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Let us say we have a cylindrical bar tied to a fixed object (same as we see in trains). Now, I hang myself onto the bar with my hands and generates a force Fpull. After this I start pushing the bar upwards with my hands along with my feet on the floor and generates a force Fpull. Which force greater, Fpull or Fpush and why ?This is the bar I am talking about

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    $\begingroup$ That depends on how strong you are! Most people can't overhead press anywhere near their body weight, so hanging is probably larger. $\endgroup$
    – knzhou
    Commented Apr 6, 2019 at 16:25
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    $\begingroup$ If you're a skinny but strong athlete, you might be able to $F_{push}>mg$. This isn't really a physics question though. $\endgroup$
    – Gert
    Commented Apr 6, 2019 at 17:38

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It depends on how strong you are. The force you apply while hanging (assuming you're strong enough to hang) is limited by how heavy you are. If you can push up more mass than you yourself are, then $F_{push}$ would be larger. For most people $F_{pull}$ would be larger.

You could roughly test this out for yourself at home, if you have a bathroom scale, with upper limit more than twice your regular weight. Put the scale on the floor in a doorframe, stand on it and push the door frame up as if it was the bar. If the scale shows anything more than twice your normal weight, your $F_{push}$ is greater than your maximum $F_{pull}$. I have to warn you that you could hurt yourself and please be sure the doorframe is actually strong enough to not cave in.

Something to keep in mind is that your pushing strength will probably vary with different heights of doorframes (so different bar heights too).

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