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When it comes to doing pull-ups (or chin-ups) does difficulty depend on where the individual's center of mass is? Someone I know contends that pull-ups are more difficult for females because they have lower centers of mass. It seems to me though that center of mass shouldn't matter for this particular exercise; so for instance if I moved my center of mass down 1 foot, it shouldn't make a pull-up more difficult as long as my net weight remains constant.

What say you physics knowing peoples?

Staff Emeritus
Gold Member
I don't see how it would matter either. As soon as your feet are off the ground, you're a pendulum -- and your center of mass will experience a restoring torque which will push it directly under the pivot. Once the center of mass is directly under the pivot, I see no way its vertical distance could make any difference.

I'd say women have a harder time with pull-ups and chin-ups because their genetics don't encourage as much upper-body musculature.

- Warren

rdecker
uh huh

yea verily.

Homework Helper
The point is not whether the center of mass is high or low but how much it is raised. A person with longer arms who raises his/her center of gravity more would do more work.

Muscle insertion plays a role, too.

VBPhysics
Halls is right,

a female with a lower center of mass has to do more work. for example consider a boy and a girl of 75 kilograms the distance to the boys center of mass from his vertically outstretched arms is .5 meters, and the distance to the girls is .5+x meters than the energy required to do a pull up for each of them is.

Boy = 75*g*.5

Girl = 75*g*(.5 + x) = 75*g*.5 + 75*g*x

meaning it takes more energy for the girl to do a pull up.

Mentor
Originally posted by VBPhysics
Halls is right,

a female with a lower center of mass has to do more work. for example consider a boy and a girl of 75 kilograms the distance to the boys center of mass from his vertically outstretched arms is .5 meters, and the distance to the girls is .5+x meters...
So girls have longer arms than boys? Do they? (hint: no).

And that wasn't Halls's point. His was a hypothetical - IF one person had longer arms than another of the same mass, it would take more energy. Someone tall and skinny has to work harder than someone short and fat (and the same mass).

And if you want to be picky, adult males being taller on average have longer arms than adult females do.

VBPhysics
Dear russ, thank you for your sarcasim(hint: your misinterpreting the problems setup)

So girls have longer arms than boys? Do they? (hint: no).

the x is meant to denote the lower center of mass that the girl would have --not some change in the arm length between the two people. give them identical heights, and appendage lengths, and the girl is still going to have a lower center of mass than the boy. Unless they are swinging around the bar like a pendelum, and even then her's will be lower until they swing above the bar.

Hall's point, and mine is not that girls have longer arms. It is that if a person is raising the point at which force is acting on them over a longer distance. than that effort requires more energy, and is thus it is harder to perform that effort.

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[The point] is that if a person is raising the point at which force is acting on them over a longer distance...

And how does anything but arm length affect the distance one raises that point?

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Gold Member
Originally posted by VBPhysics

Hall's point, and mine is not that girls have longer arms. It is that if a person is raising the point at which force is acting on them over a longer distance. than that effort requires more energy, and is thus it is harder to perform that effort.

But Hall's point was that having a lower CoG had no effect on the effort needed, but having longer arms did. This is not the same as what you said, which is that girl's, having a lower CoG, would exert more effort. The intial position of the CoG has nothing to do with how for it is raised, while the arm length does. Remember, the object of a pullup is to get your chin over the bar, not your CoG.

But a female's lower center of gravity is closer to the Earth's, so it would have a stronger pull. Of course their shorter arms would put them higher up, so maybe it evens out. But the combination of lower COG and shorter limbs gives the female a decided dissadvantage in doing squats.

Originally posted by LURCH
But a female's lower center of gravity is closer to the Earth's, so it would have a stronger pull. Of course their shorter arms would put them higher up, so maybe it evens out. But the combination of lower COG and shorter limbs gives the female a decided dissadvantage in doing squats.

Do you recall weighing less on the top floor of a building compared to the basement? At least enough to matter? Give me a break.

Mentor
Originally posted by LURCH
But a female's lower center of gravity is closer to the Earth's, so it would have a stronger pull.
Lol, got to give you that one.
Originally posted by VBPhysics
Dear russ, thank you for your sarcasim...
Damn, and I thought I was being nice - explaining that you had misinterpreted what's going on here, without trying to cut you off at the knee.

If you want to see some REAL sarcasm from me check the politics forum out - or that thread on expanding earth. I can be downright nasty.

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VBPhysics
I now see where you got the x being the arm length. I was trying to put the CoG over the bar. Something tells me that the fact that you edited that post before I saw it was a good thing.

We have a politics forum?

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Originally posted by hypnagogue
When it comes to doing pull-ups (or chin-ups) does difficulty depend on where the individual's center of mass is? Someone I know contends that pull-ups are more difficult for females because they have lower centers of mass. It seems to me though that center of mass shouldn't matter for this particular exercise; so for instance if I moved my center of mass down 1 foot, it shouldn't make a pull-up more difficult as long as my net weight remains constant.

What say you physics knowing peoples?

The vertical location of the center of mass is not important. Where the arm connects to the body implies that the arm-lever does not know where the vertical location of the center of mass is.

The length of the arm is important since doing pullups you're using the arm as a lever.

However muscle is important here. There is an effect that is very important that has been overlooked in this thread so far. And that is the idea of ratios.

Suppose you take a look at this only from a physics standpoint and not from a muscle efficiency etc point of view. Consider a person of a certain height and weight. His muslces have a certain cross-sectional area. Let's assume that the strength of the man is proportional to the cross-sectional area of the muscle. Now if the man doubles in size such that all his physical dimensions increase in direct proportion then the cross-sectional area of the muscle will double in size. However his weight has now increased 4-fold. So he got twice as strong but now he has to lift 4 times the weight! That tanslates to less pullups.

Pmb

Bartholomew

One issue that nobody's looked at is that a pull-up doesn't happen directly under the bar. It happens off to one side, especially as you finish the pull-up. That means that you're not just pulling straight up--you also have to hold your center of mass out. Since men have a higher center of mass, they have to hold it out at a greater angle. Therefore, center-of-mass alone means men do harder pull-ups.

Mentor
Nice catch. I actually did think of that as I'm relatively skinny and that's a problem for me doing pullups - I start swinging back and forth. To compensate I lean back(or rather pull my legs up in front of me), but then that just means I'm lifing my COG further than if I could lift myself straight up.

Besides where your COG is located though, this is also due to muscle geometry. Your biceps lift your body up at the shoulder while your lats just pull your body forward to meet your elbow.

Originally posted by Bartholomew
One issue that nobody's looked at is that a pull-up doesn't happen directly under the bar. It happens off to one side, especially as you finish the pull-up. That means that you're not just pulling straight up--you also have to hold your center of mass out. Since men have a higher center of mass, they have to hold it out at a greater angle. Therefore, center-of-mass alone means men do harder pull-ups.

This is incorrect. When you're doing a pull-up then your body will be arched a bit and at an incline. Your center of mass will most definitely be exactly under your hands - unless you're the superman and can rotate your wrists with so much torque as to move your center of mass from under the bar. However if you think of this from the standpoint that your hands are grabbing a bar which is suspended by ropes/wire then it would be impossible for your center of mass not to be directly under the bar.

Pete

Bartholomew
It's not just wrist rotation that moves your center of gravity--if you push the bar away from yourself with your pectoral muscles, which testing tells me that you _do_ do in order to get over the bar, you also alter your center of gravity. You could do that even on a wire.

Originally posted by Bartholomew
It's not just wrist rotation that moves your center of gravity--if you push the bar away from yourself with your pectoral muscles, which testing tells me that you _do_ do in order to get over the bar, you also alter your center of gravity. You could do that even on a wire.

No. It may appear that way but its most definitely not true. If your body is not moving and your wrists are not providing a torque then with no doubt your center of mass (COM) is exactly under the support at all times - no matter what. When your body is in motion then it can be off. Doing normal pullups your COM will always be under the support - That's a basic fact of physics. You may push the bar away from you as you pull yourself up, but your body's COM will still be reagrange to place the COM under the support. Its rather difficult to see in your minds eye but it is a fact. As your arms extend to push your chest away the rest of you th rest of your body tilts/contorts such that the COM is right under the support. Its not the person doing the tilting but gravity pulling back and providing the torque. Otherwise there is a net tourque which will act to bring the COM back to center.

Pete

Mentor

Originally posted by pmb
This is incorrect. When you're doing a pull-up then your body will be arched a bit and at an incline. Your center of mass will most definitely be exactly under your hands - unless you're the superman and can rotate your wrists with so much torque as to move your center of mass from under the bar. However if you think of this from the standpoint that your hands are grabbing a bar which is suspended by ropes/wire then it would be impossible for your center of mass not to be directly under the bar.

Pete
That is true only if you do the pullup really really slowly. Like I said, doing pullups makes me swing back and forth. It isn't just the torque in your grip, its the change in your body's geometry and the accompanying accelerations.

You are assuming an equilibrium situation that doesn't exist. Forces are unbalanced, otherwise the center of gravity wouldn't be moving up and down.

Originally posted by russ_watters
That is true only if you do the pullup really really slowly. Like I said, doing pullups makes me swing back and forth.
That depends on how one does pullups. The correct way is to do them slowly. Otherwise you don't get the full effect of the workout. Obviously when you're swinging the COM is not below as support.

You are assuming an equilibrium situation that doesn't exist. Forces are unbalanced, otherwise the center of gravity wouldn't be moving up and down.
No. I'm not assuming equilibrium. The slight swing brings the bodies COM only slightly off of the line of support. However the topic of this thread is about doing pullups and in all physics problems there are approximations one makes which are geared to solving the problem at hand. This thread was about the difference between boys and girls and their center of mass etc. It's not about swinging. So that 4 to 6 inches off center can be ignored for this question. This question was about torque etc. And I don't believe that the offset is 4-6 inches either.

Pete

Bartholomew
I've never heard anyone say that you're supposed to do pull-ups particularly slowly. IMO it's a hard enough exercise so that you get sufficient benefit no matter how you do it--and more cardiovascular benefit if you go fairly quickly, allowing you to do more of them. The body is a fairly long pendulum, so even if you do go pretty slowly it will take a second to return to center. And if you go faster it will take longer to return to center--probably long enough so that you'll complete the pull-up before it happens.

However, I do think you raised a good point about how much the off-center COM matters. I had thought it mattered more than I think now.

Originally posted by Bartholomew
I've never heard anyone say that you're supposed to do pull-ups particularly slowly.
That applies to all exercises. At the gym I used to watch the new kids come in and start yanking the weights around. All they were doing is getting some exercise and letting the momentum of the weight do the rest. You sounded like you were lifting so fast that your body was really swinging fast. A normal pullup would take about 5 seconds for a cycle. But the faster you go the less you get out of it. It should be a slow constant force both up and down with a short hesitation at the max. If you're serious about exercising then you should study this - ask the instructors at your gym about this. They'll tell you the same thing.

This applies mostly to weight lifting, rather than pullups, since that's what I do most (back problems). But the princiople is the same and that's what I do when I would to pullups.

Pete

Mentor
That's all well and good, pmb, unless you are in the military in which case you get tested (and punished ) on how many you can do.

In any case, what I learned from an instructor was that you should go up relativley fast (about a second) and down relatively slowly (about 5 seconds). The down slowly is the key.

Originally posted by russ_watters
That's all well and good, pmb, unless you are in the military in which case you get tested (and punished ) on how many you can do.

In any case, what I learned from an instructor was that you should go up relativley fast (about a second) and down relatively slowly (about 5 seconds). The down slowly is the key.

The military has different goals. In boot camp they drive you towards endurnace and its endurance which the absolutley most imporant thing. I recall getting up at 4:00am and running a few miles then doing 1,000 jumping jacks etc. I wasn't that much stronger when I got out but WOW could I run!

Advice: Opinions are like *******s - everyone has one. :-)

Never listen to one single instructor. Find the most common opinion from fitness experts and go with that. Yanking a barbell up uses the momentum of the weight and that means less force and work being done by the muscle - don't be in such a hurry. No pain no gain.

Pete

While arm length may be a factor, neck length is the important thing.

Julian Solos

Originally posted by pmb
Suppose you take a look at this only from a physics standpoint and not from a muscle efficiency etc point of view. Consider a person of a certain height and weight. His muslces have a certain cross-sectional area. Let's assume that the strength of the man is proportional to the cross-sectional area of the muscle. Now if the man doubles in size such that all his physical dimensions increase in direct proportion then the cross-sectional area of the muscle will double in size. However his weight has now increased 4-fold. So he got twice as strong but now he has to lift 4 times the weight! That tanslates to less pullups.

Pmb

I think the situation is a lot worse:

"Now if the man doubles in size such that all his physical dimensions increase in direct proportion then the cross-sectional area of the muscle will quardruple in size. However his weight has now increased 4-fold. So he got twice as strong but now he has to lift 4 times the weight! That tanslates to less pullups.

Julian Solos
Originally posted by pmb
That applies to all exercises. At the gym I used to watch the new kids come in and start yanking the weights around. All they were doing is getting some exercise and letting the momentum of the weight do the rest. You sounded like you were lifting so fast that your body was really swinging fast. A normal pullup would take about 5 seconds for a cycle. But the faster you go the less you get out of it. It should be a slow constant force both up and down with a short hesitation at the max. If you're serious about exercising then you should study this - ask the instructors at your gym about this. They'll tell you the same thing.

This applies mostly to weight lifting, rather than pullups, since that's what I do most (back problems). But the princiople is the same and that's what I do when I would to pullups.

Pete

Pete is correct. Not many men can do even 10 pull-ups if required to perform in strict form which is to raise and lower the body slowly without swinging, kicking, jerking, etc., and at the down position, the arms are FULLY extended. The foolish male ego entice many men to cheat.

I have seen many women/girls who can't do even one pull-up in strict form.