Posted by Nick Hall (195.74.122.243) on May 14, 2003 at 10:14:08:
In Reply to: Any reason why this idea wouldn't work? posted by Joel L. Lewis on May 14, 2003 at 08:17:58:
Joel wrote:
: Okay, here goes: imagine a simple lever with two equal weights, one on each arm, and one twice the distance from the pivot as the other. like this- ____o_____0________o Got it?
: ^
: Okay, now imagine letting the lever swing untill it is sticking straight up and down. Picture that moment in your mind.
Let's put numbers on this Joel. Assume 1 Kg masses. Assume G = 10, each mass therefore weighs 10 newtons. Assume the whole thing turns very slowly clockwise, and as it turns we 'tap' the energy out into some kind of storage device.
The critical question is: how much energy will we get?
Assume the weight at the shorter end (left) is 1 metre from the pivot. The one at the longer (right) end is ==> 2 metres.
Total energy given out when it rotates clockwise to vertical position is loss of PE of right minus gain of PE of left.
Left gains 1 metre. PE = mgh (assume G=10) = 1*10*1 = 10 joules.
Right loses 2 metres. PE = mgh = 1*10*2 = 20 joules.
==> total theoretical energy output (assuming no losses) = 10 joules.
Now, the energy needed to raise the lower weight to the 'same distance from the pivot' as the top weight = m*g*height rise = 1* 10 * 1 metre ==> 10 joules.
Sadly therefore, Energy output = energy needed to move lower weight to balance point with upper weight with respect to pivot.
Actually it is slightly 'worse' than that because the true starting point would mean rotating the - now balanced - wheel anti-clockwise to a point with a very slight slope to the right, allowing the right hand weight to roll to the right (2 metres from pivot), then lifting it back a bit more to true horizontal. It takes energy to turn and then brake even a balanced wheel (even with regenerative braking there are losses).
That's the problem!
The misleading picture you assume is implied by your statement ", it only needs to rise HALF THE DISTANCE THAT IT FELL to counterballance the other weight" - it didn't fall the whole distance in isolation, half of its energy 'output' was gradually being 'used up' raising the other weight to the top....in other words when falling through two metres, only half of that loss of potential energy was available to do work - and as we have seen at least that much is needed to restore to balance.
But don't stop thinking about it! I have several box files full of pieces of paper with similar mind-games! "The truth is out there"
Thanks for your post.
Nick