The body's chemical energy, and the physics concept of "work"

Let’s say I grab a 20-pound dumbbell off the floor and hold it out in front of me at 90 degrees. Once I have lifted it into position, I am no longer doing any “work” on the dumbbell, using a physicist’s definition of “work”. And certainly, if my arm operated like a purely mechanical device, no work would be exerted anywhere in the system once it was in position.

In reality though, it takes energy for my muscles to keep holding the thing up. How much energy is that, in watts, and where does it go (all into heat)?

I estimate that lifting the 20-pound weight to about 5 feet requires about 140 joules, so if I do that in 1.4 seconds that’s about 100 W.

In comparison, how much energy does it take to hold it there?

Bonus question - how efficient is my body in lifting the weight into position? I.e. I delivered about 100 W of power to the weight - how much power did my body actually consume in the process of lifting it?

You are correct; once the dumbbell has been lifted up and is held stationary, no work is being done on it, just as if the dumbbell were instead supported by a shelf.

Therefore, any energy your muscles expend holding the dumbbell in place is not being turned into useful work, but is instead turned into heat.

I don’t have any quantitative information to add; you’d likely have to figure out the energy utilized by your body empirically.

Missed the edit window - I was sloppy about my terminology in the last sentence. Please read as:

“I delivered about 140 joules of energy to the weight - how much energy did my body expend in the process of lifting it? Alternatively, what was my instantaneous power consumption (above the base metabolic rate) while I was delivering 100 W to the weight?”

Your arm is a purely mechanical device, and on a per/time basis there is as much work done in the *system *once it is in position as there was when it was being moved into position. depending on exactly how you are holding the weight, there may in fact be *more *work being done because of inefficiencies in the system.

Your confusion is caused because of two factors:

1)You are conflating work done on the dumbbell with work done by the system. You note that no work is done on the dumbbell, and then ask where the energy is the muscles is going and whether it is dissipated as heat. The dumbbell itself won’t get hot, of course because, as you note, no work is being done on it.

2]You are not not considering the muscles as cyclical motors. But that’s exactly what they are. Every muscle consists of gazillions of little linear electrochemical motors. All of those motors are whizzing backwards and forwards at about 4 cycles/second, and on every cycle they are grabbing and retensioning the muscle fibres.

And that pretty much answers the basic question. The muscle motors are wizzing back and forwards constantly and doing work constantly in the sitrictest: sense they they are exerting force over distance. This is no different to if your were to hold a dumbbell using an internal combustion motor: your “purely mechanical device”. Once again, no work would be done on the dumbbell, but the pistons would be flying back and forth and doing work on the gasses and the crank. That work wouldn’t translate into movement of the dumbbell, but the work is still occurring and is needed to *maintain *the position of the dumbbell.

And just as with an IC motor, the energy of the muscles leaves the *system *as heat and vibration. It’s no different to when you drive your car to work, then back home again at the end of the day. The position of all the parts of the system is unchanged at the end. Because you drove it in a cycle, no “useful” work has been done by your car, despite it being driven on a 10km round trip and using 2 litres of fuel. All the energy generated by your car engine every day is “wasted” as heat and vibration. In the same way, the energy generated by your muscles is cyclical and because the position of the dumbbell doesn’t change over the course of the experiment, the energy is “wasted” as heat and vibration.

That depends a lot on your physiology, where you are holding the weight and so forth.

You need to be very careful in assuming that since you need to apply 100 W to the weight, that tells you how much energy your *body *needs. In lifting the weight you are also lifting your arms and probably lifting your whole body via the knees.

Your body has preferred areas for holding objects of various weights. Outside of those ranges it becomes less efficient because of changes in leverage and circulation.

To illustrate this, try holding your arms out at right angles from your shoulders without a 1 kg weight in them. Most people struggle to manage more than about a minute before the muscles become fatigued. Then hold your hands straight above your head. Because the bones are now acting as columns, most people can hold the weights for twice as long.

Different people also have different muscle sizes and composition. As muscles become tired they become less efficient, so someone with small muscles or primarily fast twitch muscle will use much more energy than someone with large or slow twitch muscle.

That depends on your level of fitness, your physiology and what lifting technique you used. The general rule of thumb is that the musculo-skeletal system is ~25% efficient, so you would have used about 600 joules.

As an extremely broad SWAG, if you needed to apply 100 watts to the weight, then you would need at least 500 watts of energy above basal. The body is only 25% efficient anyway, and once you figure in losses to fatigue and losses to sub-optimal holding positions it’s probably less than 20% when holding a dead weight.

Thanks for the response, but I understand all that. Perhaps my OP was too simplistic.

I recognize that no additional work is being done to the weight while I’m holding it up, and thus it won’t heat up or anything. My question is exactly where the energy I’m expending goes.

By purely mechanical device, I meant something like a rope and pulley system with a ratchet. Once it has been raised into position and the ratchet locked, no energy is being expended, anywhere, to support the weight.

An internal combustion engine is not a purely mechanical device - it is a chemical/mechanical device, just like my arm. And it would require an additional component - a clutch or transmission of some sort - to hold the weight in a fixed position, since it can’t do anything useful at 0 RPM. It is obvious where the energy consumed by an ICE in this configuration would go - the chemical energy from the fuel is transformed into vibrations, exhaust velocity, heat in the clutch, etc., and most of it ultimately ends up as heat somewhere (EDIT: I suppose if you closed all the valves and stopped the engine you might be able to support the weight by compression of the gas in the cylinders, at which point I would call it a “purely mechanical device”, but that’s not really the intended purpose of an ICE)

I am looking for a similarly detailed description, and quantification, of where the chemical energy in my muscles ends up. Does it all get turned into heat relatively quickly, or does some of get bound up in chemical waste products that are later excreted?

I see your second post on preview, thanks, that helps.

Basically it all gets turned into heat and noise instantly.

Instead of a clutch, the body just shuts down some of the cylinders to regulate the force applied. The muscles are basically bundles of fibres that pull against each other. If the body senses that the muscle is slipping, it orders more fibres to start pulling. If it senses the weight is being lifted instead of held, it shuts some of the fibres down. So there’s no loss to the clutch in a muscle.

Almost none of the energy gets converted into chemical waste. There is a chemical conversion occurring to provide the energy, but it’s a net source of energy, not a loss. The only significant chemical products are water, CO2 and ADP, which are effectively “spent” and don’t represent a loss.

There is also no loss to exhaust velocity because the muscles are electrochemical rather than heat engines, so there is no change in gas volume.

The chemical energy from the fuel (ATP in the case of the muscles) is transformed into movement. The movement energy is in turn dissipated as vibrations, heat and a tiny amount of electrical energy, the vast majority being heat. You can hear the waste vibratory energy if you stick your thumbs in each ear and tense your fists real hard. There should be a low hum at ~4Hz, that’s your muscles losing energy as noise. Detecting the electrical loss is much harder… unless you are a platypus.

First of all, just because your body is expending energy, does not mean that it’s doing work. In order to be doing work, you have to be both exerting a force on something and moving it. Second, even if we’re talking about energy expended and not about work specifically, there’s no basis for saying that the power dissipated in holding the dumbbell must necessarily be greater than that dissipated in lifting it, and in fact I see very little reason to expect that it would ever be greater: Any efficiencies present when you’re holding it will also be present while you’re lifting it, plus you also have the addition energy expenditure from doing work on it. And of course it’s possible for a system to hold a weight in place without expending any energy at all.

Oh, and to the OP: As an excellent rule of thumb, whenever the question is “where does the energy go?”, the answer is almost always “heat”.

Which is exactly what I said and exactly what the body *is *doing when it is maintaining muscular tension. I did go into this at some length in my posts.

Regardless of what you see, the fact is that the energy expended in holding in most positions is significantly higher than the energy expended in lifting, for the reasons that I already gave and several others.

Wrong, for the reasons already given.

Yes, and…

Did you actually read my posts. I am guessing not, since I already addressed all these points, except for the last one which is utterly irrelevant to what I wrote.

And yet for some reason you quoted me. :dubious:

I find this very hard to believe. Anyone who has ever lifted something heavy knows it’s easier to hold it in place than to lift it. If what you say is true, weightlifters shouldn’t bother doing reps, they should just hold the weights.

:eek:

I assume this is a joke.

If not, find a 1/2kg weight and lift it to shoulder height with a straight arm for 2 minutes. Anybody can do this without even raising a sweat.

Now hold the weight out with straight arms at shoulder height for 2 minutes.

Didn’t succeed did you?

When you lift an object, the individual actin molecules only fire sporadically over a portion of the action, which prevents fatigue. Moreover the leverage systems of the body are optimised for lifting. So the muscles only take the muscle only takes the strain during the hard bits for a fraction of a second. Holding an object puts constant strain on the same fibre segments and the same mitochondria, causing rapid fatigue.

Except that muscles can only grow if the fibres are lengthening under load. By definition, if an object is held steady the fibres can’t be lengthening.

Holding a load is a great training technique for martial artists or gymnasts because it causes a proliferation of slow twitch, fatigue resistant muscle. Basically it causes a conversion to posture muscle. But what it won’t do is cause an increase in muscle strength. This is the reason why marathon runners don’t have hugely thick legs. When holding a posture, once the muscle reaches a size where it can maintain the load without lengthening it stops growing.

That’s not a fair comparison. Your first scenario has me lifting for half of the time, some of the time is spent going down.

Try the second scenario, but move your arms up and down just an inch. You think you can do that for longer than keeping it still?

I acknowledge I know nothing about the science of this. I am very likely wrong about this. I’m just stating what seems logical to me based on personal anecdotal evidence.