Lanky like me? Don't be ashamed of your push-up count.

Lanky like me? Don't be ashamed of your push-up count.

In the gym here at Colgate, I have been working out with an average sized friend of mine, and I, measuring a lanky 6'5", have found myself having to defend my weaker push-up abilities with the excuse that I have longer legs and arms. Today, I realized that because of PHYS 111, I can prove that it's harder for me to do push-ups! So here goes nothin':

If we generalize and say that my longer legs cause my center of gravity to be 1.25x further away from my feet, and that I weigh 1.25x his weight, we can plug mass and center of gravity length (as r) into

Torque=rFsinΘ

Torque=(1.25)(1.25)sin90

Torque=1.6 Nm

Thus, there is 1.6x as much torque acting on me due to gravity than my friend. In order to counteract that gravity and hold myself up above the ground, I must apply a force while pushing up of at least

Torque=rFsinΘ

1.6=(77 inches/69 inches)FsinΘ

1.6=1.12Fsin90

F=1.43 N

1.43x as much as my friend. And this doesn't even begin to take into account the length of my arm, which means that I would have to apply a larger force over a longer distance, requiring more energy. I'll be showing him these numbers next time we do push-ups. 

By Chris Wetzel