Does it take more energy to go downstairs than upstairs?

I just found this website today, and there's some very interesting information here. One thing I do have to comment on, although I'm sure someone has already mentioned it: there are two types of actions your muscles can make--concentric and eccentric. A concentric movement is one where you use your muscle to move a weight e.g. pushing the bar away from your chest in the benchpress or pulling a weight toward your chest in a barbell row. An eccentric movement is one in which you use your muscles to resist a motion e.g. lowering the bar to your chest in a benchpress. Eccentric movements cause the build-up of lactic acid in your muscles, which is what causes soreness. Since walking down stairs is a primarily eccentric movement, it would cause more soreness than walking up stairs, which is where someone would get the idea that wlaking down staris requires more energy.

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Link to the Mailbag Item inserted by CKDextHavn, Board Moderator: http://www.straightdope.com/mailbag/mdown.html



[Note: This message has been edited by CKDextHavn]

Actually, eccentric motions cause soreness for another reason. If you can, imagine your muscle fibers have a series of "hooks". These hooks (upon muscle contraction) grab, pull, and move to the next "hole". This is actually a chemical action, but I'm not going to get into it here. During a concentric contraction, these hooks are climbing in the direction they were meant too.(since muscles can only contract one way) During relaxation phase, these hooks are withdrawn. If you do an eccentric contraction instead of relaxing, these hooks are grabbing and trying to pull up, however, they are moving the wrong way. This tearing motion is what causes the soreness. Lactic acid will build up during any type of muscle movement.
I can get the chemical process for you, but I thought I would explain it like it was taught to me.

Roksez: The hook and hole analogy is utter nonsense. Our muscles are arranged in pairs so that what one muscle cannot accomplish by contraction, another one can. "There is no "reverse gear," so to speak. Anaerobic activity (operating oxygen-starved) and the build up of waste products in the muscle cells is what causes the "burn" (and the later soreness) that signifies the tissue damage that body-builders so crave. You gotta destroy some to get bigger, better ones.

The walking downstairs vs. upstairs is a matter of which muscle group you're using.
Our climbing muscles have been fighting gravity for eons, and are correspondingly bigger and use more oxygen than their coasting-downhill counterparts. Oxygen consumption is a very accurate gauge of how much work a muscle is doing, and anyone who has hiked uphill one day and down the next can tell you, uphill requires more oxygen and downhill cause supreme agony in muscles unused to such nonsense.

Ok simple test to show what I'm talking about. Grab anything in your hand, and do a bicep curl. Now slowly lower it back down, letting it fall naturally, but with some resistance. Your tricep muscle is not contracting, your bicep muscle is. It is resisting the downward motion. It is contracting, but it is moving "backward". This is taught as fact in my human kinesiology book, which I will dig out and get some exact quotes from. Perhaps you have a source for your information??

The eccentric motion does cause more soreness, not from oxygen depletion, but because of the method I described earlier. Unless the body of knowledge on this subject has changed in the last 2 years, I can assure you I am correct. If you doubt me, I will contact my professors to see if I have missed something, but my major is fitness/exercise physiology. I would hope I am not paying to be taught "nonsense". Also, the "hook" thing is an analogy, as I said. It is actually a chemical reaction, which produces a ratcheting effect in the muscle fibers. These only connect in one direction, thus when you do an eccentric contraction (not a relaxion) you tear more of these fibers.

Yes, I understand what you mean by "eccentric" and "concentric," although I have never heard these words used to describe muscle movements, and they really don't make much sense when used as such. I guess the idea is that an "eccentric" muscle movement is one that goes against the "normal, accepted pattern?" (I cannot fathom how "concentric" figures into this. The whole thing sounds like a bunch of body-builder hooey). Anyway, it makes no difference, the muscle is contracting in the same manner - muscle cells move our body parts by making themselves shorter and fatter, regardless of which direction they are moving or whether they are actively or passively effecting movement. I cannot imagine where this idea of a "ratchet" arrangement came from, or maybe I don't understand why you are using a mechanical analogy for what you say is a chemical process. I don't understand how a chemical process can be responsible for the mechanical damage ("tearing"?) you describe. Or are you saying the muscle fibers somehow "let go" of each other and "reattach" in a different position? This I never heard.

Until you can provide me with some physiological basis for your claim - a reverse Krebs cycle, say - I'll stick to Human Anatomy & Physiology 101 and stand by my original statement.

Ok, found the book,(actually my anatomy, this is not as detailed, but I digress). Here goes the technical explanation, and this will take awhile.
First, the structure and organization of a muscle.
1 Muscles are made up of cells known as muscle fibers, which are long cylandrical shapes up to 1 foot long.(Picture a fibreoptic phone line).
2 Each cell is further made up of myofibrils. Myofybrils are composed of units called sarcomeres, which lie end to end. (Again, fibreoptic phone line)
3 Myofibrils are composed of sarcomeres, stacked end to end. Sarcomeres are the contractile units of a muscle.
4 Sarcomeres are composed of two types of myofilaments called (this is real technical here) the thick one and the thin one. The thin one is composed of actin molecules, the thick one of myosin molecules. These filaments overlap, and when the actin molecules are slid past the myosin, contraction results.
Ok, now for the actual contraction.
On each myosin filament, the are myosin heads(which look somewhat like hooks). On each actin filament, there are binding sites, each covered with troponin(negatively charged)
When an impulse is sent to contract a muscle, positive calcium ions are released, which attach to the troponin, and pull it away from the binding sites on the actin.
Once the sites are exposed, the following occurs.
1 The active myosin heads are attracted to the exposed binding sites, and cross bridging occurs.
2 As the head attaches, it bends, pulling the actin filament toward the center of the sarcomere. At this point, adenosine triphosphate(ATP) binds to the head, and returns it to its original position. The actin filament has now been slid slightly towards the center of the sarcomere.
3 The head is now ready for another "step" and it binds to the next site on the filament. Keep in mind there are many, many heads, and some are always in contact with the actin filament. If this were not the case, the filament would simply slide back to its original position.
Now picture all these heads, attaching, bending, releasing, grabbing again, attachin, etc. This is a muscle contraction. Usually, one "pull" generates a shortening of about 1% of the muscles length. Some muscles can perform 30-35% shortening, so many of these cycles are repeated.
side notes:
1 Since dying cells cannot exclude calcium ions, they promote the cross bridging of dead muscle tissue. These contractions are more commonly known as rigor mortis.
2 When ATP is relatively depleted, the heads cannot detach and move on. The muscle is in a continual state of stationary contraction. Writer's cramp is an example of this.
3 There are three types of contractions:
a)isotonic (regular contraction, the vertical lift in a bench press)
b)isometric (contraction, no movement. Push on a wall, your muscle contracts, but does not move)
c)eccentric (contraction with reverse movement. When you bring the bar back down on a bicep curl, you are not pulling it with your triceps, you are contracting your biceps in a way that you slowly let it down. A true eccentric workout is one in which you cannot physically lift the weight. Someone else helps you lift it, you let it fall as slowly as possible.

All this brings us to why eccentric contractions cause more soreness. You are correct in stating that muscles only contract one direction. The heads cannot contract , release, and move backwards. When you do an eccentric motion, the heads are attaching and trying to ratcht to the next site. However, the muscle is lengthening. You are actually tearing the heads away from the binding sites. This causes the extra soreness associated with doing an eccentric workout.
We are taught to use simple explanations so that we can pass them on to people we are doing rehab or workout programs for. Everyone knows how sore you get after the first few times you work out, and there can be several reasons for the soreness. If your job is to make sure this person continues to follow their program, you have to explain the reasons in everyday language.
Thus, the "hook, pull, and ratchet" analogy. I'll try to recall more of the chemical reaction, it involves positive and negative ions, and the signal from the neural net that says "contract"
And yes, it is possible to get sore walking down a hill, as well as up. But who wants to climb a hill and wait two days, see how sore you are, recover, and walk down, and see how sore you are, and compare. If you are out of shape, you're probably going to get sore.

forgot this as well--
Your krebs cycle comment is on the right track, it is the cycle which provides the energy for the above movement. The krebs cycle produces ATP, which is necessary for the above to happen. It is actually the first step in all of this.

I stand by my original explanation. I've attached an abstract from medline that says
(a) Lactic acid is a factor contributing to muscle soreness, and (b)DOMS is biased toward eccentric muscle actions. Sorry it took me so long to respond, especially since I started the thread, but I had some quals. occupying my time.


1.
Miles, MP; Clarkson, PM. Exercise-induced muscle pain, soreness, and cramps.
Journal of Sports Medicine and Physical Fitness, 1994 Sep, 34(3):203-16. (UI: 95131528)
Language: English; Pub type: JOURNAL ARTICLE; REVIEW; REVIEW, TUTORIAL


Abstract: The three types of pain related to exercise are 1) pain experienced during or immediately following exercise, 2) delayed onset muscle soreness,
and 3) pain induced by muscle cramps. Each is characterized by a different time course and different etiology. Pain perceived during exercise is considered to
result from a combination of factors including acids, ions, proteins, and hormones. Although it is commonly believed that lactic acid is responsible for this
pain, evidence suggests that it is not the only factor. However, no single factor has ever been identified. Delayed onset muscle soreness develops 24-48
hours after strenuous exercise biased toward eccentric (muscle lengthening) muscle actions or strenuous endurance events like a marathon. Soreness is
accompanied by a prolonged strength loss, a reduced range of motion, and elevated levels of creatine kinase in the blood. These are taken as indirect
indicators of muscle damage, and biopsy analysis has documented damage to the contractile elements. The exact cause of the soreness response is not
known but thought to involve an inflammatory reaction to the damage. Muscle cramps are sudden, intense, electrically active contractions elicited by motor
neuron hyperexcitability. Although it is commonly assumed that cramps during exercise are the result of fluid electrolyte imbalance induced by sweating, two
studies have not supported this. Moreover, participants in occupations that require chronic use of a muscle but do not elicit profuse sweating, such as
musicians, often experience cramps. Fluid electrolyte imbalance may cause cramps if there is profuse prolonged sweating such as that found in working in a
hot environment. Thus, despite the common occurrence of pain associated with exercise, the exact cause of these pains remains a mystery.

I totally agree with you; the pursuit of a cure for DOMS is of great concern in my profession-to be. You can either decide to go easy when you first work out, and gradually build your intensity, or just blow it all out at once and be sore for a few days. After taking a break from working out, I usually will work out twice at low weight, medium rep, then start working out hard. If I still get DOMS, I just so low weight/high reps for a few days til it's gone. Potassium and drinking water seem to help some people offset the effects.

Not for nothing, kids,but I drink Diet Tonic Water. The Quinine therein not only keeps me from getting wicked leg cramps, but keeps down the Malaria.

More biking, less worrying !!

Typer

I dunno how the science/medicine works, but it definitely takes me more energy to go up than go down. FWIW, though, you are more likely to hurt yourself going down.

Ok, Rok - that explanation makes sense. What threw me was the mechanical analogy for chemical process. The "tearing" you cite is chemical, not mechanical. (I still don't know how this equates to "tissue damage").

I'll stand by every single statement in my original post with the exception of the first sentence.

Sorry, folks, but all this scientific info is quite unnecessary. I know from daily personal experience (not to mention common sense) that it takes more energy to go up stairs than down. Jeeeeeezzzz....gimme a break!

I think the original question should have been: Does walking downstairs result in more soreness than walking upstairs. It obvioulsy does not take more energy. I can answer the following question: will a workout consisting of nothing but eccentric contractions result in more soreness that a concentric workout. Assuming equal levels of intensity, yes.

Geez, you guys obviously aren't physicists. And for that matter you weren't paying much attention in high school. Not counting any special forces from the human body (like one muscle having more friction than another) it takes exactly the same amount of energy to go upstairs as to go down.

When you push a ball down the stairs the energy goes into motion and the ball smashes into something. People (well at least me) don't randomly collide with walls after going down the stairs. You start going down the stairs at a nice pace and the length of the staircase doesn't affect the speed you leave it at. Therefore you have absorbed the energy (mgh whether going up or down).

In a ball all the potential energy goes into speed, and lacking any survival instinct, it doesn't absorb it.

I think that is the most ridiculous application of physics I have ever seen. How does the ball go upstairs??? If your application is correct, then slowing a 100 pound weight as it falls takes as much energy as raising it. Does anyone believe this? I think you are saying if it takes X amt. of energy to go from pt.A to pt.B, then it takes the same amount to go from B to A. Which is fine if you don't account for gravity. When you climb stairs, you are doing concentric muscle contractions of (mainly) the gastocnemius muscle. When you descend, you are doing eccentric contractions of the gastrocnemius muscle. Concentric contractions use more energy than eccentric contractions to control the same amount of weight. However, due to their nature, eccentric contractions cause more soreness. For this reason, you lift higher weights doing an eccentric workout, and will be sorer, but you can do more reps, and actually need to, to use the same amount of energy . (an eccentric workout would be one in which if you were doing bench press, someone else lifts the weight up, and then you slowly lower it back down.)

I think that is the most ridiculous aplication of physics I have ever seen. If your application is correct, then slowing a 100 pound weight as it falls takes as much energy as raising it. Does anyone believe this?

*********************

Boy one would have the knowledge of science had advanced since the middle ages.
First of all I specifically said that I wasn't including any special forces from the human body. So we're assuming that the human body is frictionless here. Besides the original question was what takes more energy not which makes you more sore.

As for your question: Obviously it does! If it didn't where would all the energy go? You raise a brick 1 meter and then lower it back down and it releases less energy, so where does the energy go? By your logic the universe would be doomed to a quick dissappearance from all this "leaking" energy.

Look, simple physics. Potential energy is mgh. You raise a 1 kg mass 1 meter and you use 9.81 joules. You lower same mass 1 meter and you get back 9.81 joules. What's the controversy? Are you going to tell me that there are different laws for going up and down?

Konrad: <<Are you going to tell me that there are different laws for going up and down? >>

Different laws? No. Different effects of gravity? Yes.

I have a ball at rest on a stair in the middle of a stairway. I give it a horizontal push of two inches towards the edge of the stair. The ball bounces down the stairs, pulled by gravity.

Are you telling me that it can fall up?

Or that that same amount of force (the horizontal push) could propel the ball to the top of the stairs?

If you're being serious, Konrad, then you're talking about the total energy of the whole system (or in a gravity-free vaccuum). The rest of us are talking about the additional force needed needed to propel up vs down.

You're not talking about the right energy here. The energy you put into a ball to get it to go down the stairs doesn't even come into consideration because it can be infinately small as long as the ball is right on the edge. The energy that we're talking about is the energy the ball gains as it falls down the stairs. The ball speeds up as it falls down, right? And the longer the flight of stairs the faster the ball is going at the end. But humans are not like a ball, they do not speed up as they go down stairs because they slow themselves down by absorbing the energy of each step down.

Now the proof that the energy is the same:

You should know that if a ball that fell down the stairs then (neglecting friction) went on a ramp that launched it straight up it would reach the same height that is was released at. Therefore the kinetic (speed) energy that the ball gained from going down the stairs is exactly equal to the potential energy lost.

A person will absorb the speed they gain after going down each step so that they don't speed up after each step and break their necks. The energy they must absorbed is equal to the energy it takes to slow them down after each step. This is equal to the potential energy they lost at each step. And the potential energy is *by defintion* the energy it takes to go up the steps.

I realize this is not a very clear explanation but the main point is that (if you want to use the ball analogy) it takes more energy for a ball to go down the stairs then just the initial push. You have to slow it down at the end of those steps so that it is going as fast as it was when it started falling. That way it simulates the way a human goes down.

[[ball. . . the initial push. . . it is going as fast. . . the way a human goes down.]]

I'm sorry, what was the topic again?

Rich

I think the original post related to the amount of energy your body uses to traverse a flight of steps on this planet. When we need to walk around in a vacuum tube, we'll let you know.

I see the confusion here, I think, Konrad. The correct answer is: (c) Boston, MA, in the year 1792.

Here's the link to the original question and answer: http://www.straightdope.com/mailbag/mdown.html ... you might try to read it first?

The question is not the energy amount of the total system, the question is how much energy the human being needs to exert to traverse stairs.

Well, how about that. I just actually read the column in question. Cecil is right, of course, the body will burn more energy going upstairs. However, you can become sorer from walking downstairs. The extra soreness derived from doing the negative or eccentric phase of any motion would make it seem like you had expended more energy, but it isn't so.

Just to clarify, though, rok -- that Cecil is always right is axiomatic. (The word "always" in this context is defined as an item of faith, and ignores the situation of later evidence not known at the time of Cecil's initial statement...)

The Mailbag items, however, are not written by Cecil, but by his loyal staff, the Straight Dope Science Advisory Board, who are a bright and energetic lot, but not infallible. Just wanted to clarify.

Ok, I think this question is really simple. I don't see why you're talking about the "energy of the entire system". My answer is that it takes a human just as much energy to go down as up stairs. That was the question and that is my answer, I don't really see much room for confusion.

Now I'm a first year physics student, and this question seems completely, beyond obvious to me. Now, you haven't actually said what's wrong with my explanation so I can't really rebutt your points. I don't see what air has to do with it anyway, neglecting friction (as I specified) air pressure would not change anything.

Try posting this question on sci.physics if you don't want to take my word for it.

A) That answer is wildly, ludicrously wrong in physics. I suggest you try another major.

B) The answer is also wildly wrong in biology. A human body is not a friction-free 100%-efficient machine. (Or have you never noticed that you can get tired just standing still?)

------------------
John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams

Well, I am a fourth year fitness therapy/kinesiology student, and I can assure this IS a simple question. Read all my responses. If you live in a frictionless gravity free environment, then yes, it would take the same amount of energy. But till then, trust me. You should find the kinesiology class there and take it. It about applying physics to the human body and its motion.

John:

First of all I specifically said I was not counting any biological factors so either you haven't read my post or you're merely a cretin.

Secondly, it is not sufficient to say "Your answer is ludicrous" to prove a point. But I guess if you can't actually find anything wrong with my explanation you have to try other ways...

RokSez: Yes, but as I said I wasn't counting any friction. And like I said in my last post, I don't see why you are saying my answer only applies when there is no gravity. You haven't actually said what is wrong with my explanation apart from stating that it is wrong.

Your major might be fine if we were arguing what makes you more sore but the question is pretty simple: What takes more energy? So it is strictly a physics question.

Again I invite you to post the question to sci.physics. And remember the question is not whether it takes more energy to walk up stairs than to throw yourself down the stairs which is obviously what you and Ckdexthavn are talking about. It is about walking up/down.

I still don't understand your point, Konrad, so I'm not sure what I'm supposed to "disprove." The question is worded, does it take more energy to walk upstairs or downstairs. We are saying that gravity exerts a force to assist you in going downstairs, whether you are walking or sliding; and that gravitational force opposes you in going upstairs, whether you are walking or sliding.

You seem to be saying that the answer is different for walking than for sliding? That you concede it takes more energy to slide upstairs than to slide downstairs, but you think it is somehow different from walking?

I have asked our unofficial physicist and penguinist to comment on this thread, I'm hoping she will do so soon. I don't visit other sites, my time is way too limited to playing online.

The original post is being read too literally if you take it to mean how much actual energy is being used as it relates to the universe. The poster is asking if your body uses more energy (read-works harder) to go upstairs or downstairs. It has nothing to do with potential or kinetic energy, but how much work your muscles do to go upstairs or downstairs. If someone just ran a marathon, and came up to you and said "gosh, I'm all out of energy." they arent saying they have no more potential for motion. They are saying they are fatigued. Like I said, this has nothing to do with physics, it is ridiculous to apply it here.

roksez: What you have just said about my reasoning is exactly what I'm trying to say about yours. It takes as much energy for your muscles to go up or down the stairs. Not the universe or any of that crap but simple muscle power. What you are talking about is the energy of the entire system.

ck: Exactly, sliding is different from walking. When you slide your clothing absorbs the energy that your muscles would normally take up and that's why it heats up.

Here's an example: You jump out a window. It doesn't take any work at all for your muscles. That's cause at the end of the jump you are moving very quickly and the energy is absorbed by your bones breaking etc etc...

When you walk down the stairs, even if you started at the same heigh as the window, you are not going very fast at the bottom. Why? Because your muscles had to work to slow you down.

So in the case of the jump you did do work but not with your muscles and it was all at the end in the form of friction and breaking. In the case of the slide that same work was absorbed gradually by friction between you and the slide.


Remember, this is like one of those 12 step programs. To see the truth you must first accept you are wrong. You must want to change. In moments of doubt, say to yourself "I think I am right, while Konrad knows he is right." There is still hope for you!

The fact that I abandon discussion of a topic does not mean that I concede, but only that I am tired of banging my head against a wall.

Hey, did you know that banging your head against the wall uses the same amount of energy as.... oh hell, I'm sick of it too. But a great new invention awaits develpment: are you tired of walking upstairs on a stairmaster?? Now you can go downstairs. It's just as good a workout.
Seriously-I will give you that the total energy expended is the same, but your muscles do MORE work to go upstairs than down. This means they expend more energy. On the way down, you have bones, tendons, etc. also absorbing energy, so your muscles don't do as much work.

Roksez: So you're basically agreeing with me? I specifically said not counting any special forces from the human body, ideal human, no friction etc... Yes compression of bones and tendons does absorb some energy which makes it easier to go down. If you want to test just how little energy is absorbed this way try jumping even one inch off the ground and absorbing the impact on your heels with your knees locked... it hurts. And it doesn't hurt that much to walk normally so normal walking absorbs even less than that.

BTW the reason they don't have reverse stair masters is that it would give you almost the same workout but with more likelyhood of knee or ankle injuries.

I'm not agreeing or disagreeing with your argument about total energy consumption(as far as energy in E=MCsquared goes). That argument isn't my bag, baby :) The problem I have is your literal interpretation of the word energy in the original question. This is not a question having anything to do with physics. If the original post wasnt clear to you, well, sorry, but everyone else understood it. The post should have read,
"Does walking downstairs result in a greater oxygen deficit than walking upstairs?" The answer is NO. However, walking downstairs (the eccentric phase of the exercise) CAN produce more soreness than the concentric phase. This is where the original question comes from. If walking upstairs causes a greater O2 depletion, then why doesnt it necessarily cause a greater soreness. I also addressed this earlier. Like I said, don't take every use of the word energy so literally. If you see an ad for a Powerbar, and it says "get a BOOST of ENERGY", do you get mad because you think they are advertising a bar that increases the total amount of energy in the universe? God I hope not. I know you are eager to spread the knowledge you gained in the past year, but use it in appropriate forums.

It take s more energy to walk upstairs than down stairs. after all, you can slide down the bannister, and the only energy you would use(or lose) would be Heat caused by friction.............anyway.. you cant slide back upstairs........ never mind....

roksez: I understood the question perfectly. I am talking about the same energy you are, why can't you accept this? Oxygen depletion is proportional to energy used since that's where you get your energy from. I keep repeating this but you don't seem to get it: I'm not talking about total energy in the universe, just the energy your muslces use.

I don't know what else to say. I just keep repeating that statement and it's like you're ignoring me and just saying the same thing over and over. Have you actually reread your own posts? It's like you suffer a lapse of memory each time I say I'm talking about the same energy you are.

John: Exactly. But when you slide down a bannister you aren't walking. That's why you don't get tired from sliding down a bannister (except from holding yourself up).

To be simplistic:

When I hike to the top of Camelback Mountain, I'm winded, tired, and need a few minutes of rest. After resting, I hike back to the bottom. I'm not nearly as winded or fatigued when I get there.

when moving upstairs, you have to use enough force to carry your mass in 2 directions, forward, which would be the same as walking normally, and upward, against gravity.
as muscles work in pairs, walking upstairs and downstairs use the same muscle groups,
but because your moving against gravity, walking upstairs uses more energy.

a quick annalogy,

you dont have an excercise machine called a stair-decender. they only go up.

The question it self is bad cause most people (as yourself's) don't understand energy very well!
If your talking about Human energy (calories and that stuff) then even a child knows it takes more enery to go against gravity than with it!!!!
If your talking about real enery then you must realize IT IS EXACLY THE SAME! All you do is change potential to Kenetic (neglecting friction due to the small speeds).
Look up conservative systems in a scientific Encylopedia and you'll get some idea about what is Energy.
As for who ever wrote the question: maybe you should think about the answer first and ask more intellegent questions!

Ok, I hate typing long responses, but I am tired of this topic. So here goes.
Muscle contractions are not all or nothing responses. You only contract as many sarcomeres as you need. This is why you do not slam a can of coke into your face when you lift it. This is also why you cannot hold a weight suspended forever. As your muscles fatigue, more and more sarcomeres are recruited, until there are none available and failure results. Assuming equal weights(your body, in this case) any concentric contraction requires more sarcomeres to be involved than the corresponding eccentric contraction.
Ok point 2-
Energy derived from the food(sugars and starches) that we eat is stored as energy in the form of adenosine triphosphate (aka ATP). As you will remember from my earlier lecture, ATP is the chemical which binds to each myosin head as it release from its binding site during a contraction. Now if we just put 2 and 2 together, we understand that-
any concentric muscle contraction requires more sarcomeres working than any eccentric contraction(assuming equal weight). The more sarcomers you have contracting, the more ATP is needed to bind with the myosin heads as they release. ATP is the chemical in which the body stores its energy. It is the chemical which allows the myosin heads to "reload" and contract again. Since you need more ATP to produce a concentric contraction(assuming equal weight), your body is burning more "energy".

Eddie just summed up everything I have said. And you don't have stairmasters going downhill because there is a negligible aerobic benefit.(Your muscles do less work)

[John W. Kennedy]

Eddie -- roksez -- your "explanation" has the slight practical disadvantage that it gives the same answer for all experiments, practical or gedanken, that do not involve divine intervention or the use of magic. Of course energy is conserved! But when potential energy is entered into the equation, you can say equally well that an ant sneezing uses the same energy as a supernova.

You're arguing like a doctor who answers the question: "Will my wife live or die?" with "Yes." Technically true, but useless and rude.

------------------
John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams

[Konrad]

Strainger: Hiking is not the same thing as stairs, there's a lot of friction when you walk down an incline but not much when go down stairs. Also read there is the other thing which John Larrigan said:

JohnLarrigan: Actually, that's a good point. I didn't want to bring it in before because it would confuse things but since you brought it up... It does take more energy cause you have to make yourself move forward when you go up but once you make that first initial push forward at the bottom of the stairs you pretty much keep the momentum. When you walk up the stairs you sort of bend forward and push almost straight down. I'm sure you lose some of the forward momentum from friction and stuff but I don't think it's a major effect. (If you have gain .5m/sec horizontal speed each step it takes .125 joules/kilo of body mass whereas going up one step takes 2 joules/kilo.)

roksez: Out of your 2 points how do you get that it takes more energy for concentric than eccentric? I'm not saying it's not true but you just made a statement, not an argument. You have no proof for that. Either way as I said before we're not counting any friction so that point is irrelevant.

What is also irrelevant is the fact that your body uses ATP for energy. I took bio, I know what ATP is. What are you trying to do? Impress me by pointing out an obvious and COMPLTELY irrelevant fact? It wouldn't bloody well matter if your body used goat sperm for energy, it would use just as much goat sperm going up as down if it weren't for friction.

John Kennedy: I think what Eddie is trying to say is that because energy is conserved then all the extra energy you used going up must come back out as friction when you go back down. The whole point is when you go downstairs you spend a whole lot of energy as friction dragging your hands on the rails and so on and that takes the load off your muscles.

[mr john]

A prime exmple of why the original poster needs to post a link. Cecil said every bit of this with a lot less and simpler words.None of that extensor vs. contractor,chemical processes etc has any thing to do with it. In physics you allways assume a perfect enviroment,africtionless,gravityless,vaccuum, then start adding conditions. Sliding down a bannister causes friction which results in heat which is energy.Same amount of energy as heat as it took to climb? Probably in that perfect place with friction and gravity added. A downstairsmaster? What a concept,I'll be in the basement developing that,if Igot the energy to go downthere.(My brother's down there now anyway cussin at the government or something). Any way can I ask you physiology people the question this way? "Do I use different muscles to go upstairs or down? If so, is one set more efficient than the other? If not,are they more efficient one way or the other? In other words, do less efficient muscles take more "energy" to operate? Does my body have to "work' harder? Note the quotes physics people. It takes just as much energy to conteract gravity when raising something as it does to resist it when lowering it at the same speed. Get a rope, pulley,scale, and weight and check it out.Now if i tie the rope off with weight suspeded no energy is being created or used, it is all stored(kinetic) energy. But if I hold the rope in my hand,then for sure my body is expending energy.Ty this stand at the top of the stairs like this and LOOKOUT! OOF BLUHHH WHAP CURSE OOOF YOU OOF NEWTON! OUCH ARGHH KIN AHHHH ETIC OOF POW> BANG

[mr john]

That enough spaces Dex?

------------------
Signitorily yours, Mr John
" Pardon me while I have a strange interlude."-Marx

[Nickrz]

Wow, this whole thing turned into an argument with a moron? Dangit, I miss all the good stuff.

[Konrad]

Do a search on deja news for "Konrad stairs" under sci.physics. Most people agreed with me.

Also the 2 physics Ph.D.'s I asked said I was right, and I think they're a lot more likely to be right than some moderator on a message board.

[C K Dexter Haven]

OK, once more from the top.

IF the question had been whether it takes more energy to lift an object in the air or to lower it gently the same distance, then the argument from physics says that it takes the same amount of energy.

Please note: if the object was not being lowered gently, but was being lowerd most of the way and then dropped.... then it would take less energy (exerted by the person) to lower/drop the object than to lift it.

IF the question was about whether it takes more energy (exerted by the human) to push an object (like a ball) to roll down the stairs, vs throwing it up the stairs, I think we agree that it takes less energy to let the ball roll down the stairs.

Neither of those were the question.

The question was about a human walking down and up stairs. The energy involved in walking is different from the energy involved in lifting an inert body.

I have used the rolling ball as the example, but I probably should have used a person "jumping." If I stand on the top stair and take a little jump, I go down one stair. This takes less energy (I contend) than if I tried to jump (or walk) UP one stair.

The physical process of walking down stairs involves a little "lifting" and a little "jumping" -- letting gravity set your foot down. To that extent, gravity is helping you go down, but does not help you go up.

Does that resolve the seemingly irresolvable differences?

On a further note, Konrad, you can take the gratuitous insults to the BBQ Pit. This is not a question that is resolved by majority vote, not even if two Ph.D.'s vote with you. The author of the Mailbag item has a Ph.D., and he sought (and got) agreement with a physics Ph.D. prior to posting the article. So we're even. I don't think that your attempt at one-upmanship is productive.

I have edited the first posting on this topic to include a link to the Mailbag item.

This reminds of the old claim that pops up now and then: "Mathematically, it is impossible for a bumblebee to fly."
Save your breath and no, I ain't interested in your cipherin'. Fact is, I seen the sumbitches fly. 'Nuff sed.

[DSYoungEsq]

Hmmmmmmm pretty bad when even the moderators can't approach an issue with rational discussion.

If the bunch of you would stop talking apples and oranges, you might reach an agreement.

First of all, the question originally posed was: "I have a dispute with my
significant other. She claims that going *down* stairs takes more energy
than going up stairs. At first glance, anyone can see that this is
clearly wrong ... or is it? She says that when you go down stairs, you
have to absorb the energy from gravity pulling you down, and that takes
energy on your behalf. I give her the argument that I get much more tired
going up 50 flights of stairs than down!"

To answer the question: Does it take more energy to climb or descend a flight of stairs? one needs to define the terms of the question.

Konrad is defining the term 'energy' using its meaning in Physics. As was cogently noted in Resnick and Halliday ("Physics, Part I" Robert Resnick and David Halliday 3d ed. 1977) at pg 119, "A person holding a heavy weight at rest in the air may say that he is doing hard work - and he may work hard in the physiological sense - but from the point of view of physics we say that he is not doing any work. ... In many scientific fields words are borrowed from our everyday language and are used to name a very specific concept." If one says 'energy' and means 'vigorous exertion of power' (see Mirriam-Webster), one can't argue this issue with someone who means 'the capacity for doing work.'

Having said that, let us look at a force diagram (in our mind, since I can't draw one here). First, let us simplify the diagram to eliminate the horizontal component, since the horizontal component of travelling up and down stairs is the same each way (same distance, same mass, same work). (By the way, this is why talking about friction makes no sense in this question... it affects horizontal motion only) Now, we have to agree HOW to draw the diagram. To do that, we have to agree upon the parameters. Konrad is assuming that the mass in question (the person) starts at zero velocity and ENDS at zero velocity, in the vertical direction. The equivalent would be a ball, dropped from a hight onto a spring that slows the ball to 0 velocity vertically. The force diagram is simple. There is downward force (gravity) accelerating the mass in a negative y direction. There is an upwards force (the spring), accelerating the mass in a positive y direction. Going up the stairs, the same things are true. Gravity pulls down, but the spring pushes up. The 'energy' involved is the same, because the same mass, distance and net acceleration are involved. (If you don't accept this, I suggest you review the basic occilating spring problem). Both Konrad, AND the spouse in the original question, assume that the positive y force is provided by the human.

The Anti-Konrad forces are making different assumptions, or defining 'energy' differently. They correctly note that to go up the stairs, the body must do work, that is, exert force to propel the body upward, but that the body need do nothing to propel it downward, the force of gravity accomplishing that task. Since the body isn't moving in a positive y direction when descending, then it is expending less 'energy' (meaning something closer to 'vigorous exertion of power'). The definition answers the question.

However, I must point out that the original question SHOULD be answered in terms of physics, since the spouse was making a physics argument. Under that circumstance, Konrad is quite right in his assertions, despite the rather ad hominem responses to the contrary.

As for the answer from SDSTAFF Dex, no offense, but the Staff should really try to answer a question with some actual thought, rather than making an offhand response based on potentially incorrect assumptions. The answer TOTALLY ignores the force needed to accelerate the object positively after gravity has accelerated it negatively, and that is NOT the same as the force needed to just hold us upright.

Sheesh, some of the answers we get....

[DSYoungEsq]

Allow me to briefly dispose of the 'how your muscles feel' responses to this question. Crawl on the ground 100 yards pulling yourself with your arms, then walk the same distance. What makes you more tired? Which used more energy? (Answer, crawling, and neither).

Sometimes, the issue isn't how you feel, but what you used...

[C K Dexter Haven]

I see in rereading some of the past posts that we can probably make an additional Mailbag item out of some of the different interpretations (which, admittedly, did not occur to the author of the original column at the time.)

[DSYoungEsq]

If I stand on the top stair and take a little jump, I go down one stair. This takes less energy (I contend) than if I tried to jump (or walk) UP one stair.

Absolutely correct, if all you want to do is consider the effort needed to start down the stair. Gravity will force you down the stair without any effort on your part (the effort to move horizontally being the same regardless of vertical direction involved).

HOWEVER, we are not just starting down the stairs, we are stopping when we get there. We can't consider only the effort needed to accelerate vertically down, we have to consider the effort to DECcelerate vertically down (that is, accelerate vertically up). THAT effort, absent some springiness to the floor, is also provided by our body. Specifically, your foot, ankle, leg, knee, hip, back, etc. combine to slow you down, so that you don't continue on through the floor. If you don't manage to do it in a co-ordinated fashion, you end up like I have on more than on occaision, sprawled on the floor having absorbed the energy of the collision in a VERY inelastic fashion.

Throwing the ball up would take more energy than letting it fall. But the correct question is, how much energy would it take to catch it? Sending a rocket up would take a lot of energy, but the same energy is needed to brake a falling rocket so that it doesn't crash.

If you don't believe the energy involved in going down the stairs, try falling onto the floor from one story high. Trust me, your body will feel the energy!

But do we think of that as 'effort'? Likely not... again, a question of definitions.

[C K Dexter Haven]

Well, if it comes to that, consider the motion of walking up a stair. You raise your foot HIGHER than the level of the stair, and then lower your foot onto the stair. (Similarly, in walking down stairs, you first lift your foot a slight height in order to move it off the step.) So the effect of "stopping" gravity from pulling you down is the same, whether going up or down.

In any case, we now have some different takes on this that were not considered in the original Mailbag post --
* biology (the muscles and bone used in going up vs going down)
* pure physics (motion of an inert body) and the technical definition of "energy"
* further insights into the definition of "energy" in the common sense of effort expended

Anyone wanna tackle number of calories used, or is that the same as (3)?

[DSYoungEsq]

Well, if it comes to that, consider the motion of walking up a stair. You raise your foot HIGHER than the level of the stair, and then lower your foot onto the stair. (Similarly, in walking down stairs, you first lift your foot a slight height in order to move it off the step.) So the effect of "stopping" gravity from pulling you down is the same, whether going up or down.

Oh, please. Now we reach the absurd. The issue would be the same if you stepped higher then let a foot down, or if you were precise in your mechanics.

The original question from the couple couldn't be answered is my point. The wife, like Konrad, was talking physical energy. The husband, like Dex and many others, was talking effort, a subjective physiological feeling. The energy expended to stop the step down is not felt the same as the energy expended to lift the body up. The couple, as are the teeming millions, were talking two different things, which the original answer posted should have noted.

As for calories, again it depends on what you mean. Do you mean total calories expended by the human, or calories of energy involved in the physical process of raising a mass up the stairs or stopping it at the bottom of the stairs?

Example: run 100 yards, then walk 100 yards. The energy in moving the mass is the same, if there is constant velocity involved. BUT, the body expends more calories to run, because the machine involved is less efficient at higher speeds. The analogy would be the same for a car, which will get different gas milage depending on speed. So the calories expended climbing versus descending may change depending on which the body is better at doing.

Anyone want to run some trial climbs and measure? <eg>

[C K Dexter Haven]

I mean calories expended by the human... that's the only topic under consideration.

Restating the question: the escalator going down is broken, but the escalator going up works. Does it take more energy to go down or up? Sorry, but I believe the plain reading of the question (like the original question in this thread) has to do with what causes the human being to expend more effort, to burn more calories, to use up their energy (note: energy in this sense has nothing to do with physics because I'm claiming it to be USED UP.)

The other interpretations are interesting, no question, but tangential.

[Konrad]

I'd just like to point out that I specifically stated my interpretation of the question when I posted. I said no friction, no special forces from the human body. So if the disagreement comes from a matter of definition then it's a problem of people not reading my original post. Like I consider moving your foot up above the stair and then putting it down a "special force from the human body".

And yes friction does make a difference in the y component. If you drag your hand on the handrail as you go down you are using friction to diffuse the energy of going down. That's one of the reasons you don't get as tired going down. So the problem is not that I'm using a different definition of energy. If we take out friction both defintion must be the same.

CKDext: It's you who's been rude and patronizing all the while so don't get huffy because I went and got the opinions of some experts in the field.

[AuraSeer]

Okay folks, think of it this way.

I'm standing at the top of a short staircase. Instead of walking down the stairs, I step sideways off the staircase and fall straight to the ground. Before landing, I lock my knees, so that I hit the ground with a loud bang and maybe a slight bounce. (We'll assume that I don't hurt myself doing this.)

How much energy have I expended in vertical motion? Zero! I was accelerated in the negative direction by gravity, then accelerated in the positive direction by the normal force exerted on me by the floor. On impact, my kinetic energy was converted to sound and heat, and possibly some damage to the floorboards.

Now I teleport back to the top of the steps. This time instead of stepping off and falling the whole way down, I step off each stair, and fall to the next one in line. I still lock my knees before impact. For each step there is a bang! as I am accelerated to a stop.

Once again, I have expended zero energy in vertical motion. I provide horizontal motion; gravity makes me move down; the normal force makes me stop.

Teleport back to the top again. This time I walk down the stairs normally. I exert some energy to slow myself down as I descend, and some amount of energy is still "bled off" into sound and heat.

The amount of energy I expend in vertical motion while walking downstairs is equal to my potential energy at the top of the steps, minus that absorbed by frictional effects here.

Now I turn around and walk up the steps. Each time my foot hits a stair, some small amount of energy is lost to sound and heat.

The total energy I expend in vertical motion while walking upstairs is potential energy plus the energy I must expend to overcome friction. (The potential energy is obviously the same number as in the above situation, since my location is the same.)

Let's see those numbers again:
Energy to walk down = Potential - Friction
Energy to walk up = Potential + Friction

If you are ignoring friction, as Konrad did, then the required energy in the two cases is identical.

However, this question was asked about the Real World (tm). In the Real World, friction always exists, and is always positive. Therefore, in the Real World, it will always take more energy to walk upstairs than to walk downstairs.


Sorry for the long post, but I hope it's now clear what everyone was arguing about.

------------------
Of course I don't fit in; I'm part of a better puzzle.

[AuraSeer]

On a completely different note, Konrad, your approach to this problem reminds me of a story I heard a long time ago. (This'll be another long post, but hey, I feel like it.)

It seems that there was a rich man who liked to bet on horse races. He loved the excitement of winning, but absolutely hated to lose. So he decided to invest some money and learn how to win more often. He sought the foremost experts in statistics, biology, and physics, and offered a $10,000,000 prize to the one who could offer him a foolproof system for choosing which horse to bet on.

Lots were drawn to determine the order in which the experts could make their attempts. Each was to be given one year to work on the problem.

The statistician came first. After a year of intense study and work, he came back to the rich man and said, "Sir, I have gathered and analyzed data on all the winning horses since records have been kept. I used the world's fastest computers, and the most efficient algorithms. I found no consistent pattern which could predict the winner; I'm sorry, but there is no foolproof system." The rich man thanked him and sent him on his way.

The biologist was next. After a year of intense study and work, he came back to the rich man and said, "Sir, I have measured and examined over three thousand racehorses. I checked their muscle structure, lung capacity, blood chemistry, bone density, and many other factors. But when I compared the winning horses to the losers, there was no factor that could tell them apart for certain. I'm sorry, but there is no foolproof system." The rich man thanked him and sent him on his way.

The physicist's turn was next. Just one day after he was given the task, he returned to the rich man's house with an envelope in his hand and a huge grin on his face. "Sir, this was hardly a challenge," he said. "I have your foolproof system."

The rich man, astonished, paid the physicist his ten million dollars, and thanked him profusely. He tore open the envelope, took out the sheet of paper within, and began reading: "Assume a spherical horse travelling in vacuum..."


(Yes, there is a point to this story. Ideal conditions are fine for use in the classroom, but if you try to solve a Real World problem with them, your solutions will make no sense.)

[Konrad]

Auraseer: Yes, I understand your point. In fact that's a joke I often tell.(Except about mathematicians) But I clearly said I wasn't talking about the real world. My point was to say that the question was answered wrong. It was to say that it was right for the wrong reasons.

What got me to post was that the person who answered the question (like others on this board) shrugged off the idea that you use energy to go downstairs like it was some crazy lunatic theory. Obviously they had no idea what they were talking about.

The whole argument here was not that I disagreed with them on the answer to the real world application, but that they were acting as if they knew what they were talking about, which they obviously did not.

I specifically laid out the terms, they called me crazy, I proved them wrong under the terms I laid out.

[AuraSeer]

Konrad, I've gone back and re-read the Mailbag column, and I agree with you that it wasn't answered well. The SDSTAFF writer did over-simplify it.

(Hey, can it be true? Is the arguing over?)

Is anyone still here? This thread has been inactive for a while now, apparently because everyone's head is about to explode. But I just got here, so I hope it isn't too late to try to she some light on the subject.

First of all, as many of you have perceived, there are two issues bound up in the question of the energy required to climb stairs versus the energy required to descend: a basic physics issue (of particular interest to Konrad), and a physiological issue that ultimately resolves the question. From a pure physical point of view, if I could design the human body any way I might wish, descending could cost more energy, less energy, or the same amount of energy as climbing. I could even get some back! It is the physiological mechanics of muscular contraction that ultimately decide the issue, not considerations of basic physics.

Okay, the physics first. "Work" is defined (leaving out calculus) as the product of force times the displacement produced by that force. When work is done, an equal amount of "energy" is transferred from one part of the system to another, often changing form as well. When you climb stairs, your muscles produce forces that act between your feet and the stair treads to raise your body. The force required is your weight (equal to mass m times gravity g); the displacement is the height h of the staircase; hence the total work, and the energy produced by your muscles is E=mgh. Yes, of course, there is also energy required for basal matabolism, static load bearing, gait irregularities, and so forth; but all these are also required to descend, so the energy required _specifically_ to climb the stairs is just E=mgh.

Where does this energy come from and where does it go? I hope we all agree that it comes from ATP metabolized in muscle, and that it goes into gravitational potential energy. I hope we can also agree that gravity is a conservative field, so gravitational energy is completely available to do work. All you have to do is come back down the stairs and that energy is available. Slide down the bannister and the work of friction converts it into heat. The frictional force of the bannister against your rear, times the length of the bannister will always turn out to be mgh. If you just jump off the landing, then the gravitational force does work accelerating you and thereby converting gravitational potential energy to kinetic energy. By the time you get to the floor, your kinetic energy will be equal to mgh. I think we're all together on this.

But suppose you _lower_ yourself down by walking. First of all, the forces involved in lowering yourself are exactly the same as those involved in raising. It does _not_ take any extra force to go up, or less force to go down (at constant speed). (This point is counterintuitive for many, but it's true. We can discuss it separately, if necessary.) The distance is the same, too. So if the muscles are exerting the same forces, and moving through the same distance, then they do the same work, right? Wrong. This suggestion is a common error (and a trap physics professors like to lay for the unwary). The forces are the same, but the _sign_ of the displacement is opposite: the direction of travel is reversed. The muscles do not _produce_ mgh of energy in going down, they _absorb_ mgh of energy in letting you down.

Where does this energy come from and where does it go? Well, it comes from the gravitational field. And it goes into the muscles. The mechanism by which the muscles absorb this energy is a physiological question, not a physics question. If we imagine a sort of ideal, frictionless human, as Konrad suggests, then the energy cannot be dissipated as heat. It must be stored somehow. Capture and storage of this energy is certainly not impractical. Electric cars do it all the time through a process called regenerative braking.

The "muscle" of an electric car is an electric motor. In climbing a hill, the motor(s) must do mgh of work converting electrical energy into gravitational potential. Coming back down, the car does work on the motors which run as _generators_ converting the gravitational energy back into electrical energy which is returned to the batteries. The motors/generators don't _do_ any work in this process; work is done _on_ them.

There's no _fundamental_ reason that muscles couldn't work the same way. In such a case, it would not only take less energy to go down stairs, you would actually get your climbing energy (or part of it) back! In physics, we call such a process "reversible."

Another possibility is that our idealized human would just use controlled friction inside the muscles to provide the lowering force. Ordinary cars do this all the time. That's how brakes work. The car burns mgh worth of gas to get up the hill, and it converts mgh worth of energy into heat in the brakes on the way down. The frictional force times the distance the brake pads move adds up to mgh by the time you reach the bottom. In this case it costs you exactly zero energy to descend. All the energy is converted to heat where it is unavailable for use by the engine. In physics we call such a process "irreversible." It costs you no gas (energy) to descend, even though the car is "lowering" itself down the hill. And you certainly don't get any gas put back in the tank as a result!

There's a third possibility. We know that muscles consume energy just bearing static loads. When a muscle is contracting isometrically just to hold you up, it is producing a force, but no displacement, so it is doing no work. But it still needs a supply of energy just to produce this force. An isometrically contracting muscle has zero efficiency. This action is analagous to holding your car on a hill by riding the clutch. The engine is doing work to produce a frictional force in the clutch to support the car on the hill, but you aren't going anywhere so mgh=0. You could use this same technique to descend a hill in a car: point downhill, put 'er in reverse, juice the accelerator and ride the clutch to _lower_ the car down the hill. (Don't try this at home, folks...) If you use slow engine speed and lots of clutch, you won't use much gas (energy); if you use fast engine speed and light clutch, you could use tons of gas--all the way up to the maximum power output of the car! Very inefficient! (If I have observed correctly, many carnival rides use clutches and engines in this way.)

So, depending on the physiology of muscles, descending a staircase could require a negative amount of energy (regeneration), it could require none at all (pure braking), or it could require any amount up to the maximum available ("clutch-riding"). But there's no pure physics argument that can decide the issue.

So the question is, what's the physiology of muscles? Well, we've already been treated to a lucid discussion of the contractile process. Fantastic as it sounds, muscle contraction really does involve a mechanical ratcheting process as myosin filaments crawl along adjacent actin filaments, thereby shortening the muscle. The mechanical bending of the myosins is powered by oxidation of ATP; that is, the energy used by the muscle is equivalent to the amount of ATP oxidized. I hope we're in agreement that what we're looking for is this energy, and not gravitational energy dissipated as heat due to irreversible processes.

Evidently, the process involved in extending a contracted muscle (that is, a muscle under load) is much like riding the clutch as you coast downhill, motor revving. There is friction as the actin filaments slide over each other and the myosin filaments between claw away trying to prevent slippage. (By the way, this process inevitably tears up myosin and actin filaments, resulting in soreness.) The only reason any more force is needed (and thus more ATP metabolized) to walk than to stand is to deal with accelerations of the limbs and body. So walking takes more energy than standing still--despite the fact that you are doing no work against gravity and a trivial amount against friction

[Konrad]

Geezer: The sign means nothing. No human gets energy by walking down stairs. You can't get simulate eating a meal by taking the elevator up a tall building and walking down. I know I said ideal human but that's ridiculous. Ideal means it feels no friction, not that it's an electric car.

[Strainger]

Mommy! Mommy! Make the bad thread stop!

[Geezer]

First, I owe everyone an apology. I'm a rookie, err... newbie.., and I made a rookie blunder in not realizing that there was a second page to this thread. Consequently I waxed a bit lengthy without having read all that came before. I sincerely apologize.

But still.... I think the essential issue for Konrad and DSYoungEsq, is a pure physics matter, not specifically related to the (rather messy) stair-climbing example. Konrad, I brought out the electric car to illustrate precisely the point you make: human muscle tissue is an irreversible machine. You _do_ get (abssorb) energy walking down stairs, but not in any useful form. It's all plain old heat. But we can't even talk about stair-climbing until we settle some basic physics. DSYoungEsq's comment that it takes energy to stop a falling ball, and your comment that "the sign means nothing" describe the essence of a very interesting pure physics question. I'm not taking sides in a debate; I'd just like to see if we can understand the physics.

First, this significance of the sign. Consider:

A cube of steel sits on a smooth, horizontal surface with a non-zero, finite coefficient of friction. An agent (your finger, for instance) applies a horizontal force F in the +x direction and moves the block through a displacement s in the +x direction. We say that the finger did work on the block. The amount of work is U=Fs. Energy from your body was transferred to the block and finally to the molecules of the block and the table as heat.

Now, Newton's third law says that if the finger exerts a force F on the block, the block exerts a reaction force F on the finger. This force acts through a displacement s. Does the block do work V=Fs on the finger? No. It doesn't have any energy available to it to do any work. The block does work V=-Fs on the finger because the reaction force is in the -x direction, that is, opposite the direction of the displacement. The sign means that the (negative) work the block does on the finger is actually the work the finger does on the block. A positive value of work means the object to which the calculations are applied is doing work; a negative value means it is having work done on it. Work is the dot product of the force _vector_ and the displacement _vector_. The sign counts. Otherwise, inert blocks of steel with no source of energy could do work on fingers.

So do you do work to catch a falling baseball? No; the baseball does work on you. Yes, your hand supplies a decelerating force; and yes, that force acts through a distance; and yes, the force times the distance is good ol' mgh. But the force your hand exerts is the reaction force to the force exerted by the baseball on your hand. The baseball's force is the one acting in the same direction as the displacement. Your hand supplies no energy in stopping the baseball; it must _absorb_ mgh to stop the ball.

If you raise a barbell of mass m through a height h, your muscles must metabolize mgh worth of energy to do the required work. To lower the barbell, the problem is not to supply _more_ energy, it is to get _rid_ of the energy the barbell already has--that is, to absorb the energy. If you raise a barbell and then set it on a dashpot so that it gets lowered just as if you lowered it by hand, would the dashpot be supplying energy?

Konrad, are you and DSYoungEsq (and others) suggesting that it is physically necessary to supply energy to a machine that decelerates a moving mass or that lowers a mass through gravity, or am I barking up the wrong tree?

[C K Dexter Haven]

I'm really tired of this one, but:

-After you have walked upstairs, do you not have more potential energy (from being higher up) than when you started?
- After you have walked downstairs, do you not have less potential energy (from being lower down) than when you started?

[Geezer]

Don't get tired Dex! There's a nifty little physics paradox here that the original respondent's spouse, and now Konrad and a few others have put their fingers on. It's been around for a while, but it's as interesting as ever. We just have to dig down to the basic question, separated from the details of the stair-climbing example and any semantic and communications issues.

[Konrad]

Geezer: As far as the block and the finger goes, A doing work on B means to me that B is absorbing energy.

Yes, it does take energy to lower something down. How? Well look at it this way. Suppose instead of doing it slowly we let it speed up. Now we have something moving with a speed relative to us. What's one way to stop it? Well we could launch another object at it of the same mass going the same speed. The two will collide and stop. (Without it doing any work on your arm. In fact your arm does work on the second object.)

So we have used energy to stop an object, and we have not gained any ATP from this. Of course all the energy goes into heat. (The amount of heat energy will be twice what you would absorb if you could somehow extract all the energy from the first object.)

If you are decreasing the speed of something relative to you, you can theoretically absorb the energy instead of using more energy to slow it down. That is what is meant by the object doing work on whatever is slowing it down. But that doesn't mean you have to absorb it, a human doesn't. When you are walking down stairs, gravity isn't doing any work on you unless you are speeding up and therefore absorbing its energy. You are using equal but opposite energy instead.

[AuraSeer]

I think Geezer's point is that, if you were redesigning a human from the ground up, the muscles could be redesigned to work differently.

I also think that he has spent far too much time in Physics 001, and not nearly enough in the Real World. But that's just IMAO.

[C K Dexter Haven]

Yeah, Aura, but if you were redesigning a human from the ground [b]down[/i], would it be different?

Ah, AuraSeer, you have seen my aura truly--but, ummmm.... you have the sign reversed. Long, long ago in a galaxy far, far away, I was a physics professor and I _did_ spend quite a bit of time in Physics 101. I liked it, too, and was good at it. But, alas, I was incompetent at academic politics and had to go and make my way in the Real World (TM). Nowadays I spend way too much time in the Real World building machines that raise and lower things, and not enough engaged in the elegance of pure physics discussing tricky concepts with bright young physics majors like our friend Konrad. You read me right, and I thank you for it.

Interestingly, the main point in my first post was that a pure basic physics argument could _not_ answer the question at hand. You have to know how real muscles work to know if they need to expend energy (ie, burn fuel) in order to lower a mass through gravity. Konrad's point is that, with suitable idealization, pure physics _can_ give an answer--and that the answer is that it takes equal energy to raise and lower a mass. He's now given us a lucid and elegant explanation of that assertion.

I'm very interested in this question because I keep seeing it pop up, usually in the form, "Did you know that, as strange as it sounds, it actually takes _more_ energy to descend a staircase (mountain, hill, ladder, etc) than it does to climb it? Isn't that cool?" Usually, however, the respondent cannot justify the assertion because he or she lacks the facility with physics. Now here's Konrad, clearly bright and articulate, a physics major, making a somewhat more nuanced claim: it takes exactly the _same_ energy to descend as to climb. I want to know how he draws this conclusion.

So... Konrad. If you'll permit me, let's parse your theory.

1. | |As far as the block and the finger goes, A doing work on B means to me that B is absorbing energy.| |

Yes, it means the same to me, too. Your earliest few posts indicated that we agreed on this, but later material gave me pause. I hope you see my point about the sign. Note that at constant velocity, B is not speeding up, but it is still absorbing energy (and dissipating it as heat). Hold that thought.

2. | |Yes, it does take energy to lower something down.| |

This is the nub of the discussion. My claim is that it _can_ take energy, but it does not _necessarily_. It depends on the mechanism employed. These fall into three classes: regenerative (reversible processes required), friction (simplest irreversible process), or "clutch slipping" (energy required to regulate the amount of friction).

3. | |How? Well look at it this way. Suppose instead of doing it slowly we let it speed up. Now we have something moving with a speed relative to us. What's one way to stop it? Well we could launch another object at it of the same mass going the same speed. The two will collide and stop. (Without it doing any work on your arm. In fact your arm does work on the second object.)| |

Very nice! This description seems to me to be perfectly rigorous. It's just that it isn't _general_. It describes one method of the class of methods I've called "clutch-slipping." Suppose instead of launching an interceptor of equal mass and speed, you launch one of much less mass--a bullet to stop a brick, as it were. With no bouncing, the interceptor must have the same momentum as the object you are trying to stop, so as mass goes down, speed goes up proportionally. But energy goes up as the _square_ of the speed, so the lightweight interceptor needs to be supplied with much _more_ energy to get up enough momentum to do its job. At the other extreme, suppose you use an interceptor that is much _more_ massive than the object you are trying to stop--a brick to stop a spitball, as it were. Now to match momenta, the brick hardly needs any speed at all, and has near zero energy to bring to the party. This is "clutch slipping" at the limit of pure friction.

4. | |So we have used energy to stop an object, and we have not gained any ATP from this. Of course all the energy goes into heat. (The amount of heat energy will be twice what you would absorb if you could somehow extract all the energy from the first object.)| |

Right. But perhaps a more rigorous statement would be that we have used _momentum_ to stop an object. The energy used depends on the mass of the interceptor object chosen. By the way, nobody ever claimed that _real_ muscles were reversible and you could gain ATP from descending under muscle power. If I gave this impression, I apologize for being unclear.

5. | |If you are decreasing the speed of something relative to you, you can theoretically absorb the energy instead of using more energy to slow it down. That is what is meant by the object doing work on whatever is slowing it down.| |

Yes. Except that in your example of "using more energy to slow it down" you still end up absorbing the kinetic energy of the object being stopped. The object being stopped does work on the interceptor. Since you specified an inelastic collision, all that work goes straight to heat, which is absorbed by the matter of the two objects now in contact. I'd say that the energy of the object being stopped was absorbed by the object doing the stopping at the _incidental_ expense of the original energy of the object doing the stopping.

6. | |But that doesn't mean you have to absorb it, a human doesn't.| |

This I don't understand. In your early posts you indicated that you _do_ absorb it, but that it costs you energy to do so. In your discussion of paragraph 3 you tell what you mean. If _something_ in the problem doesn't absorb the energy of the object being stopped (or slowed, or lowered), where does the energy go? You say it goes into heat. I agree. Does that not count as being "absorbed" by the body being heated? Do we have a definition-of-terms problem here?

Or is the issue that the energy is absorbed (as heat) by the interceptor particles, but not by the arm that launched them. If so, I'd have to point out that in a muscle, the interceptor particles and the agency that launches them are in thermal contact.

Finally, it's a non-sequitur to go from "doesn't mean you have to" to "doesn't." To assert that the human doesn't absorb energy because it doesn't have to does not follow. You have to look at the mechanism of real muscle contraction to decide the case.

7. | |When you are walking down stairs, gravity isn't doing any work on you unless you are speeding up and therefore absorbing its energy.| |

I don't see how this statement follows. If gravity makes you move, it is doing work on you no matter what your speed profile. Work represents the conversion of gravitational potential energy into kinetic energy if you just fall, or heat if you lower yourself gradually. Either way, you are absorbing energy under the terms of paragraph 1. (There's also the third possibility of absorbing energy and storing it in springs or batteries or whatever, but we've agreed that that is an irrelevancy for muscles since they are irreversible machines.)

Furthermore, you very astutely used the abstraction that gradual lowering consists of an infinite number of infinitesimal drops and catches. So even in your example, gravitational potential is first converted to KE, and _then_ reduced to heat by collision with your interceptor particle. Gravity (or more precisely, the gravitating bodies) are most certainly doing work on each other in raising and lowering processes.

8. | |You are using equal but opposite energy instead.| |

Fundamentally, the energy used is more or less irrelevant. It is _momentum_ that is doing the heavy lifting, so to speak. If the mass of the interceptor is arbitrary, the energy of the interceptors could be anything--and whatever it is, it all gets absorbed as heat during the collision.

Konrad, I think I understand

[Konrad]

Geezer: I think I was a little unclear about the term "absorb". In some cases I was using it to mean negate and in others to "absorb the energy back".

But either way, since we know that the human body isn't reabsorbing any of that energy as ATP and since we know how much energy has to be negated/absorbed and since we're assuming there's not much friction we can conclude that you have to do an equal amount of work. You can consider the work negative or whatever but we know it either has to be absorbed or negated and it ain't being absorbed, so the person is really doing positive work.

Actually I just refuse to accept negative numbers in physics in general...

As far as the momentum vs. energy thing goes it doesn't make a difference if there is no friction.

I've got another interesting problem for you: A chain of total length a is resting on a table with length b hanging off the end of the table. Neglecting friction find the speed of the chain just as its end falls of the table. Integration is verboten.

Auraseer: If you do know anyone who is redesigning the human ask them to make it perfectly spherical and of uniform density. It will makes physics problems much simpler. Then people can just roll down the stairs and it won't take them any energy to do it.

[Geezer]

Well, Konrad, my friend, I think this thread has run itself out. If you refuse to accept negative numbers in physics, then, well, you just aren't practicing physics, you are practicing religion. That's fine, but it can't answer the question at hand, which is a physics question.

It's too bad, because we're so close... Consider your statement that
since we know that the human body isn't reabsorbing any of that energy as ATP and since we know how much energy has to be negated/absorbed and since we're assuming there's not much friction we can conclude that you have to do an equal amount of work. You can consider the work negative or whatever but we know it either has to be absorbed or negated and it ain't being absorbed

In physics (as opposed to religion or magic) energy doesn't "negate" energy. (Heck, you'd have to have negative energy to do that.) Even in your example, you assert correctly that all the energy is turned to heat. Where does that heat (which is energy) go? It gets absorbed. It raises the temperature of muscle tissue. How does the energy get converted to heat? Friction--inelestic collisions specifically. The collisions you describe constitute a frictional mechanism internal to the muscles.

When a muscle lowers a weight, if the gravitational energy does not go into storage (e.g. making ATP), and if it doesn't go into KE (which is what we mean by "lowering"), then it must go into heat. There's no other choice. Sorry. Muscles absorb energy through friction, not magic. The friction arises between actin and myosin filaments mechanically rubbing against each other.

As far as the energy versus momentum thing goes, it does matter, just as I've described it. You've got enough physics to do the calculation. If you make the collisions elastic (ie, no friction as you now suggest) rather than inelastic (ie, with friction as you originally described), then the interceptors bounce off with varying speeds depending on their masses. In order to stop the moving object you still have to pick the interceptors so that their momentum change in the collision matches the momentum of the object you are trying to stop. Now you have the problem of stopping all those interceptors ricocheting back at you. Friction will work.

For your chain question, I get v=sqrt(g*(a^2-b^2)/a). (No calc, but I did use those pesky negative numbers.) If you want to discuss how I got this answer we should start a new thread or communicate privately, since the topic here is supposed to be muscle soreness.

Konrad, tell me you were kidding about the negative numbers. Otherwise I feel it my moral duty to warn you that if you refuse to accept negative numbers in physics, you're just going to implode when you are asked to accept imaginary numbers in physics.

[Konrad]

Geezer: Ok for the chain question email me at konrad@axess.com.

I have no problems working with imaginary numbers, I just refuse to accept them. What I mean is that there is no negative number you can't make positive by shifting the origin. Using negatives is just a convenience. The only case where negatives do what they're supposed to is things like matter/antimatter.

Ok now back to the stair problem. I agree that all the work goes into heat. As I see it, what's happening is like 2 balls bouncing off each other in a perfectly elastic collision but being stuck together with a rubber band, they are still going as fast as they were before but now instead of being free the kinetic energy is heat. The stair atoms hit your foot atoms and heats them up while at the same time the average momentum of your body decreases. (Pretend for a moment that instead of walkng down the stairs normally you are stamping your feet so your legs go fast enough downwards that your torso stops moving down and then they hit the stair and stop themselves, it ends up being the same thing, it just makes it easier to put the motion into chunks.)

Does that make sense to you?

[Devaronian]

Well, you could always just lean over the staircase and go limp. Then you'll practically not use any energy at all going down... But then again, it will be harder to stand up afterwards...

[Geezer]

Amazing! There's actually someone still following this thread. (Or maybe just laughing at us.) With that encouragement, ummm... what you say makes sense, Konrad, it just isn't germane. A smooth descent does no work on the stair tread--the tread doesn't move (remember your idealizing assumptions). Sure, you can stamp your feet going down and use up a lot of energy doing it, but you don't have to. If you descend smoothly, all the energy goes into heat in the muscle--and the muscle need not supply any additional energy to allow that to happen.

I take your point about looking at this on the molecular level--but it doesn't help your case. The process you describe takes place at the interface between the actin and myosin filaments in your muscle. As the filaments slide over each other their molecules bang into each other, exchanging energy and momentum. The energy goes into the oscillating chemical bonds and random molecular motions we call heat. The momentum transfer is force (F=dp/dt). That's what supports your weight as you descend. No energy input required.

In order to prevail, you are going to have to explain why it is that a dashpot can lower a weight gradually with no energy input, but a muscle can't. There's no essential difference.

As for the chain... Energy is conserved so the initial potential energy is equal to the final PE+KE.

U1 = -b^2*g/2 (Density is arbitrary and cancels.)
T1 = 0
U2 = -a^2*g/2
T2 = a*v^2/2

U1 + T1 = U2 + T2
Solve for v.