How does a balance work?

1. Dec 12, 2005

eosphorus

ive asked this before but i was answered that what made me think a vertical balance should level to horizontal. well here is a reason:

http://www.pbs.org/weta/roughscience/series3/gold_rush/balance.html

if the weights are the same in both arms and you lean the balance 45º it will go to horizontallity but how? if the horizontal arms are equal in both sides and also the weight, how gravity level the balance if the axle is exaclty in the middle of the bar?

how comes that gravity produces movement when the balance goes from vertical to horizontal without lowering the center of gravity of the balance?

2. Dec 12, 2005

nazgjunk

Basically, you are wrong. If you have a balance, equal weights and distances on both sides, you can turn it all around as much as you want, gravity will not have an effect on things.

Try to draw the following, because my ascii art wasnt really working out.

A and B are of the same weight, the distances to the point of balance are the same. The effect a body has on a balance is defined as [itex]M=Fr[/itext], where F is the force (in Newton) that acts upon a body, r the distance to the balancing point (horizontally measured), and M the momentum. I hope you can see that M is the same for both A and B.

I would like to excuse for my English. My English is fine, but related to physics, it is crap. If anyone could point me to a list of physics vocabulary or something, I'd be very grateful.

Last edited: Dec 12, 2005
3. Dec 12, 2005

eosphorus

probably who built this center beam balance didnt know about momentum:

http://en.wikipedia.org/wiki/Image:Balance_scale.jpg [Broken]

if this doesnt level whats the needle for?

i know an offcenter beam balance levels because it works as a pendulum

but i cant understand how a center beam balance like the one in the picture works

Last edited by a moderator: May 2, 2017
4. Dec 12, 2005

nazgjunk

Yugh, my teacher is going to be angry at me for this. I have been doing this stuff endlessly last year... yugh again.

Well, I've got physics class again tomorrow, I might ask him

/me is very annoyed with himself...

EDIT: Afaik, with the wiki picture you showed, you can only check if two things are of the same weight, but you are right about the needle. Oh, btw: no one ever built this thing, it's a 3D picture. I think such things with needles would require some more work with springs and stuff.

EDIT again: BUST: i quote from the wiki site you posted:
That is the only function of the needle.

Last edited: Dec 12, 2005
5. Dec 12, 2005

DaveC426913

I am not sure if this helps you or not.

If the distribution of weight in the balance is vertically aligned with the axle (i.e. height above ground), a balance will not level itself (i.e. it will not work as a balance at all). The centre of mass must hang *below* the axle.

However, in a proper balance, the CoM hangs below the axle. If you attempt to rotate the freely moving part of the balance through any angle, you are actually raising the centre of mass. The balance, left to its own devices will attempt to keep the mass as low as possible.

See diagram.

Last edited: Jul 20, 2007
6. Dec 12, 2005

Astronuc

Staff Emeritus
Slight correction, M would be the moment, which is the product of the forc F and the moment arm, r, which is the distance between the point of action by force F and the pivot point. With respect to the balance, the force F is just the 'weight', which equals the product of the mass and acceleration of gravity, i.e. mg.

On the balance, the moments must be equal for the balance to be horizontal.

If the fulcrum is rotated about the pivot, but the pivot point does not move with respect to either moment arm, then the balance arm stays horizontal or in whatever equilibrium position in which it settles before the fulcrum is rotated.

In general, Momentum is considered the product of mass and velocity.

7. Dec 12, 2005

nazgjunk

Sorry, stupid piece of translation. We don't learn any english terms at school...

8. Dec 12, 2005

eosphorus

if the pans are hanging like the ones in the picture the center of gravity will also be always lower than the axe

i have tested it my self, a beam centered balance will level very weakly not as strong as an off centered balance but it will level

this makes it ideal for high precision measures, because a tenth of gram difference will make the balance much more vertical in a centered beam balance than in a off centered beam balance

but how is produced this levelling if the center of gravity remains constant

9. Dec 12, 2005

eosphoro

thanks for your time dave but i disagree with you in what you say it doesnt act as a balance when the center of mass is in the axe:

the simplest balance of a beam hold in a razors edge will level even the center of gravity is above the razor edge or axe of spin

i linked this balance picture that falls into what you calify as not acting as a balance

i put a needle in the middle of a straw and put one gram of plastiline in each end of the straw

i built a support out of a meccano and shaped the plastiline so the straw would balance

i would test it also with the straw upside down to make sure the center of gravity of the straw was in the needle axe and not over or under the axe

the straw would level even when you put the straw upside down to make sure it wasnt working because the center of mass was under the axe

if you want to reproduce the experiment to see how a balance will level eve though the CoM is in the axe remember it took me two hours to shape the plastiline right

10. Dec 12, 2005

Staff: Mentor

You provided two links. In both of them, the center of mass is below the axis.

11. Dec 12, 2005

eosphorus

http://en.wikipedia.org/wiki/Image:Balance_scale.jpg [Broken]

http://members.aol.com/ricnakk/scale.html [Broken]

you are right doc in this two cases the center of gravity is under the axe i got confused because the balance i built has the CoG and axe in the same spot and it works

but still analize the two balances provided by the links

consider the balance has a 2 meters long beam and the pans are hanging down one meter, total potential energy with respect to the axe when levelled -1m-1m=-2m

now put the balance vertical it will have 0m-2m=-2m

the pans will always add a total potential energy of -2m however the position

obviously these balances work because otherwise they wouldnt have been built

my question is if starting from vertical with a total potential energy of -2 the balance levels and ends with a potential energy of -2 what has caused this levelling if no potential energy has been spent

Last edited by a moderator: May 2, 2017
12. Dec 12, 2005

daniel_i_l

This only happens because the razor isn't perfectly sharp. Because of this, as the razor tilts in one direction, the axis will shift in that direction making the other end pull down a little harder. If the razor blade had a perfect point then it would never go to horizontal from a non horizontal position.

13. Dec 12, 2005

Homer Simpson

Anything where the combined CoM of the axe is below the fulcrum point will balance out if each side balanced

Anything where the combined CoM of the axe is in plane with the fulcrum will stay where it is if each side balanced (like a 2 vane airplane prop)

Anything where the combined CoM is above the fulcrum will begin topple as soon as the CoM moves left or right of the fulcrum point. Like the razor blade and beam example, consider the beam having a height equal to its length, the effect is amplified.

Just sum all the moments. That said, my mental picture would agree with you: If the axe is straight, and pinned at the center, no friction, infinately small pin, I think that the suspended tray version would stay in whatever position you put it in if both sides are balanced. The moments would be excacly the same for CW and CCW.

14. Dec 12, 2005

eosphorus

http://en.wikipedia.org/wiki/Image:Balance_scale.jpg [Broken]

what i dont see is how this balance works because the moments are the same always in both arms

even the force that levels the balance has to beat the vertical needle that tends to go down

so can anyone explain me how this balance works because according to you i understand it shouldnt work as shouldnt work the balance i built

besides in the razor edge and beam balance which i suppose someone must know about because once i was given here its oscilation phrequency
i agree that one arm becames bigger than the other when leaned because of the thickness of the blade

but on the other hand the center of g of the beam is displaced to a side of the axe much more when leaned that what an arm grows with respect to each other because of the thickness of the blade because the beam is thousands of times thicker than the blade

Last edited by a moderator: May 2, 2017
15. Dec 12, 2005

Homer Simpson

In that exact picture, the only thing that I can see that would cause it to act as a balance is the enlarged diameter ends where the trays attach. Because of the larger diameter, the downward force is actually applied slightly below the center of the bar. So, as it tips over, the moments would not be equal. If the trays were attached to the very center of that bar, this would not be true.