Not just balanced as in the static case but the position of the balance on the lever is critical because of the squared radius term,this explains the overshoot on the half mass.
I've only watched the first half so far but already I'm really impressed by your clever, counter intuitive demonstration - I don't yet know what is to follow but this part alone, surely is worthy of the likes of Bruce Yeany etc showing to pupils. You could win a pub bet on this - if you didn't mind carrying your apparatus around with you lol! I confess that until you hinted the results wouldn't go the way we intuitively think about it, I was automatically thinking it would go less high without the "assistance" of the balancing weight. When this happens, I could either feel st00pid and defensive, pull a Gary excuse out from where the sun don't shine, or I could thank you for teaching me something I should have realised already - which is what he should be doing. Obviously I'm gonna thank you cause I think this is quite brilliant and memorable. This IS something that should be taught in schools. In fact, I'd love to build it just to show off and trick people, wishing it was my invention lol. I will probably just share it with people instead as I've become a bit lazy for doing experiments lately, distracted by various things I need to tend to - but you have certainly inspired me again. Possibly related ... Thinking back two or three years to when Gary was talking about dropping a mass on one side of a lever (or whatever term applies) then predicting how the mass at the other end would launch upwards and miraculously come back down to RE-launch the first mass back up (he showed a pathetic animation demonstrating this reciprocal action as if it were fact) I wasted a fair bit of time constructing something to attempt to replicate this idea of his but it was the most troublesome, unsatisfactory experiment ever, getting even the first launch to happen... ... I had to reduce the mass of the first object being launched to something like a TENTH of the mass dropping onto the other end, just to get it to launch a few inches - getting it to land back in the right place was A) near impossible - random at best - and B) a bit pointless trying to acheive anyway, seeing as I had already found that his idea didn;t even work when the masses were the SAME, so a tenth of the mass wasn't gonna fair any better at launching the far bigger mass - obviously. But I tried it just to demonstrate the futility of his "IF WE DO THIS THEN THAT WILL HAPPEN" type assumptive thinking. It looked too simplistic to be true but I wanted to check with reality before criticising it. I think your demonstration goes a long way to explaining why it was never gonna work. None of us would mind his assumptive thinking IF he was man enough to just ACCEPT that he had been proven wrong and if he just took the opportunity to LEARN something from his mistakes - which most of us make - None of us are pretending to be perfect - only him. It's so ironic how far from perfect he is. He's virtually never right - which is sad really - a bit of me would LOVE him to be right about SOMETHING! But this is what happens when ego is made more important than discovery.
2) Now I've watched the second half I think Pyrroh314 & Postiemania's succinct explanations clarify it best for me. I think they've narrowed it down to it's essence, just as your demonstration does. Thank you for teaching me something the best way possible.
The increased height is because you have reduced the amount of mass you are trying to rotate. Yes you have reduced the moment of inertia thus proving inertia. Well done Ian.
nice. this is good stuff. interesting. The help from the weight doesn't help because the spring has to move that mass too, the help is weak compared to the spring trying to move the mass as fast as possible. cool
I'm not sure if I understood your point completely, maybe you are right, but I would say the problem was that, because of its mass, the lever (or the spring actually) was less sensitive to the difference between the setups. If the weights were very very small, it's easy to imagine the velocity ratio would be 2:1, even when balanced like that, because the spring would basically feel just the mass of the lever. But this still shows the difference between 2m1d and 1m2d setups.
