[Physics] When we do pull-ups, does the bar takes more weight than when we hang down on the bar

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When I do pull-ups, I feel I push down to the bar. But does the bar really take more weight than just hang down?

For people who don't know pull-ups and hang down, here is an illustration.

Left: Hang Down———————–Right: Pull ups

Pull-Ups

So, does in right picture the bar take more weight than the left one?

Best Answer

Let's suppose you are pulling yourself up and down in approximately simple harmonic motion so your height above the ground will be give by:

$$ h = h_o + h' sin(\omega t) $$

Bar

Your acceleration is just $d^2h/dt^2$, and the force is just your mass times the acceleration, so the force due to your motion will be:

$$ F = - m h' \omega^2 sin(\omega t) $$

and the total force on the bar is:

$$ F = - m \left( g + h' \omega^2 sin(\omega t)\right) $$

So in this model the force is greatest at the bottom of your cycle as you are slowing your decent and accelerating yourself back up. It is lowest at the top where your ascent is slowing and you're allowing gravity to pull you back down.