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Consider the following image:

enter image description here

Is it possible that the man pulls himself up (suppose the weight of the platform is negligible), or just lift the right part of the platform up? How to analyse this problem physically in detail?

I consider this thing as a kind of lever arm which where the resting point $Q$ is the left end of the platform.

Then you have in some distance $x_M$ away a force pointing downward $F_G$ which is equal to the weight of the man. Additionally there is another force $F_1$ pointing downwards which occurs because the man is pulling.

Last but not least some larger distance $x_P$ away there is the force $P$ pointing upwards. I am not sure if $P = F_1$ holds. But let's assume this for a moment:

Considering the torque around $Q$ this gives $x_M \cdot (F_G + P) - x_P \cdot P $. Thus if $\cfrac{x_P}{x_M} > \frac{F_G + P}{P} = \cfrac{F_G}{P} + 1$ he can lift up the right part of the platform. If $\cfrac{x_P}{x_M} < \cfrac{F_G}{P} + 1$ everything will be stable.

I am completely unsure if this analysis is correct. So it would be great if someone could post a complete correct and detailed analysis of this problem.

This is not a homework problem. I am just a fitness freak interested in physics who discovered this crazy video of a self made resistance band deadlift platform. This made me curious about the physics behind this construction and variations of it.

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    $\begingroup$ This works just as well as pulling yourself up by tugging on your shoelaces, which is to say it doesn't work at all. $\endgroup$ Oct 11 '13 at 14:52
  • $\begingroup$ Notice how the legs are spread out. They impart a torque on the platform which counter acts the force imbalance you calculate. $\endgroup$ Oct 11 '13 at 19:15
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The way to analyze the problem is to consider the platform and man to be one system. Then the net external torque on this system comes from the tension in the rope connected to the wall. This tension pulls to the right so it is pulling the wrong way (that is, making the platform want to be flat). Now if the rope were attached to the ceiling (so the rope after coming out of the pulley on the right went straight up instead of continuing to go to the right), then the guy could rotated the platform + him system by pulling on the rope. This would cause the platform to be tilted though, which sounds dangerous.

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No, he will be never able to pull himself up because the amount of force he applies is balanced by the equal and opposite amount of normal force on the platform

But if the platform is not bolted to the floor then according to this image the plank will obviously move forward

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