Can a buoyant object achieve perpetual motion?

AI Thread Summary
A buoyant object cannot achieve perpetual motion, as perpetual motion machines violate the laws of thermodynamics. Attempts to create such machines often overlook the energy required to maintain buoyancy, such as pumping air underwater. The discussion emphasizes that regardless of the design, perpetual motion remains impossible. The thread concludes by stating that this topic is not suitable for further discussion.
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Would a buoyant object be able to achieve perpetual motion or even past perpetual motion if it were in a machine as portrayed below?https://mail.google.com/mail/?ui=2&ik=93e42fc0d8&view=att&th=12ca0732e35fe2f9&attid=0.1&disp=inline&realattid=f_gh5sgy4n0&zw
 
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You can't post images from attachment like this.

But regardless, no. There is no such thing as perpetual motion. Usually, the attempts involving buoyancy ignore the fact that it takes energy to pump air under water. Since I can't see that image, I can't tell you if that's what it is, but that'd be my blind guess.
 
And since we do not discuss perpetual motion machines here, this is a good spot to finish this thread.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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