Silly question about pull-ups

  1. hypnagogue

    hypnagogue 2,195
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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?
  2. jcsd
  3. chroot

    chroot 10,351
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    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
  4. uh huh

    yea verily.
  5. HallsofIvy

    HallsofIvy 41,264
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    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.
  6. Muscle insertion plays a role, too.
  7. 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.
  8. russ_watters

    Staff: Mentor

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

    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.
  10. Hurkyl

    Hurkyl 15,987
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    And how does anything but arm length affect the distance one raises that point?
  11. Janus

    Janus 2,524
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    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.
  12. LURCH

    LURCH 2,507
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    But a female's lower center of gravity is closer to the Earth's, so it would have a stronger pull. Of course thier 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.
  13. Doc

    Doc 0

    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.
  14. russ_watters

    Staff: Mentor

    Lol, gotta give you that one.
    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.
    Last edited: Oct 13, 2003
  15. 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?
    Last edited: Oct 14, 2003
  16. pmb

    pmb 0

    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 lenght 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. Lets 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 dimesions 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.

  17. Re:

    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.
  18. russ_watters

    Staff: Mentor

    Nice catch. I actually did think of that as I'm relatively skinny and thats 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.
  19. pmb

    pmb 0

    Re: Re:

    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.

  20. 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.
  21. pmb

    pmb 0

    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.

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