# Thread: I need to prove these two things require equal energy to do.

1. You have a bucket of water.

I want to put 10cm/3 of air 10 cm under the waterline.

First way: I push it down from the top with a weight. Eks a tube vertical and 10 cm into the water. Then push 10cm/3 down there through the tube with a weight or pump of some kind.

Second way: I drill a hole in the bucket 10 cm under the waterline and put a tube in there. And then press 10cm/3 of air in.

Can anyone help me prove that these two things take the same amount of energy? Any help would be much appriciated.

Thanks

2.

3. I assume you mean 10 cubic centimeters of air? The work required to pump the air into the bucket will be the pressure multiplied by the volume. The pressure in each case will be 10 centimeters multiplied by the density of water multiplied by the acceleration due to gravity. The volume is 10 cubic centimeters.

4. Yes i mean 10 cubic centimeters of air.

I am not very good at math.

I need to know if the second method requires less enenrgy than the first one.

Any help would be much appriciated

Thanks

5. Is this homework? If it is, we can't work it for you.

6. But we can advise you to use Pascal's law.

7. The fact that they both amount to doing the same thing isn't proof enough? It sounds like your first and second option are both describing the same thing, with the only difference being that in the second option the air ends up being in a bucket. Maybe I'm not understanding you correctly...

8. I think perhaps the intent was, in the first method you would take a balloon or something filled with air and submerge it.

9. Originally Posted by Harold14370
I think perhaps the intent was, in the first method you would take a balloon or something filled with air and submerge it.
So either you push a container+air into the water, or you push just air into the water while the container stays stationary...but we're obviously supposed to neglect the container and consider just the air, which seems to negate the only difference between the two scenarios.

10. Hello again

It is not homework :-) I just need to convince a friend that i am right.

@Harold. A Baloon describes the first scenario much better. thank you very much.

1 Scenario. Press a baloon with 10 cubic centimeters of air 10 cm under the water.

2 Scenario. Or press the air (10 cubic centimeters) through the side of the container. Via a hole in the container 10 cm beneath the water surface.

These two examples creates precisely the same updrift. And therefore i assume that it takes precisely the same energy to put the air there. Thats the only argument i have. I would just very much like it to be put in numbers so i can prove it.

And again it is not homework. I am 27 years old and having a discussion with a friend.

Thanks for the replys so far.

11. I dont know if it is allowed here in the forum. But anyone that can give me the answer in math (psysics) will get a reward in form of \$. Lets say 15 \$ for the trouble of setting it up.

Paypal or Neteller

Thanks

12. The formula for work is force multiplied by distance. In the first method, the force is the buoyancy of the balloon, which is equal to the weight of the displaced fluid. We will assume the weight of the air is negligible. The weight of the displaced fluid is 10 cubic centimeters multiplied by the density of water, which is 1 gram per cc, multiplied by the acceleration due to gravity,g. So the force is 10 grams*g. The distance is 10 centimeters so the work is 100*g.

In the second method we could have a piston of 1 square centimeter cross-sectional area, and if the stroke of the piston is 10 centimeters, we would inject 10 cubic centimeters with one stroke. The force would be equal to the pressure multiplied by the cross-sectional area. The pressure at a depth of 10 centimeters under water is found by the formula rho*g*h where rho is the density of water, 1 gram per cc. So the pressure is 10*g, the force is pressure multiplied by the cross-sectional area of the piston, which is 1 square centimeter, so force = 10*g*1, and work is force* distance, or 10*g*1*10, or 100*g.

13. Originally Posted by Harold14370
The formula for work is force multiplied by distance. In the first method, the force is the buoyancy of the balloon, which is equal to the weight of the displaced fluid. We will assume the weight of the air is negligible. The weight of the displaced fluid is 10 cubic centimeters multiplied by the density of water, which is 1 gram per cc, multiplied by the acceleration due to gravity,g. So the force is 10 grams*g. The distance is 10 centimeters so the work is 100*g.

In the second method we could have a piston of 1 square centimeter cross-sectional area, and if the stroke of the piston is 10 centimeters, we would inject 10 cubic centimeters with one stroke. The force would be equal to the pressure multiplied by the cross-sectional area. The pressure at a depth of 10 centimeters under water is found by the formula rho*g*h where rho is the density of water, 1 gram per cc. So the pressure is 10*g, the force is pressure multiplied by the cross-sectional area of the piston, which is 1 square centimeter, so force = 10*g*1, and work is force* distance, or 10*g*1*10, or 100*g.
Or you can simply invoke conservation of energy. If the initial states and final states are the same then the work required to reach those states is also the same.

BTW you actually must assume that the weight of the balloon is negligible since otherwise the energy of the initial states is not the same -- the second scenario starting at lower gravitational potential energy.

14. Thank you cery much :-)

Just what i need

Just tell me where to send the reward :-)

15. Originally Posted by Uberkelner
Thank you cery much :-)

Just what i need

Just tell me where to send the reward :-)
Send the reward to the National Rifle Association, Institute for Legislative Action.

16. Originally Posted by DrRocket
Originally Posted by Uberkelner
Thank you cery much :-)

Just what i need

Just tell me where to send the reward :-)
Send the reward to the National Rifle Association, Institute for Legislative Action.
Good idea. You can send my half there too.

17. Hmm.

I can send the money to you. I live in Denmark and we dont have weapons in our household. And it is certainly not something i support.

Weapons in the household are for 3rd world countries as far as i am concerned.

But you are welcome to give me an account i can transfer to.

18. Originally Posted by Uberkelner
Hmm.

Weapons in the household are for 3rd world countries as far as i am concerned.
No they are for the top of the first-world countries that value individual rights and freedoms and do not intend to become third-world countries, like the U.S. and Switzerland.

It why Denamark was occuppied in WW2 but Finland defended itself.

"You cannot invade the mainland United States. There would be a rifle behind each blade of grass." -- Admiral Isoroku Yamamoto

19. http://factcheck.org/2009/05/misquoting-yamamoto/

We make no argument either for or against gun ownership. But we do object to fabricating quotes and passing them off as historical fact.

20. Originally Posted by Bunbury
http://factcheck.org/2009/05/misquoting-yamamoto/

We make no argument either for or against gun ownership. But we do object to fabricating quotes and passing them off as historical fact.
Who knows ? Yamamoto is dead. One guy says that the quote is misatributed.

But there are many places where one can find that quote. If he did not say it, then maybe he should have.

I can assure you that during the cold war, Russian officers stationed near me visited local gun shows and took note of an armed citizenry.

http://www.skylighters.org/quotations/quots6.html

http://www.rmgo.org/quotes.shtml

http://www.larrywillis.com/quotes.html

http://www.rmgo.org/quotes.shtml

21. Originally Posted by DrRocket
Originally Posted by Bunbury
http://factcheck.org/2009/05/misquoting-yamamoto/

We make no argument either for or against gun ownership. But we do object to fabricating quotes and passing them off as historical fact.
Who knows ? Yamamoto is dead. One guy says that the quote is misatributed.

But there are many places where one can find that quote. If he did not say it, then maybe he should have.
I'm not interested in debating gun control in a Physics thread. It's the way your usual skepticism deserted you as soon as your pet beliefs became the subject that suprised me.

22. Originally Posted by Bunbury
Originally Posted by DrRocket
Originally Posted by Bunbury
http://factcheck.org/2009/05/misquoting-yamamoto/

We make no argument either for or against gun ownership. But we do object to fabricating quotes and passing them off as historical fact.
Who knows ? Yamamoto is dead. One guy says that the quote is misatributed.

But there are many places where one can find that quote. If he did not say it, then maybe he should have.
I'm not interested in debating gun control in a Physics thread. It's the way your usual skepticism deserted you as soon as your pet beliefs became the subject that suprised me.
It is not a lack of skepticism regarding history or the accuaracy of the citation. I just don't care if he actually said it or not. Historical accuracy of the quote is not the issue.

23. Guerilla war can only be succesfull in countries where there is no or almost no citizens registration. The access to such information is far more critical then if there are guns or not.

24. Originally Posted by Ghrasp
Guerilla war can only be succesfull in countries where there is no or almost no citizens registration. The access to such information is far more critical then if there are guns or not.
Ah yes, coming from a country occupied by the Nazis in which guns and radios were confiscated.

http://www.stephenhalbrook.com/regis...istration.html

http://www.zum.de/whkmla/sp/0910/bhw/bhw1.html#v

We are way off topic now and apparently not headed back to the question of the OP. Perhaps this should be taken to another forum.

25. I was referring to citizens registration, not registration of armery there wasn,t such a registration in Holland. To fight a guerilla war if the occupating force has acces to registration of familyties, adresses aso (as they did in Holland) means all relatives have to join the guerilla,s, or hide somewhere all of which puts there lives in too much danger. In practice it means that a guerilla war is not gonna happen when there is such a registration. As far as I know the us has such a registration just as well.

On topic ,

I,m not convinced the energy needed is the same. Entropy before and after is not the same for both situations air from different altitude has never exactly the same temperature.

Energywise the situation after may be the same and the situation before also but that is not a guarantee the energy is the same.

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