Little physics question: potential energy / free fall

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Remundo
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by Remundo » 07/04/10, 16:39

Hi buddies...

Elephant talks about bringing the mass down ... by raising another of the lower mass.

I have the impression that you forget that the latter takes the potential energy of gravity during its ascent. :P

The kinetic energy acquired by the heaviest mass is therefore much lower than that which would be acquired by free fall ...

Let 1 be the index for mass 1,
Let 2 be the index for mass 2

We assume the altitude h for the descending mass, and 0 for the rising. At the end of the movement, the altitudes are swapped.

The system evolves to constant mechanical energy. The mechanical energy balance gives:


m1 gh = 1/2 (m1 v1² + m2 v2²) + m2 gh

As v1 = v2 by inextensibility of the cable ...

(m1 + m2) v² = 2gh x (m1-m2)

From where v² = 2gh (m1-m2) / (m1 + m2)

When m2 = 0, we find the famous expression "v² = 2gh" of free fall.
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by zorglub » 07/04/10, 17:01

except that in the case cited in reference, we slow down the descent of the main weight by another mass which obviously says to be taken into account, which should change the result

damn, I had not read the previous message! which must be the obvious mathematical solution
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by zorglub » 07/04/10, 17:07

in summary the energy of the mass which "goes down" is the result of the energy of the mass which falls minus the energy of that which goes up
ignoring friction
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by elephant » 07/04/10, 19:16

Aaah Remundo to the rescue!

Elephant talks about bringing the mass down ... by raising another of the lower mass.


Not quite !

In both cases, it is about harnessing energy, of course. But in the second case, the mass is indeed free to fall with an acceleration g, we want to recover its kinetic energy, plus its weight when it hits the ground heavily (ouch :D )
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by Remundo » 08/04/10, 18:11

Hi Elephant,

I do not understand well because a weight is not an energy ... :?

En the absence of any dissipation and in free fall, you can only recover mgh on impact. 8)
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by Christophe » 08/04/10, 18:13

Remundo wrote:I do not understand well because a weight is not an energy ... :?


A weight is a force.

It depends on the point of view ... it can be a potential energy ... in both senses of the word!

A mass at X m height = energy potentially released if the mass "falls".
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by elephant » 08/04/10, 20:56

Remundo:

you're right, but going down (quickly or slowly), it can produce a job: going up an elevator or smashing a floor (or squeaking a piiiiiiiiiied! : Cry: )
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by Aumicron » 14/04/10, 09:56

For formula pros, a quick question on this subject:

https://www.econologie.com/forums/petite-que ... t9597.html

Goods.
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