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Pumping Iron

We now try to calculate how much weight a human being can carry. Just as strings muscles can only pull. In the human arm the biceps lifts the arm and the triceps lowers the arm. The humerus bone pushes down on the forearm. Muscles contract when subject to an electric stimulus from the brain. The max pulling force is approximately
equation55
where A is the cross sectional area of the muscle. We ask how much weight a weight lifter can hold in a position where the forearm is horizontal. The torque equation with the end of the humerus bone as reference point is
equation58
Where d is the distance to the tendon attachment point and L is the distance to the point of contact with the weight being held and tex2html_wrap_inline180 is the pull by the biceps muscle. Solving for m we have
equation60
We consider a biceps with radius 4 cm and thus area tex2html_wrap_inline184 cmtex2html_wrap_inline186 and use d=4 cm and L=35 cm. Putting in numbers we find
equation65
Remembering that we have two arms we conclude that the max mass which can be supported is 80 kg. Note that as is the case for most muscles in humans they are at a severe mechanical ``disadvantage''. In this case for example the muscle exerts a force of 3500 N for lifting a weight of 392 N. The benefit is that motion of the arm is faster by the ratio of these forces which evidently was more important for our ancestors than brute force.



Collin Broholm
Tue Oct 28 10:29:48 EST 1997