Debunking the myth that women can’t do pull ups

A few weeks ago at lift, our coach told us that pull ups are much harder for girls than guys because our center of mass is lower. Of course I wanted to prove her wrong, so I attempted to look at the pull up from a physics perspective.

The work that a person needs to do for a pull up does not depend on center of mass at all.

                                                        W= m*g*d

It depends only on the mass of the person and the distance, which in this case would be the length of their arms (from shoulder to top of knuckles). This means that pull ups would theoretically be harder for a person with greater mass or longer arms. Because men are typically built heavier than women, this puts women at an advantage. Arm length is generally proportional to height, and since men are typically taller than women, this gives women the advantage again. Even though I am heavily generalizing here, there is definitely no way that someone can conclude that women are at a huge disadvantage based on height and arm length.

I then decided to see how big of a difference a small change in either mass or arm length would make in the amount of work that would need to be done for a pull up.

W=m*g*d

W= (70kg)(9.8m/s²)(0.48m)

W= 329.28 J

Changing arm length:

W=(70kg)(9.8m/s²)( 0.55m)

W=377.3 J

Changing mass:

W=(90kg)(9.8m/s²)(0.48m)

423.36 J

So ultimately, I was able to prove that a lower center of mass will not affect the difficulty of pull ups, and so women should theoretically be able to do them with the same ease as men (with the same muscle mass).

Sources:

https://blogs.scientificamerican.com/guest-blog/the-mechanics-of-the-pull-up-and-why-women-can-absolutely-do-them/