from one shelf to another shelf at the same height, are not doing any work on the weights or tray. But I then come across articles that say a car is doing work.

The explanation is that for work to be done, the force has to be in the direction of displacement. Gravity is working vertically, but the tray is moving horizontally, so no work is being done. Well.... that means no work is being done on the tray by gravity, but that's obvious because the waiter isn't dropping the tray in this scenerio. The same could be said about the car, since the horizontal movement of a car or even the waiter themselves is not in the direction of gravity.

But the waiter is applying a force horizontally upon the mass of the tray right? Meaning work is being done on the tray, right? What if you put the dish on top of the car?

2nd: I've also read that you can use energy without doing work. If someone pushes on a wall, no work is being done but energy is being used.

Even if work isn't being done on the wall, isn't work still being done elsewhere? I would assume that work is being done on a cellular level in your muscles, which would be why you feel so tired after supposedly not doing any work at all.

3rd: Does generating heat or higher temperatures count as work? Because that would mean that pushing on a wall would be doing work of some sort in that sense as well.

4th: The wikipedia article on work said it can be positive, zero and negative. I understand how velocity can be like that since it's a vector quanity, but the article says that work is a scalar quantity.

5th: What is an example of zero or negative work? Does running in place count as work? What about running up some stairs and then back down again. Since you end up at the same place, has work been done?

[NobbyNobbs]

First of all, I saw the title of this thread and was going to come in here on a rampage, about to blast whoever it was that claimed waiters were lazy and didn't earn their pay.

I'm gratified to learn it's a physics lesson, instead.

The waiter is doing work, as he is exerting a horizontal force against the ground. This force provides a counter-force (a la Newton's 3rd), propelling him forward. So the work isn't done on the tray, per se. However, it is more work than if he weren't carrying the tray, because the force has to be greater than if he were empty-handed, because the mass is greater (a la Newton's 2nd.)

[John Bentley]

It may be that you are confusing the layman's definition of work with the physicist's definition of work. The physicist's definition is very specific and applies only to a specific set of equations and units of measurement.

If this is not what you are confused about, then ignore this.

Written in haste, so can't go into specifics of your questions. Besides, there are much more qualified people to discuss the physics.

[drkitten]

I have a few questions about work.

Don't. "Work" is one of the more poorly chosen words in the vocabulary of physics, precisely because it lends itself to naive interpretations that don't accord with our layman's understanding.



1st: When reading about work, it is usually said that a waiter carrying a tray across a room or someone carrying weights from one shelf to another shelf at the same height, are not doing any work on the weights or tray. But I then come across articles that say a car is doing work.

Work is applying a force through a distance. In general, moving something horizontally in a gravity well is not considered to be "work", because there is no (resisting) force applied. Offhand, I'd say the articles about cars are either wrong, misleadingly written, or you've misunderstood them.




2nd: I've also read that you can use energy without doing work.

Of course you can. Hook a battery up to a light bulb. Energy is used, but no work.

If someone pushes on a wall, no work is being done but energy is being used.

This is another example as long as you don't look too closely at the biology of it.


Even if work isn't being done on the wall, isn't work still being done elsewhere? I would assume that work is being done on a cellular level in your muscles, which would be why you feel so tired after supposedly not doing any work at all.

No, energy is being used at the biological level; it takes energy to keep muscle fibers tense. In the same way that it takes energy to keep a light bulb running.

Now, if you look too closely at the biology, you will see individual muscle fibers tense and relax.... but -- well, don't go there.


3rd: Does generating heat or higher temperatures count as work? Because that would mean that pushing on a wall would be doing work of some sort in that sense as well.

No, generating heat does not do work, because there is neither force nor distance involved.



4th: The wikipedia article on work said it can be positive, zero and negative. I understand how velocity can be like that since it's a vector quanity, but the article says that work is a scalar quantity.

"Negative" work is just a system where you get work OUT of a system instead of in.

Lifting a heavy rock involves work -- applying the lifting force against gravity through a distance. Dropping that same rock will involve negative work -- and you could use that work to balance out other work done elsewhere. You've just invented, among other things, the lever or the pulley.



5th: What is an example of zero or negative work?

See above.

[Cuddles]

5th: What is an example of zero or negative work?

That's what I'm doing now.;)

[Ziggurat]

But the waiter is applying a force horizontally upon the mass of the tray right? Meaning work is being done on the tray, right? What if you put the dish on top of the car?

The waiter needs to do work to start the tray moving. Once it's moving, no horizontal force need be applied to keep it moving, unless you want to count air resistance. Put a dish on top of your car, and you'll likely find that you can't safely ignore air resistance.

I've also read that you can use energy without doing work. If someone pushes on a wall, no work is being done but energy is being used. Even if work isn't being done on the wall, isn't work still being done elsewhere? I would assume that work is being done on a cellular level in your muscles, which would be why you feel so tired after supposedly not doing any work at all.

Yes. No work is being done on the wall. But work actually is being done on molecules inside your muscles. And that work gets quickly transformed into heat: not only do you get tired, you also get hot.

3rd: Does generating heat or higher temperatures count as work? Because that would mean that pushing on a wall would be doing work of some sort in that sense as well.

It requires work to create heat, yes.

4th: The wikipedia article on work said it can be positive, zero and negative. I understand how velocity can be like that since it's a vector quanity, but the article says that work is a scalar quantity.

Work is the dot product of the force vector and the displacement vector. If displacement is in the direction of force, it's positive. If displacement is in the opposite direction to the applied force, it's negative.

5th: What is an example of zero or negative work?

A compressed spring held in place does zero work.

Generators do negative work. Consider, for example, a water turbine from a hydroelectric dam: the turbine applies a force in the opposite direction to the direction the water is moving. The displacement of the turbine and the force that the turbine exerts are in opposite directions. Thus, it does negative work on the water. It extracts energy from the water. The water, however, does positive work on the turbine.

[ma1ic3]

The waiter needs to do work to start the tray moving. Once it's moving, no horizontal force need be applied to keep it moving, unless you want to count air resistance. Put a dish on top of your car, and you'll likely find that you can't safely ignore air resistance.


But the dish won't keep moving in a horizontal direction if you stop applying force. You have to continually apply force to overcome friction right? When you walk, aren't you constantly doing work to move yourself and anything you're holding (such as a tray or ball) horizontally?


Yes. No work is being done on the wall. But work actually is being done on molecules inside your muscles. And that work gets quickly transformed into heat: not only do you get tired, you also get hot.


Ya, that's what I thought. They should say you aren't doing work on the wall, rather than you're not doing any work at all. Those are two very different things.


It requires work to create heat, yes.


Ok, so you definitely have to continue to do work to move horizontal, even at a constant speed since their are forces opposing you.


Work is the dot product of the force vector and the displacement vector. If displacement is in the direction of force, it's positive. If displacement is in the opposite direction to the applied force, it's negative.


Oh, I see. The other few explanations I came across were harder to follow.


Generators do negative work. Consider, for example, a water turbine from a hydroelectric dam: the turbine applies a force in the opposite direction to the direction the water is moving. The displacement of the turbine and the force that the turbine exerts are in opposite directions. Thus, it does negative work on the water. It extracts energy from the water. The water, however, does positive work on the turbine.

So if you change the direction of displacement from the direction that the force is moving, then it's negative work? Does it have to be the opposite, can the direction just be at a 90 degree angle from the force to be negative?

When you say it does negative work on the water, you then say it "extracts energy". Anything doing work as a consequence of water doing work on it, positive or negative, can be said to be "extracting energy" right?

[Ziggurat]

But the dish won't keep moving in a horizontal direction if you stop applying force. You have to continually apply force to overcome friction right? When you walk, aren't you constantly doing work to move yourself and anything you're holding (such as a tray or ball) horizontally?

Friction on what, though? The only friction on the tray is air resistance, which at walking speeds is low enough that we can generally ignore it. Friction on the waiter himself (the inefficiencies of walking) may mean he's doing work when he walks, but he's not doing work on the tray. And that distinction is critical to meshing our intuitive understanding (it clearly takes effort to carry a heavy tray) with a precise picture of where the energy involved actually goes.

Ya, that's what I thought. They should say you aren't doing work on the wall, rather than you're not doing any work at all. Those are two very different things.

Indeed they are. There's a lot of bad pedagogy (sp?) out there.

So if you change the direction of displacement from the direction that the force is moving, then it's negative work? Does it have to be the opposite, can the direction just be at a 90 degree angle from the force to be negative?

If the force and displacement are at 90 degree angles, the dot product is zero. There must be at least a component of the displacement opposite to the direction of force (for example, a 95 degree angle) in order for the work to be negative.

When you say it does negative work on the water, you then say it "extracts energy". Anything doing work as a consequence of water doing work on it, positive or negative, can be said to be "extracting energy" right?

If you connect those same turbines to electric motors instead of generators, and start pumping the water back up into the dam, then the force on the water from the turbine is still in the same direction but the displacement will be reversed (so that it's in the same direction as the force). The turbines will then be doing positive work on the water, and will be depositing energy INTO the water, rather than extracting energy from it.

There are actually a few resevoirs which are used this way precisely to store energy in and extract it from the gravitational potential energy of a big mass of water.

[Zombified]

I have a few questions about work.

1st: When reading about work, it is usually said that a waiter carrying a tray across a room or someone carrying weights from one shelf to another shelf at the same height, are not doing any work on the weights or tray. But I then come across articles that say a car is doing work.
To say that they're not doing work is an approximation, ignoring frictional losses. For example in the car's case, if you put the clutch in and coast, you'll keep moving, but in reality you'll start decelerating due to various sources of friction. The car is expending energy to overcome that friction.

The explanation is that for work to be done, the force has to be in the direction of displacement. Gravity is working vertically, but the tray is moving horizontally, so no work is being done. Well.... that means no work is being done on the tray by gravity, but that's obvious because the waiter isn't dropping the tray in this scenerio. The same could be said about the car, since the horizontal movement of a car or even the waiter themselves is not in the direction of gravity.

But the waiter is applying a force horizontally upon the mass of the tray right? Meaning work is being done on the tray, right? What if you put the dish on top of the car?
The force is nonzero while the waiter or car is accelerating and zero when its coasting at a constant speed (ignoring air). For example, if you put your coffee mug on top of your car and speed off, your mug will fall off your car. But once you are zooming along, it'll just sit there.

2nd: I've also read that you can use energy without doing work. If someone pushes on a wall, no work is being done but energy is being used.
What's happening here is you're compressing your arm, etc, like a spring. Springs store energy when compressed.

Even if work isn't being done on the wall, isn't work still being done elsewhere? I would assume that work is being done on a cellular level in your muscles, which would be why you feel so tired after supposedly not doing any work at all.
Your cells in this case are a bit like little engines, as long as they're running they're consuming energy (they have less than 100% efficiency).

3rd: Does generating heat or higher temperatures count as work? Because that would mean that pushing on a wall would be doing work of some sort in that sense as well.
Sure does.

4th: The wikipedia article on work said it can be positive, zero and negative. I understand how velocity can be like that since it's a vector quanity, but the article says that work is a scalar quantity.
If you throw a ball, you're imparting energy to it, doing work on it for the duration of the throw. If you catch a ball, it's imparting its energy to you when you catch it and have to decelerate the ball. In the first case, the work done by you on the ball is positive, and in the second case, the work done by you on the ball is negative.

5th: What is an example of zero or negative work? Does running in place count as work? What about running up some stairs and then back down again. Since you end up at the same place, has work been done?
Running in place you're converting energy to heat, but you're not doing work on yourself. Going up stairs you're doing work on yourself to increase your gravitational potential energy, as well as expending the heat running.

Coming back down the stairs, because you're running you do expend some energy that way, but its less (and you can feel it) because some of the energy is being recovered from your gravitational potential energy, and you mostly have to just keep yourself from falling down the stairs uncontrollably. ;)

[ma1ic3]

Friction on what, though? The only friction on the tray is air resistance, which at walking speeds is low enough that we can generally ignore it. Friction on the waiter himself (the inefficiencies of walking) may mean he's doing work when he walks, but he's not doing work on the tray. And that distinction is critical to meshing our intuitive understanding (it clearly takes effort to carry a heavy tray) with a precise picture of where the energy involved actually goes.


I was thinking the same thing too, but wouldn't that imply that work isn't being done on most of the waiter? Such as his hands, head, knees, etc... Those things are a part of the waiter, but would you say work isn't being done on, say, his hand anymore if you cut off his hand and had him hold it on a tray? Would it be more accurate/precise to say work is only being done on the actual individual particles in his feet that are overcoming the friction?

Now that I think about it, he isn't really overcoming friction is he? He is overcoming gravity and then some air resistance as he takes a step forward. So maybe only work is being done on the parts of his body that actually life and move to walk, rather than on the whole waiter himself?


Indeed they are. There's a lot of bad pedagogy (sp?) out there.


Yep, I looked it up. You can also spell it paedagogy.


If the force and displacement are at 90 degree angles, the dot product is zero. There must be at least a component of the displacement opposite to the direction of force (for example, a 95 degree angle) in order for the work to be negative.


So if water pressure was pushing water down a straight pipe, the work on the water in the pipe would be positive. But if the pipe turned at a 90 degree angle, the work would be zero. And if the pipe turned at a 95 degree angle the work would be negative?


If you connect those same turbines to electric motors instead of generators, and start pumping the water back up into the dam, then the force on the water from the turbine is still in the same direction but the displacement will be reversed (so that it's in the same direction as the force). The turbines will then be doing positive work on the water, and will be depositing energy INTO the water, rather than extracting energy from it.


If water is falling DOWN and you pump it back UP to deposit energy back into it, then isn't the displacement in the opposite direction of the force, rather than in the same direction? Hmm... would work be positive as you push it up but then switches to negative once it comes back down from the dam?

If you used the work being done by the dam to do work in electrical devices in houses above the dam, what would the work be?

[Ziggurat]

So if water pressure was pushing water down a straight pipe, the work on the water in the pipe would be positive. But if the pipe turned at a 90 degree angle, the work would be zero. And if the pipe turned at a 95 degree angle the work would be negative?

First off, let's imagine pressurized water moving in a horizontal pipe at a fixed velocity. Consider one little cube of water in that pipe. The pressure on its forward face is the same as the pressure on its back face. So the net force applied to that piece of water along the direction of motion is zero, and so no work is being done. Not too surprising.

Now, what happens if you instead have water moving in a vertical pipe at uniform velocity, and again consider a tiny cube of water. The pressure on the top of the cube, from the water above it, is less than the pressure on the bottom of the cube, because of the added weight of the cube of water itself. There is a net force on that cube from the surrounding water in the upwards direction. If the water in the pipe is moving upwards, the water around our little cube is doing positive work on our cube, and that work is being converted to gravitational potential energy. If the water is moving downwards, then negative work is being done by the surrounding water on our cube, and energy (in the form of gravitational potential) is being extracted from it.

Now, when you ask about 90-degree bends in pipes, well, that's not enough information. You also need to specify whether the water moving through the pipes is accelerating or not.

If water is falling DOWN and you pump it back UP to deposit energy back into it, then isn't the displacement in the opposite direction of the force, rather than in the same direction?

You have to pick a perspective: are you asking about work done by the water, or by the turbine? I refered to the turbine. If you're pumping water back up into the resevoir, then the displacement of the water being pushed is in the same direction as the force being applied by the turbine blades which do the pushing. Displacement for the water and the turbine will be the same, but forces are equal and opposite (Newton's 3rd law). If the turbine does positive work on the water, the water does negative work on the turbine, and vice versa.

If you used the work being done by the dam to do work in electrical devices in houses above the dam, what would the work be?

If you want to follow the chain that far, it's the work needed to compress electrons together (or pull them farther apart) in order to create an electric potential (ie, voltage) which drives the current in all those houses. But you don't really need to go that far, because you can just convert to units of energy, and then you don't have to worry about calculating the exact forces and displacements of all those electrons.

[ma1ic3]

Bah... I have to leave. I have to socialize on a weekday.

[marting]

WwoooooorrrrrrrkkkkkkKkKKKk!!!!!
-Maynard G. Krebbs

[Soapy Sam]

Electrons have mass. The potential difference of a battery applies a force.
Why does a flashlight not do work?

[Cuddles]

Electrons have mass. The potential difference of a battery applies a force.
Why does a flashlight not do work?

Because it's a closed circuit. The electrons end up in the same place they start so the net work done on them is zero. I suppose technically there is a tiny amount of momentum lost due to resistance and so there will be a very small force, but I doubt this is big enough to be measued. There will also be a force from the photons leaving the bulb which is probably big enough to be measured if cooled near absolute zero. Assuming the torch is held still there will not be any work done by these forces.

[Ziggurat]

Because it's a closed circuit. The electrons end up in the same place they start so the net work done on them is zero.

The work done on them by the battery is positive, and the work done on them by the resistor is negative. The net work on the electrons in a flashlight may be zero, but the work done by the battery is not. If you use a battery to charge a capacitor (not a closed circuit, technically), then the work done on them by the battery remains as potential energy in the capacitor.

[ma1ic3]

Thanks for the analogy Zombified.


First off, let's imagine pressurized water moving in a horizontal pipe at a fixed velocity....

What would the work done by the water be if you pumped the water UP and then left it fall DOWN into another river right next to it? You would still be extracting energy from the first river and the work would be positive right?

And what would the work done by the water be if it displaced a man in an elevator at a 90 degree angle to the water and pushed him up into outerspace somewhere past the Moon?


The work done on them by the battery is positive, and the work done on them by the resistor is negative. The net work on the electrons in a flashlight may be zero, but the work done by the battery is not. If you use a battery to charge a capacitor (not a closed circuit, technically), then the work done on them by the battery remains as potential energy in the capacitor.

The battery will start displacing the electrons further forward but end up displacing them backwards from where they started on the other side of the battery. That's interesting to think about.

[Ziggurat]

What would the work done by the water be if you pumped the water UP and then left it fall DOWN into another river right next to it? You would still be extracting energy from the first river and the work would be positive right?

Well, positive work is being done on a cube of water while it is moving upwards in one leg of the tube, but negative work is being done on that same cube while it is moving downwards in the other leg. If the water level outside both ends of the tube is the same (so that pressure is the same, and the potential energy of water entering the tube is the same as water exiting the tube), then no net work is done moving water through the tube. If water was frictionless, then once you started moving it through the tube, it would take no external force to keep it moving - it would be a liquid equivalent of a frictionless spinning disk. Water is able to support negative pressures, and what essentially happens is that the weight of the falling water is what pulls up the rising water.

You actually can reproduce equivalent scenarios with superfluid helium. In the superfluid state, liquid helium becomes frictionless, and can do some pretty funky things.

[ttch]

He also serves who only stands and waits.
-- Milton