Newtonian Mechanics of a Push Up--How Much Weight Am I Pushing?

[phxjcc]

So I go to the gym…

…and do push ups using the bench press bar set at 3 ft off the ground.
the length of my hands to my toes is 5 ft.
Yeah, I know…3/4/5 right triangle, I am making it easy.

I weigh 250 lbs–[amazingly enough :)] spread evenly over the entire length of my body.

How much weight is on my hands?

Is it cos(angle to ground) * weight?

I don’t think so.

Thanks, Dopers!

[running_coach]

I just did a push up on a bathroom scale. At a bodyweight of 180, it registered around 140 during the move.

[Chronos]

Do the torque balance equation, with the pivot at your feet. And you might as well assume that you’re horizontal, because you are for part of the pushup, and that’s where the maximum force will be. If we assume for simplicity that your arms are at one end of your body and your center of gravity is halfway down, you’re pushing half your weight. Given runner pat’s experiment, though, this is probably not a justified assumption.

[ultrafilter]

There’s this analysis, which says that the subjects were lifting about 2/3 of your bodyweight in a regular pushup. That’s gonna vary with your body fat levels and upper body mass.

[phxjcc]

Thanks to all.

[appleciders]

Also depends on your gender. A man’s center of gravity is nearer his chest than a woman’s, which is lower.

[Machine_Elf]

@Chronos

Do the torque balance equation, with the pivot at your feet. And you might as well assume that you’re horizontal, because you are for part of the pushup, and that’s where the maximum force will be. If we assume for simplicity that your arms are at one end of your body and your center of gravity is halfway down, you’re pushing half your weight.

Re: your first sentence it doesn’t matter if your body is actually horizontal or not. The only thing that matters is the horizontal distances from your center of mass to your feet and to your hands.

[Chronos]

Right, I think I was somehow getting mixed up with the case where the floor is tilted.

[Enginerd]

Don’t you need an angle to get the rotational component of the gravity vector? What am I missing?

[Kevbo]

@Machine_Elf

Re: your first sentence it doesn’t matter if your body is actually horizontal or not. The only thing that matters is the horizontal distances from your center of mass to your feet and to your hands.

This is true, but that horizontal distance is going to vary as the cosine of your angle from horizontal. Doing pushups against a slightly inclined wall (so that you are vertical at the top) would be extremely easy, as nearly all your weight would stay on your feet.

[dstarfire]

@Kevbo

This is true, but that horizontal distance is going to vary as the cosine of your angle from horizontal. Doing pushups against a slightly inclined wall (so that you are vertical at the top) would be extremely easy, as nearly all your weight would stay on your feet.

You’re right, but so is Machine Elf. By changing your angle relative to horizontal, you’re moving your center of gravity.

Standing straight up your center of gravity is, necessarily at your feet (otherwise you’d fall over). So as you get closer to vertical (heads up) more and more of your weight is carried by your feet and less by your arms. If you were to raise your feet instead, more of the weight would be carried by your arms.

It’s been a LONG time since my high-school physics class, so there’s a good chance I’m saying this totally backwards.

[DSeid]

Another data point - 156 currently, in push up (top and bottom positions the same) 118, about 75% of my body weight. RP’s was 78% of his body weight. The difference probably related to differences in our centers’ of gravity (RP’s been disabled for a few years and does a lot of handcycling so likely has a center of gravity located higher up).

A quick google can shows us the math involved.

Yes, I am sure it should change some based on angle but little enough that my scale did not register a difference.

[Chronos]

Kevbo, you’re making the same mistake I did. Tilting the floor is not the same thing as extending your arms further. The horizontal distance from your feet to your arms will vary with cos(theta), but so will the horizontal distance from feet to center of gravity, and it’s only the ratio of those two numbers that matters.

[DSeid]

Here’s another source having done the experiment with more than n of 2:

1. Women performing traditional push-ups lift the equivalent of 71% of their body weight. For example, a 120 pound woman lifts about 85 pounds.
2. Men performing traditional push-ups lift the equivalent of 77% of their body weight. Thus, a 150 pound man lifts about 115 pounds. …

… These percentages are only averages, but there is a reason for the difference between males and females. Men usually lift more of their total body weight during push-ups than women because they tend to have more bulk in their chest and shoulders. As a result, more of their weight lies directly over the arms when performing pushups.

In contrast, women tend to have a lower center of gravity, with their weight centered around the hips and thighs. Since this weight is located below the position of the arms, less force is required to lift from a pushup position.

However, this varies widely, depending upon the individual.

Consistent with the my and RP’s results.