Little physics question: potential energy / free fall

[elephant]

A little question that bothers me:

Let a rock of mass M,

I tie it to a cable and using a pulley I make it do a job T by making it descend slowly on a slope of a height h. (for example by balancing it with a mass slightly lower than hers)

ou

I exploit the energy mV² / 2 by dropping it violently on a target on this same height h

is there equality between the energies produced?

(I know, I'm probably mixing 2 things)

[STF]

Mix I don't know, but you will clearly have more strength when you drop it, when you put it down, put a hammer (even a heavy one) on a nail, you will see that it works better by tapping.

Or are you talking about the energy produced by the displacement, the same, but depending on what you want to move (that's how I understand it) you will have to calculate its stroke with the mass in rapid motion since the possible link will collect all the energy before retransmitting it.

If you can specify more? ..

STF

[Christophe]

is there equality between the energies produced?

Yes perfect equality in terms of energy provided that you neglect the friction of the air or the pulley / rope ...

This is how the Egyptians managed to climb pyramids, and closer to "us", that we built cathedrals ... with "animal / human" force and without the least electric or petroleum joule. . just had to take the time!

[zorglub]

energy yes, because the mass is identical as well as the length of the displacement
power no because there comes the time unit

[elephant]

would someone be kind enough to write the 2 equations?

[Geepy]

1st case: T = Mgh (differences in potential energies)

2nd case: E = 1/2 MV² / 2
with V = (2gh) ^ 1/2 (which you demonstrate by starting from the basic equation "sum of the forces = M x acceleration of the solid", which here is equal to g, only gravity is involved)
By replacing V, you get E = Mgh

[elephant]

Thank you Geepy and welcome, I see that this is your 2nd message.

[Christophe]

This results in the equality of energies T = E but valabe only without friction! (That's what I said from the start ...)

If you want the equations with friction, it's there:
http://www.wikiprepas.org/index.php/Chu ... frottement

But it is complicated a chouilla ... Remundo will be welcome to help

Uh but pkoi this question by the way?

ps: zorglub you are right but we are not talking about power but about energy

[elephant]

I wanted (I'm not very good at mechanics) a mathematical explanation of the non difference in energy between a violent fall and a gentle descent (in a way "what is the heaviest, a kilo of feather or a kilo of lead?)

Thank you all.

[Christophe]

Well mathematically and without friction there is no difference.

But physically taking into account friction, since they are proportional to the speed of movement, then the energy accumulated in the stone during free fall will be LOWER than that accumulated during a slow climb ... neglected climb mechanism.

So 1 kg of feathers and 1 kg of lead do not fall at the same speed in the air (except at the "very beginning" of the release) unless their volume / strongly / surface are identical (same "capsule")!

Obviously with the naked eye on 1 or 2 m of fall we do not see the difference.