Energy thought experiment (oldschool very)

[toneboy1]

This might seem a bit weird at first but it raised an interesting question to me about power, work and energy.
I watched this show about how the trebuchet is so much more efficient than previous designs and then I sort of thought of it as a way to store energy and I wondered to myself, if you had one that was geared from the fall to be a speed multiplier connected to a 240V motor (so the long and short arms fell very slowely and the motor spun quite fast) "how long would it run for, 1 min, 1 hr?"
(to be precise I mean like the rate of which it was falling is equal to that necessary to make the motor put out 240V, approximately no more or less)

Then I realized I didn't know how much energy was stored in it. So I'd like to ask anyone, if you had a trebuchet with a mass in it (half a tonne, a tonne, whatever you want) and the height for the short arm to fall was 1m, 10m, 20m, whatever you like, and the lengths of the short and long arm were whatever you specified. How could you know how much energy was stored in it once the mass was raised to full potential (probably a bit over 90degrees) ?

If anyone is interested enough, or knows already could you share?
Thanks!

 

[CWatters]

The energy E stored in the trebuchet is simply...

E = mgh

m=mass of counterweight
g = acceleration due to gravity
h = height the counterweight falls (find using geometry).

Not all of that energy goes into the projectile because the counter weight has KE at the bottom.

The maths for this light is much the same...

http://science.howstuffworks.com/environmental/green-tech/sustainable/gravity-powered-lamp.htm

although there is a problem using gravity for lighting which I will let you figure out using the following...

Energy = power * time

so

power * time = mgh

Pick a power for your light...say 40W
Pick a run time...say 1 hour or 3600 seconds
Pick a height for your lamp...say 1meter

The required mass is ??

 

[toneboy1]

Right'o, ok so say we're running 40W (friction etc ignored), then if our mass is 500kg, g = 9.8Nm^2, and the counterweight is 15m high then it will run for half an hour?

500*9.8*15 / 40 = 1837.5 seconds = 30.635

(meaning that there is 73500 N of energy stored in it? (40W*1837s))

Nice article about the lamp btw, though I would have thought it would have made more sense to keep the energy mechanical rather than lighting LEDs with it.

 

[CWatters]

Right'o, ok so say we're running 40W (friction etc ignored), then if our mass is 500kg, g = 9.8Nm^2, and the counterweight is 15m high then it will run for half an hour?

Not exactly going to be a small desk lamp then :-)

In short. Gravity is relatively a weak force.

 

[toneboy1]

Not exactly going to be a small desk lamp then :-)

In short. Gravity is relatively a weak force.

Well you say that, but if you engineered a skyscraper so that it could be ratcheted up a few inches over the day from wind and solar power you've got yourself a respectable battery. XD