Is holding a box over my head work, or not?

[falcon32]

I know that work=force*distance.

So here's a scenario for you.

Suppose I hold a heavy box over my head. I keep holding it until I get very tired and cannot keep it up. Naturally the box then falls to the ground at my feet.

At that moment, the Earth's gravitational field performs work on the box, the work being w=f*d=(mass of box * gravitational acceleration)* distance to ground.

Now, we know that chemical energy was released in order to allow my muscles to provide an upwards force to the box. Furthermore, I got tired when the cells of my muscles ran out of fuel to sustain the upward force. Since I am holding the box above my head without letting it move, the force I am supplying is f= - mass of box * gravitational acceleration, which of course must be the case, since if the two forces, that of my arms upwards, and gravity downwards, were not equal and opposite, the box would need to move.

The mind-boggling question is: am I working? That is, by constantly supplying an upwards force, is work being done? According to w=f*d, the answer would be no, yet I am tired afterwards.

Thanks!

 

[Nabeshin]

The reason you feel tired is because the human machine operates by continually contracting and relaxing muscles. If you take this example and instead replace yourself with a table, you wouldn't claim the table is doing work! Certainly, it is not getting tired, and it could hold up the box indefinitely.

Others who understand the biology of the situation better than I can elaborate on how our muscles manage to expend energy without doing any meaningful work -- but I'll just stop at saying it's a biological peculiarity of how our muscles work.

 

[falcon32]

but I'll just stop at saying it's a biological peculiarity of how our muscles work.

There is something happening here more peculiar than that. Would you agree that it took energy for me to hold the box up? I only lost my tug of war to the Earth because I ran out of energy, and thus was unable to provide my upwards force.

My new question () is: Does every force require energy to sustain it?

 

[Nabeshin]

My new question () is: Does every force require energy to sustain it?

No! Look at the thing I said about the table. Surely you will admit a table does not possesses an infinite amount of energy!

 

[Forestman]

I agree with you falcon32. What you said makes a lot of sense.

I would also answer yes to your second question.

 

[brocks]

I know that work=force*distance.

That's really all you need to know. If the box is not moving, no work is being done on it.

Surely this isn't the first time you have come across a term in physics that has a more specialized meaning than in everyday life. Most people think "accelerate" means to speed up, but you know that in physics, it means to change velocity, including a change in direction with constant speed. "Work" is exactly analogous --- it has a precise meaning in physics that does not necessarily correspond to the common meaning.

 

[Forestman]

No! Look at the thing I said about the table. Surely you will admit a table does not possesses an infinite amount of energy!

I disagree with you Nabeshin. Not about infinite energy, but about about work.

Work is being done on the cellular level when a persons holds up a box over their head.

The table produces resistance in a different way than muscles do.

 

[falcon32]

No!

We both agree that a table sitting with a box at rest on top of it possesses zero net useful energy, barring potential gravitational energy.

But we both agree that a cancellation of forces is happening. Earth pulls the box down. But the box does not move! Therefore, an equal but opposite force is provided upwards by the table, giving us a net force of zero.

Now if the forces did not cancel (back to my arms getting tired), the box would move, and we would all agree that work was being done. Of course work requires energy.
But suddenly, when the forces DO cancel, we all shake our heads and say, "no energy here". Shouldn't we rephrase our statement to "no net energy here?"

 

[Drakkith]

There is work being done on your muscles in order to supply the force necessary to hold the box up. Ignoring the very small movements that are actually occurring, there would be no work done to the box itself.

 

[LostConjugate]

Work and energy are two different things.

You can show up for your job and sit on physicsforums.com all day and expend energy but it does not mean you performed any "Work". It is all by definition.

 

[Drakkith]

But suddenly, when the forces DO cancel, we all shake our heads and say, "no energy here". Shouldn't we rephrase our statement to "no net energy here?"

No. Energy is defined as: the capacity to do work; the property of a system that diminishes when the system does work on any other system, by an amount equal to the work so done; potential energy.

Force and energy are not the same, and a force does not require an "energy source" to keep working.

 

[Forestman]

I thought that force equaled F=ma, wouldn't acceleration require energy.

 

[LostConjugate]

I thought that force equaled F=ma, wouldn't acceleration require energy.

Not if it is only acting to conserve energy in the system.

A charge does not require any energy to apply a force on another charge, it can do so for eternity.

Gravity does not require any energy to apply a force on a massive object, it does so for eternity.

 

[AlephZero]

The amount of mechanical work you are doing on the box is zero, because it isn't moving.

What is happening to your body when you get tired has nothing much to do with Newtonian mechanics. Certainly there are a lot of chemical reactions going on in your body, which are consuming food and producing heat and electricity (in your nerves, brain, etc), whatever you are doing. If you hold the box above your head for a long time, some of those chemical reactions get out of balance, the "waste" chemicals build up in your muscles, you feel pain, and you take some action to relieve it (letting go of the box, for example).

Humans aren't very well adapted to holding something above one's head for a long time. If you supported the weight of the box on your head (which is the normal way that people in some cultures carry heavy loads) or on your shoulders, you would be able to carry it in that position for much longer without getting tired, because the weight is then being supported by your bones, not just by the muscles in your arms.

 

[Forestman]

Not if it is only acting to conserve energy in the system.

A charge does not require any energy to apply a force on another charge, it can do so for eternity.

Gravity does not require any energy to apply a force on a massive object, it does so for eternity.

A charge and a gravitational field hold potential energy.

 

[LostConjugate]

A charge and a gravitational field hold potential energy.

Ok

 

[falcon32]

Not if it is only acting to conserve energy in the system.

A charge does not require any energy to apply a force on another charge, it can do so for eternity.

Gravity does not require any energy to apply a force on a massive object, it does so for eternity.

Ludicrous. Of course forces require energy. Observe when a rocket accelerates through space according to F=m*a. W=F*d after the rocket has moved a certain distance, so obviously a force is performing work on the rocket, moving it. Now we all know that energy is the ability to do work. If the force moving the rocket did not possesses energy, it could not have performed work. Any force requires energy. To deny this would be to embrace mental insanity.

 

[Drakkith]

Lets go back to the box. If you set the box on the ground, the box is still attracted by gravity. Now, since energy is the ability to do work, does this force exerted on the box require energy? No. The force is always there and will continue to be there forever. You do not need to expend energy to keep the box on the ground.

 

[Drakkith]

Ludicrous. Of course forces require energy. Observe when a rocket accelerates through space according to F=m*a. W=F*d after the rocket has moved a certain distance, so obviously a force is performing work on the rocket, moving it. Now we all know that energy is the ability to do work. If the force moving the rocket did not possesses energy, it could not have performed work. Any force requires energy. To deny this would be to embrace mental insanity.

Perhaps we are not referring to the same thing when we say force. A rocket generates thrust by using chemical energy to expel mass. This is NOT the same thing as gravity or the electromagnetic force.

 

[falcon32]

Lets go back to the box.

I appreciate your reply. Let's go back to my rocket.
Did an applied force move it through space? If w=f*d, then was work done? Where did the energy to perform work on the rocket come from? It could only come from my force vector. Is it so strange to admit that a force contains energy?

 

[Drakkith]

I appreciate your reply. Let's go back to my rocket.
Did an applied force move it through space? If w=f*d, then was work done? Where did the energy to perform work on the rocket come from? It could only come from my force vector. Is it so strange to admit that a force contains energy?

Looks like you replied right after I added another reply myself. See my above post.

 

[falcon32]

Perhaps we are not referring to the same thing when we say force. A rocket generates thrust by using chemical energy to expel mass. This is NOT the same thing as gravity or the electromagnetic force.

Thrust is a force vector. So is any force.

 

[Andy Resnick]

I know that work=force*distance.

So here's a scenario for you.

Suppose I hold a heavy box over my head. I keep holding it until I get very tired and cannot keep it up. Naturally the box then falls to the ground at my feet.

At that moment, the Earth's gravitational field performs work on the box, the work being w=f*d=(mass of box * gravitational acceleration)* distance to ground.

Now, we know that chemical energy was released in order to allow my muscles to provide an upwards force to the box. Furthermore, I got tired when the cells of my muscles ran out of fuel to sustain the upward force. Since I am holding the box above my head without letting it move, the force I am supplying is f= - mass of box * gravitational acceleration, which of course must be the case, since if the two forces, that of my arms upwards, and gravity downwards, were not equal and opposite, the box would need to move.

The mind-boggling question is: am I working? That is, by constantly supplying an upwards force, is work being done? According to w=f*d, the answer would be no, yet I am tired afterwards.

Thanks!

There's been some fantastically off-topic responses.

Your muscles have a reservoir of free energy that is accessed by hydrolyzing ATP (adenosine triphospate) into ADP + Pi. That reaction liberates approximately 50 kJ/mol of free energy.

So, your muscles burn a certain amount of ATP which is accompanied by a loss of free energy- that's the (chemical) work you are performing holding up the box.

Now- here's the tricky bit- that free energy is not stored in a chemical bond, but stored in the displacement from equilibrium: the concentration of ATP in your cells is 10^10 higher than equilibrium conditions. So you consume free energy by sliding toward equilibrium, and your body (the mitochondria) generate more ATP via the chemiosmotic mechanism (ultimately using F1F0 ATP synthase)

So- you are not performing mechanical (P-V) work, but you are indeed performing *chemical* work.

 

[falcon32]

Looks like you replied right after I added another reply myself. See my above post.

I see your reply, thank you. But you still haven't answered my question, just side-stepped it. Thrust is a force vector, or engineers would not draw it as such on free-body diagrams.

Please answer the question: Since a force applied moved a rocket, did the force contain energy? if you answer no, then what performed the obvious work on the system, and why did this work move the rocket in the direction of the force?

 

[Drakkith]

Please answer the question: Since a force applied moved a rocket, did the force contain energy? if you answer no, then what performed the obvious work on the system, and why did this work move the rocket in the direction of the force?

Thrust is not a fundamental force, but is a macroscopic effect of the interactions of the electromagnetic force. The ability for a table to hold up a box against gravity doesn't require the expenditure of energy. You do not require a fuel source like you do in a rocket. Thrust IS a force vector, sure. Did that force contain energy? No. It was the result of the release of energy.

 

[falcon32]

Thrust is not a fundamental force, but is a macroscopic effect of the interactions of the electromagnetic force. The ability for a table to hold up a box against gravity doesn't require the expenditure of energy. You do not require a fuel source like you do in a rocket. Thrust IS a force vector, sure. Did that force contain energy? No. It was the result of the release of energy.

Ok, then a force is the direct "result of the release of energy", and when we stop releasing that energy, the force vanishes, correct?

You are agreeing with me in a round-about way by saying that to make a force, you require energy.

 

[Drakkith]

Ok, then a force is the direct "result of the release of energy", and when we stop releasing that energy, the force vanishes, correct?

You are agreeing with me in a round-about way by saying that to make a force, you require energy.

No, I am saying that the fundamental forces of nature, Electromagnetism, Strong, Weak, and Gravity, do not require the expenditure of energy to generate their forces. To get thrust you must expend energy. The thrust generates a force yes, but the thrust requires energy to work.

 

[falcon32]

the fundamental forces of nature, Electromagnetism, Strong, Weak, and Gravity, do not require the expenditure of energy to generate their forces

Then what you are in effect saying is that, while I need to consume energy to provide a force to accelerate my rocket at 9.81 m/s^2 through empty space, nature does not need energy to provide a force to accelerate an object through the atmosphere at 9.81 m/s^2 until it smashes into the ground.

So the fundamental forces of nature are magical in that it requires no energy to create them, yet they mysteriously provide us with work. They are the exception to the rule that to create a force, you must expend energy.

All I have to say is, I sure wish I had the same magic. I'd be rich.

 

[Drakkith]

Then what you are in effect saying is that, while I need to consume energy to provide a force to accelerate my rocket at 9.81 m/s^2 through empty space, I do not need energy to provide a force to accelerate an object through the atmosphere at 9.81 m/s^2 until it smashes into the ground.

So the fundamental forces of nature are magical in that it requires no energy to create them, yet they mysteriously provide us with work. They are the exception to the rule that to create a force, you must expend energy.

All I have to say is, I sure wish I had the same magic. I'd be rich.

Its very simple. If it took energy to make gravity work, where is the energy coming from? Where does the energy come from to cause an electron to exert a force on a proton? The answer is that it doesn't require any energy to do those things. What you are not understanding is the difference between a fundamental force and something like thrust.

And no, the fundamental forces do not magically provide us with work without energy. Lifting a box into the air requires energy. Once it is in the air that energy is effectively "stored" as potential energy.

They key here is that WORK requires energy, not the force.

 

[falcon32]

If it took energy to make gravity work, where is the energy coming from? Where does the energy come from to cause an electron to exert a force on a proton?

I agree with your last point, that work requires energy. But paradoxically, work cannot happen without a force. Try moving a rocket without one.

Now your question to me is a very good one. "If it took energy to make gravity work, where is the energy coming from?" Just because I can't answer it (and certainly I cannot), doesn't mean we get to conclude that the forces just exist just because. That is borderline religious. What we should do is try to find out why they do exist, and that may be a task for a future generation.

I appreciate the debate, thanks!

 

[Drakkith]

I agree with your last point, that work requires energy. But paradoxically, work cannot happen without a force. Try moving a rocket without one.

Now your question to me is a very good one. "If it took energy to make gravity work, where is the energy coming from?" Just because I can't answer it (and certainly I cannot), doesn't mean we get to conclude that the forces just exist just because. That is borderline religious. What we should do is try to find out why they do exist, and that may be a task for a future generation.

I appreciate the debate, thanks!

Anytime.

 

[douglis]

But suddenly, when the forces DO cancel, we all shake our heads and say, "no energy here". Shouldn't we rephrase our statement to "no net energy here?"

No work done doesn't mean no energy spent.It just means no energy is transferred(from the muscles to the box).
In other words your muscles contract with zero efficiency.

 

[Rap]

The amount of mechanical work you are doing on the box is zero, because it isn't moving.

What is happening to your body when you get tired has nothing much to do with Newtonian mechanics. Certainly there are a lot of chemical reactions going on in your body, which are consuming food and producing heat and electricity (in your nerves, brain, etc), whatever you are doing. If you hold the box above your head for a long time, some of those chemical reactions get out of balance, the "waste" chemicals build up in your muscles, you feel pain, and you take some action to relieve it (letting go of the box, for example).

Humans aren't very well adapted to holding something above one's head for a long time. If you supported the weight of the box on your head (which is the normal way that people in some cultures carry heavy loads) or on your shoulders, you would be able to carry it in that position for much longer without getting tired, because the weight is then being supported by your bones, not just by the muscles in your arms.

Yes - that's it. Work is being done, but not on the box.

Here is a simple model - suppose you want to hold up an iron cylinder instead of a box. You put it inside of a coil of wire and connect the ends of the wire to a battery. The current will generate a magnetic field which will magnetize the iron bar in the opposite direction, and the bar will be attracted to the coil. If there is enough current in the coil, it will hold the bar up against the force of gravity. There is then no work being done on the bar, but there will be resistance in the coil, and the battery will be doing work to overcome that resistance. The rate of work will be I^2 R where I is the current, R is the resistance of the coil. The work being done is due to the force required to move the electrons through the resistive coil. The work is being converted to heat. When the battery runs down, the iron bar drops.

I think in the case of muscles, electrons are being moved around (although the force is not magnetic) and the work being done to move them is then converted to heat. When the energy source runs out, the box will drop.

 

[Subductionzon]

Rap, I am not really fond of your analogy, though it does show how you can consume energy without doing work.

When holding a box over your head the key is that you are not holding it still. You are always slightly tensing and relaxing your muscles, resulting in very small movement of the box. You can minimize the work you do, and therefore extend the time period that you can hold the box up by perfecting your technique either locking your joints, or if you have the ability, like some animals, to actually locking your muscles. I have seen birds that have died on electric lines when they bumped up against a conductor. Even after they have been dead a day or more you can see them hanging upside down by their feet. The birds muscles can "lock" and very little energy is used to keep it in place.

 

[Rap]

Rap, I am not really fond of your analogy, though it does show how you can consume energy without doing work.

When holding a box over your head the key is that you are not holding it still. You are always slightly tensing and relaxing your muscles, resulting in very small movement of the box. You can minimize the work you do, and therefore extend the time period that you can hold the box up by perfecting your technique either locking your joints, or if you have the ability, like some animals, to actually locking your muscles. I have seen birds that have died on electric lines when they bumped up against a conductor. Even after they have been dead a day or more you can see them hanging upside down by their feet. The birds muscles can "lock" and very little energy is used to keep it in place.

Yes, I agree, if you can somehow use your body to act as a support, by placing it on your head, for example, then you will not expend energy to keep the box above your head. But I thought the point of the OP was that energy WAS being expended to hold the box over your head, and with flexible arm joints, there was no locking effect, and the question was where is the energy going?

Small movements of your arms do no net work on the box. If you drop the box a bit, then push it back to its original position, the net work done on the box is zero. If the muscles in your arm return to their original position, then no work has been done on your arms. Nevertheless, energy has been expended and turned into heat during this process. If you have to think in terms of work, then it will be microscopic, like the electrons in the wire in the bar and coil example. In the case of your arm, it's stored chemical energy being transformed into heat, I'm not sure its helpful to think of this in terms of work being done.