Do I do any work when I hold out a weight at arm's length?

September 11, 2013 2:02 PM

When I hold out a weight at arm's length, I am doing no work (which, in physics, is motion over a distance against a resisting force, iirc) on it, because it remains stationary. But it feels like work! What about at the level of biophysics? Is keeping the muscle fibers of my arm contracted doing work in any way, perhaps at the cellular level?
posted by thelonius to Science & Nature (29 answers total)

You sure do! It's called "isometric exercise."
posted by infinitywaltz at 2:06 PM on September 11, 2013

You're forgetting about the acceleration of gravity.
posted by fontophilic at 2:06 PM on September 11, 2013

Response by poster: No, that is the force I did work against to raise the weight to the height that I hold it at.
posted by thelonius at 2:08 PM on September 11, 2013

I think it's just a mix-up of the technical definition of Work (F*d), with the colloquial definition of work (expend energy on an action).

When you hold something still, you're exerting a force on it (opposite and equivalent to the force of gravity) and you're expending energy to exert that force. But in a technical sense, no Work is being done on the weight.
posted by no regrets, coyote at 2:08 PM on September 11, 2013 [6 favorites]

The issue is that you've conflated two definitions of the word "work" - the scientific physics definition, and the casual every-day defintion of "exertion".

Just because you're not performing work in the classical sense doesn't mean that you're not exerting energy - your body is applying a constant upward force to the weight to counteract the downward force of gravity (Force = mass x acceleration, so Gravitational Force = object mass x 9.81 m/s^2)

On preview: To raise a weight, you have to exert a force greater than gravity. To support it above the floor, you have to exert an equal and opposite force. Additionally, to lower a weight against gravity in a controlled manner also involves exerting a force to dampen the gravitational acceleration. All of that requires muscle exertion.
posted by muddgirl at 2:11 PM on September 11, 2013 [6 favorites]

Response by poster: What I am asking is, is my body doing any work, in the technical sense, during this? I am quite sure that I am doing no t.s. work against the weight. But what's happening inside my arm?
posted by thelonius at 2:12 PM on September 11, 2013

Well, but it's not 100% stationary. Your muscle fibres aren't all perfectly contracted simultaneously; some fatigue and relax, and after refractory period contract again. Meanwhile, other fibres take over, but not in perfect synchronicity- your arm will bob and tremble measurably, though not significantly. The weight is still moving through space to some degree, so i'd argue that you are still doing work.
posted by windykites at 2:15 PM on September 11, 2013 [7 favorites]

But in a technical sense, no Work is being done on the weight.

If no work is being done on the weight and the weight-holder is consuming energy, where does the energy go? My guess is heat (when energy is missing in a complex system, it's usually waste heat), and the formation of chemical compounds in muscles.

It is also possible no (or very little) energy is being spent - but fatigue/stress damage is caused in the muscle, and the body must spend energy _later_ to correct the damage.
posted by Dr Dracator at 2:18 PM on September 11, 2013 [1 favorite]

Response by poster: The other place the energy could go is, heat, I think.
posted by thelonius at 2:20 PM on September 11, 2013

Of course energy is being spent. Blood's carrying oxygen to the tissues and once you hit anaerobic you're producing lactic acid through cellular metabolism. This stuff doesn't just happen by magic. Blood doesn't move without energy, sodium-potassium channels don't open and close without energy.
posted by windykites at 2:21 PM on September 11, 2013 [3 favorites]

here's wiki on muscle contraction
posted by windykites at 2:23 PM on September 11, 2013 [2 favorites]

I was just about to post the article on muscle contraction. On the scale of biochemical reactions, "Work" becomes a poor descriptor of the processes that are going on.
posted by no regrets, coyote at 2:28 PM on September 11, 2013 [1 favorite]

Best answer: No, that is the force I did work against to raise the weight

You are conflating physics meanings and day to day meanings of terms.

Physics is impersonal. "You" did not do work to raise the weight. A force applied to the weight raised it. You caused the force to be applied. Even if gravity was not acting on the weight, moving the weight a distance would still be work.

When you hold the weight there, no work is being done on the weight. Work, in the physics sense, is being done on muscle fibers and blood cells and all sorts of other things inside your body. Work is being done on your blood by your heart muscles. Work is being done on air molecules by your lungs.

This is a completely different meaning than the day to day usage of work, feeling like you've done a lot of work, getting some work done, working on understanding physics, etc. Think of it as a different word that just happens to be spelled with the same letters.

I should get back to work
posted by yohko at 3:05 PM on September 11, 2013 [11 favorites]

Missing from the junior-high-school physics model of "work done" are concepts of USEFUL work done, input, output, efficiency, etc. With concentric or eccentric muscle contractions, the efficiency would be the work done divided by the energy expended. Of course energy is still being expended in an isometric muscle contraction -- this is best thought of as "overhead" since efficiency cannot be calculated by simple division of one figure by the other.

This is the stuff that is explored in excruciating detail in engineering or sports science.
posted by wutangclan at 3:05 PM on September 11, 2013

Best answer: What I am asking is, is my body doing any work, in the technical sense, during this? I am quite sure that I am doing no t.s. work against the weight. But what's happening inside my arm?

Inside your arm, there's muscle fibers. Muscle fibers are made of muscle cells. Muscle cells are long stretchy/squishy things. Inside, they contain a sort of rack-and-pinion like arrangement except there is no pinion: both sides are racks. Also, they are squishy. Sorry, this metaphor sucks.

Basically, there are these things called sarcomeres. Sarcomeres are the bundled strands that actually contract the muscle. So all these long fibery things inside the sarcomere are stretched out and interlocked with one another. Then, the sarcomere grabs onto a molecule of ATP and busts it apart. The energy that was stored in this bond is used to change the shape of part of sarcomere, which causes the muscle fiber to contract. This is a gross oversimplification but if you want to google it, those are the words you need.

What you are doing to hold the weight is contracting muscle fibers. For them to contract, they are breaking the bonds of the phosphate group to the ATP molecule through hydrolysis. This bond energy is the thermodynamic energy you are looking for.

What happens when you eat food is your body does all kinds of organic chemistry synthesis to turn things like complex carbohydrates into ATP. ATP is an easy-for-cells-to-use chemical battery: the energy required to do work is stored in the bonds to its phosphate groups.
posted by jeb at 3:47 PM on September 11, 2013 [10 favorites]

Best answer:

What I am asking is, is my body doing any work, in the technical sense, during this? I am quite sure that I am doing no t.s. work against the weight. But what's happening inside my arm?

So your arm is at a position, lets call it "d", measured in distance from the ground. A large weight is pressing on your arm, causing it to move down a distance, let's call it "x". In order to "resist" the movement from d to d-x, your body (at the command of your nervous system) transforms adenosine triphosphate (ATP) in order to "fuel" the contraction of a group of muscle fibers to raise your arm up. Your body uses ATP to store energy acquired from food. The energy released in the chemical process of transforming ATP to rebuild your muscle fibers is equal to do the work required to move your arm back to the position it would be in if it hadn't move at all (W=F*x).

F=m*g
W=m*g*x

But in this example I'm assuming that this is a one-time force. This isn't a one-time force. It's gravity. So to hold your arm out in the real world, you have to apply this work equal to (m*g*x) over a period of time t, for very tiny (read: infinitesimal) values of x. To get the total amount of work required to hold you arm out for a certain span of time, you'd have to get the sum of these very tiny values of work over time (which we call an integral). So the total work grows as time goes on, and eventually your body runs out of ATP that can be easily pumped into your muscles and your arm drops with exhaustion. You have literally run out of energy to resist gravity.
posted by deathpanels at 4:05 PM on September 11, 2013 [4 favorites]

Response by poster: I don't think I am confused about the sense of work in the way that a few people said. But I muddied the waters by saying "it feels like doing work!". That is, I understand that not all expenditure of energy is (physics) work. But it's just as well I failed to communicate that, since a lot of interesting points were made in that line of answer. The point where I am definitely confused is not real far from just understanding the very basic elements of this stuff, after all.
posted by thelonius at 4:06 PM on September 11, 2013

Death panels has it. In order to resist a continuous force, you have to apply continuous force. If no work was required to keep the weight stationary, you could let go and it would stay where it was, like Koschek the floating cat from Night Vale. As it is, though, the weight is being continually acted upon by gravity, and so you must continuously oppose that force with work of your own.
posted by KathrynT at 4:55 PM on September 11, 2013

I disagree with deathpanels. A table holds a weight against gravity for as long as you like without expending any energy. The problem is that he has reinterpreted the formula for gravitational potential energy to mean something it doesn't - "W = m*g*x" gives the gravitational energy it takes to lift the weight to some change in height "x", not the energy it takes to hold it there an infinitesimal amount of time.

The key is that a table produces the force required to balance the gravitational force with the covalent bonds within starch molecules, which are stable.

Your arm uses the bonds between actin and myosin proteins - these bonds are also quite stable, but your brain causes many of those proteins within your arm to continuously release and re-attach in order to keep the weight stable. It's that process that produces lots of microscopic expenditures of energy (from ATP) that cause your arm to be tired. So even though it looks like you're just holding your arm steady, fibers within your muscles are un-tensioning and re-tensioning continuously to balance and control the muscles.
posted by Salvor Hardin at 5:26 PM on September 11, 2013 [5 favorites]

Salvor Hardin and I have been discussing this over dinner. (He's a physicist, I'm a biologist.) I just want to add that this resource(bottom of 348, top of 349) explains pretty well what happens.

One interesting fact that SEEMS to complicate the issue - but it doesn't, I swear! - is that actually, it doesn't take ATP to hold a muscle in a contracted state. It takes ATP to release a muscle fibril from a contracted state. There is a very obvious demonstration of this: corpses with rigor mortis. When your body stops producing ATP, your muscles are able to cleave ATP one last time, which allows the contraction to occur, but they aren't able to relax and start the process over because the ATP (which normally is the "key" that allows the release of the fibril) has been used up. This leads to permanent muscle contraction.

The reason you, a living person (unless you're secretly a zombie, and then I'd have to get back to you about this), can't contract your muscle once and then keep it there without doing work is because, as Salvor Hardin said, your nervous controls thousands of microadjustments to your musculature to maintain stability.
posted by Cygnet at 5:42 PM on September 11, 2013 [5 favorites]

Here is what I am understanding from people in this thread. Is this right:

Holding an object up does not (or at least does not always) require the expenditure of energy. (for example, as SH notes - if you put a weight on a table, the table can hold it up indefinitely, without expending energy.

The thing is, to hold a weight up *with my extended arm*, I have to contract the muscles in my arm. This is not because of some inherent fact about gravity and force and holding up objects- it's just about the way my arm is made - that it's made so that, in a relaxed state, it is soft and bendy, but with the application of some energy, it can become un-bendy.

So my understanding is that some *real* work is being done, in the physics sense, but it's not being done to hold up the object (which is, as OP points out, something that requires no work), but, rather, to keep the network of muscles in my arm stiff (just because that's how those muscles work).

Is that right? Does that help clarify? Is it accurate?
posted by ManInSuit at 5:44 PM on September 11, 2013

Also, see this for an explanation of isometric muscle contractions (contractions where your muscle does not change length).
posted by Cygnet at 5:49 PM on September 11, 2013

To put together the comments from several people: as I understand it, when you contract a muscle, you're telling your nervous system to contract a certain percentage of muscle fibers a certain amount. The muscle as a whole is contracted the same amount holding up a 5 lb weight or a 12 lb weight (ignoring the difference in stretching of the tendons, it's the same arm position). In order to exert difference forces, the number of muscle fibers contracted varies.

On top of that, your nervous system varies which muscle fibers are active at any time, so fibers in an isotonic muscle are continually relaxing and contracting. Since it takes energy from ATP to contract and to relax a muscle fiber, you're constantly expending energy to do the work of moving each muscle fiber back and forth over and over.

If you hold a weight above your head, with your arm vertical, your solid bones are supporting more of the weight passively. You don't have to contract as many muscles to keep your joints locked in position. It's the same force opposing gravity, but less effort; therefore, less work being done shuffling muscle fibers, less energy lost as heat.

I've heard stories of marathon runners who literally run out of energy - there's no more ATP (or maybe other biochemicals to break it down) to feed their leg muscles - so their legs freeze in place. Just like rigor mortis. The muscle fibers can't contract or relax until they get more energy, so they're stuck in one position.
posted by WasabiFlux at 5:59 PM on September 11, 2013

ManInSuit:
I think you've got the idea, but I wanted to clarify this point: Real, actual factual physical work is done when you lift the weight to its height, however, it's not the fact that your arm's muscles must be contracted to lift up the weight that explains the anomalous energy use during isometric weight holding. The process of lifting the weight UP to the height takes energy in a gravitational field regardless of whether it's your arm, a hydraulic lift, or anything else doing the lifting.

That counterintuitive energy use that occurs while you're holding the weight at one height happens because of the peculiarities of what goes on in your muscles when you're holding it. And what's going on is that your brain is constantly signaling the actin & myosin proteins in your muscle fibers to release, and re-tension themselves as it actively stabilizes your arm (balancing the weight side to side, as well as maintaining the correct balance of tension between opposing muscle groups).

A table does not undergo this process, because it has no brain worrying about holding the weight steady, and even if it did the molecular structure that holds up the weight is, of course, not capable of active stabilization.
posted by Salvor Hardin at 5:59 PM on September 11, 2013 [1 favorite]

I should also clarify that real, actual faction physical work is done when you hold your arm and the weight out steady, but it's being done at a microscopic level - the work is being done to put tension on the proteins in your muscles.
posted by Salvor Hardin at 6:14 PM on September 11, 2013 [2 favorites]

One issue muddying the waters here is that we have a terminology problem dating back hundreds of years, related to the fact that we were building things to get useful mechanical work done long, long before we figured out there was an underlying unified concept that we decided to call "energy." Combined with the near-brain dead pedantry of many high-school physics teachers it makes for an unfortunate situation.

The Physics 101 definition of Work (F * d) is more fully the definition of mechanical work. By this definition, holding an object totally, literally motionless in your outstretched hand does no (mechanical) work on the object because you are moving no distance.

The definition fails here in (at least!) two obvious places. One is this totally unreal concept of "motionless" -- in reality you hold things up through a constant series of microscopic adjustments, and it's this reality (and consequent infinitesimal distances) that I think deathpanels was trying to capture with the integral idea up above. I don't know enough about the biophysics to know if that captures all the energy expended, but reading quickly it seems that probably it doesn't entirely.

The second failure is the common-sense "it sure feels like work!" response. Of course it feels like work. Obviously, if you stopped eating food, you would eventually run out of chemical fuel and be incapable of holding your arm out anymore. There must be some energy expenditure at play here, even if it's not capital-M capital-W Mechanical Work. The basic concept of Work gets all screwy because a couple hundred years ago we figured out that all these devices we were building to affect the world were all delivering (and consuming) different varieties of a unifying entity called Energy, which the physics department promptly set exactly equal to Mechanical Work so we could keep all our old equations. But Mehcanical (W = F*d) Work is just one tiny corner of the vast universe of Energy.

So, in this system, sure, there's probably little to no Mechanical Work being delivered to the barbell, but that doesn't mean no Energy is being expended -- obviously, chemical energy is being expended, sometimes is great quantity, to keep that arm stationary. The (sorry to generalize) high school physics teacher pedants are generally totally cool with Work = Energy, but tend to leap atop the high horse the second you accidentally think that maybe Energy = Work. It's a dumb distinction, and made worse by calling it by its nickname ("Work," which if you recall we stole wholeheartedly and equated to Energy) instead of its full name ("Mechanical Work").
posted by range at 6:16 PM on September 11, 2013

Response by poster: The thing I think I was most confused about here is the subjective factor - I now see better, I think, that expending energy (by keeping your arm tense) feels like expending energy, whatever the thermodynamic analysis of that energy. This is, I guess, a failure to appreciate the "impersonal" quality of physics, as mentioned above.

I recently read a popular introduction to thermodynamics, and have been wondering how these concepts relate to what happens inside body systems, at a low level., and this is what motivated my question. Thanks all, for your time and responses.
posted by thelonius at 5:09 AM on September 12, 2013

Best answer: Clearly holding up a weight at arms lengths requires energy. However, dangling a weight by a string from a tree branch requires no energy input at all, so it can't be holding the weight up that is costing energy.

So where does the energy go? What's happening internally is that your body doesn't contract a bunch of muscle fibres and then leave them contracted: it's continuously releasing some and contracting others with the end result being a continuous force being exerted on the weight. So the work being done is the work required to stretch a bunch of muscle fibres over and over again.

Clearly this is quite wasteful, but it doesn't really matter because it's very rare for human muscle to be required to exert a continuous force in this fashion in the real world.
posted by pharm at 5:27 AM on September 12, 2013 [1 favorite]

My explanation was intended as a hand-waving gesture to help ease thelonius's confusion about the interconnectedness between "this feels like work" and "physical work". Please don't take away my physics minor. :)
posted by deathpanels at 5:38 AM on September 12, 2013 [1 favorite]