## Push-up as Lever - How Much Weight Moved?

I'm trying to determine approximately how much (percentage) of an athlete's body weight is moved when doing a push-up. I know it's a second class lever, but the lever itself is the load, and worse, the load is not evenly distributed along the length. I know approximate body segment weights, but I'm not sure how to proceed.

Any ideas? Thanks.
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 Key points:First of all, don't worry about the load/resistance being the lever itself. All levers with mass present some sort of resistance. The work needed to move a mass on the lever is a product of both it's distance from the fulcrum (hinge, toes in this case) and the weight itself. A 50kg mass in the center of a 2nd-class lever presents the same work load as a 100kg mass placed on the very end. Now, I'm not sure what you mean by what percentage of weight must be lifted. Do you mean "what is the ratio of force needed to do a pushup to the person's bodyweight?". That depends on the person's weight distribution. If all their weight is directly on the shoulders, it's 100%. If all the weight is directly on the toes, it is 0%. I'll leave you with that for now. Hint: It has a lot to do with the center of mass's position along the lever. If the center of mass is right smack in the middle, the person must apply a force equal to 1/2 his/her bodyweight.
 What I meant by percent moved is, say I weight 85kg - that 85 kg is obviously not all located at my shoulders, although the majority of it is pretty close. In a full push-up (sternum travels from floor to 20 cm above the floor), how much of that 85kg was moved that 20 cm? I can figure out pretty well the weight distribution - e.g. thighs are about 14.5% of body weight, torso about 45%, etc. Maybe I'm approaching it incorrectly... Not too sure anymore. Ultimately, I want to be able to approximate the work and power of a number of push-ups at a certain body weight.

## Push-up as Lever - How Much Weight Moved?

First, approximate a point along the body at which you calculate (or speculate;)) the center of mass is. I do not know what your approximations are, so I will make up a simple distribution to use as an example. Say your legs (first 40% of length) are 20% of bodyweight. Say your midsection (middle 20% of length) is 50% of your bodyweight. Then your upper-body is 30% of your weight.

With these numbers, your center of mass would be at 52% of the length of your body, counting up from the toes. In other words, this is the "balance point", or the point along the length of your body at which the weight is equal on both sides of the point.
Once you figure out the center of mass, you can treat the whole body as a single mass resting on that point.

Perhaps a diagram will help:
http://img452.imageshack.us/img452/2...diagram3it.jpg

In this example, a person 85kg, 182cm tall is lifting one extreme end of his body 20cm off the ground. If we speculate that the center of mass is at 100cm from his feet, we simply figure out the work needed to lift his mass the distance that his mass gets lifted.

Since 100cm (center of mass measured from feet) is approximately 11/20 of his body length, then the distance his center of mass is lifted is 11/20 of 20cm, or 11cm. Work done is simply this distance times force (weight of body).
 Awesome. That helps completely. Thanks a lot. by the way, your estimation of center of mass is pretty good - 55-56% of height is the general rule among kinesiologists, et al.
 Could you explain this to a non-technical person? It seems to me, the formula works if you are lifting the weight at the center of mass. But one is lifting at one extreme of the body. How is that factored in or how do you calcuate that? Apologies, but I'm not good with math. Thanks!
 I did a pushup on a bathroom scale and it read 80% of my weight. I only have one scale and it would be more accurate with two scales. I think 75% would be close to the number.
 Thanks for the idea, nucleas. I did the same thing and got about 70% of my total weight. That could just mean I have less upper body mass than you.

 Quote by ben357 Could you explain this to a non-technical person? It seems to me, the formula works if you are lifting the weight at the center of mass. But one is lifting at one extreme of the body. How is that factored in or how do you calcuate that? Apologies, but I'm not good with math. Thanks!
The formula doesn't work only if you lift the weight at the center of mass, but rather: the formula of lifting from your center of mass is a simplification of real situation. But while it's a simplification, the answer will be exactly the same (if you determine the center of mass correctly).

The alternative is to cut the body - on paper - in an arbitrary high amount of small parts (the more the better) and calculate the contribution of lifting each of those to the corresponding heights, and sum all of them. But much easier is to average all of those parts to one center of mass, multiply that by the height of the center of mass, et voila!
 Hi All, Sorry to bump this thread, but I had a question: If I were to measure the amount of water I dsiplace when fully submerged, and then slowly lower myself until 50% of that original displacement had been reched; would that depth be my midpoint for use in determining the amount of weight I move during a pushup? Also, how does the formula change for pull-ups?