Gravity equivalent of Ohm's law

[Nathi ORea]

Conceptually I have never really understood Ohm's law, other than using it in calculations. My brain just cannot understand why this equation works.

I was wondering if there is some sort of gravity equivalent to perhaps conceptualise it a bit better.

Voltage: would be the acceleration due to gravity: 9.81 m/s/s.

Resistance: Perhaps the slope of something falling down, like down an incline ramp?

Any help would be much appreciated

 

[PeroK]

Your question makes no sense to me, I'm sorry to say.

 

[A.T.]

I was wondering if there is some sort of gravity equivalent to perhaps conceptualise it a bit better.

Voltage: would be the acceleration due to gravity: 9.81 m/s/s.

Resistance: Perhaps the slope of something falling down, like down an incline ramp?

If anything, then the analogy would rather be:

Voltage: height difference between two points.
Electric field strength: slope of the incline.
Resistance: friction on a sliding block

But I assume this analogy will break down in many aspects.

 

[Nathi ORea]

Sorry I screwed up.

Wouldn't the gravitational field equivalent of voltage which is work per unit charge;

V = W/q
V= qEd/q
V= Ed

be

Work per unit mass

V(g) = W/m
V(g) = mgh/m
V(g) = gh

V(g) means 'gravitational' voltage

 

[Dale]

Summary:: Is there an gravity equivalent of Ohm's law?

Conceptually I have never really understood Ohm's law, other than using it in calculations. My brain just cannot understand why this equation works.

Looking for flawed analogies is going to be a waste of time.

Do you understand voltage and current?

For any material you can plot voltage vs current. For some materials, when you do that you get a straight line.

 

[davenn]

Sorry I screwed up.

Wouldn't the gravitational field equivalent of voltage which is work per unit charge;

V = W/q
V= qEd/q
V= Ed

be

Work per unit mass

V(g) = W/m
V(g) = mgh/m
V(g) = gh

V(g) means 'gravitational' voltage

Why are you making something very easy, much more difficult ?

There's no relationship/association between the other things you are trying to associate with V, I and R

cover the one you want to find and do the math on the other two

"I" is inversely proportional to resistance -- increasing the resistance decreases the current for a given voltage
"R" is inversely proportional to current -- an increase in the current means the resistance has to decrease for a given voltageOthers here may like to add more combinations :)

 

[anorlunda]

I'm not sure what the OP wants. Perhaps f=ma. Perhaps $f = (\frac{Gm_1}{r^2})m_2$

 

[DaveE]

Summary:: Is there an gravity equivalent of Ohm's law?

Conceptually I have never really understood Ohm's law, other than using it in calculations. My brain just cannot understand why this equation works.

I was wondering if there is some sort of gravity equivalent to perhaps conceptualise it a bit better.

Voltage: would be the acceleration due to gravity: 9.81 m/s/s.

Resistance: Perhaps the slope of something falling down, like down an incline ramp?

Any help would be much appreciated

You'll learn more about this stuff in your upcoming physics classes (or self-study). In the mean time, if I were you, I would focus on learning more about electricity and gravity as separate subjects. In order to compare (or unify) two different models, you will first need to understand those models pretty well.

BTW, if you do come up with a real unification theory between gravity and electricity, you will will all of the prizes. (Nearly) every one of the theoretical physicists out there have been trying to do this for decades. You just may have accidentally picked the hardest problem ever. Of course all of their work is way too complex for us to understand; way, way, way beyond classical physics.

 

[A.T.]

Sorry I screwed up.

Wouldn't the gravitational field equivalent of voltage which is work per unit charge;

V = W/q
V= qEd/q
V= Ed

be

Work per unit mass

V(g) = W/m
V(g) = mgh/m
V(g) = gh

V(g) means 'gravitational' voltage

This is fine, as it's just the general concept of a potential. But to extend the analogy to Ohm's Law, you need to postulate some mechanical resistance that matches it, so that the mass flux (~= current) is proportional to work per mass (~= voltage).

 

[sophiecentaur]

Why are you making something very easy, much more difficult ?

Absolutely.
There's nothing wrong with OP looking for analogies but that's the sort of exercise to be done privately in one's head. I'm sure we all have some very questionable private models about these things, going on in our heads, but the way to communicate things (particularly the relationship between V and I) is to use Maths, which is a good common language.

I do have a problem with the habit of calling R=V/I "Ohm's Law", though. As a Law, that expression is incomplete and misses out the fact that an 'Ohmic' resistor maintains that rational relationship only at constant temperature and it basically only describes metals. We don't call Velocity = Distance / time the "velocity law" (or choose any other 'triangle' formulae) so why "Ohm's Law?

 

[jbriggs444]

There's nothing wrong with OP looking for analogies but that's the sort of exercise to be done privately in one's head. I'm sure we all have some very questionable private models about these things, going on in our heads, but the way to communicate things (particularly the relationship between V and I) is to use Maths, which is a good common language.

Strongly agree. My mental model for a resistor involves a viscous fluid in a pipe so that flow is proportional to pressure difference. But I try to think this way privately and am a bit ashamed to be talking about it in public.

 

[DaveE]

I do have a problem with the habit of calling R=V/I "Ohm's Law"

Me too. I've always thought it was more of a definition of terms than a "law". Although. I suppose you could say the same thing about F=ma, too. Perhaps my problem is that I don't actually know what a law is, really.

 

[sophiecentaur]

Me too. I've always thought it was more of a definition of terms than a "law". Although. I suppose you could say the same thing about F=ma, too. Perhaps my problem is that I don't actually know what a law is, really.

There is a big difference here, though. m doesn't change during the 'graph plotting' experiment but R can vary unless all the Ohm's Law conditions are satisfied

I try to think this way privately and am a bit ashamed to be talking about it in public.

Haha No shame involved. I bet you sometimes check on simple arithmetic with your fingers too as we all do.

 

[Fredbonyea]

Ohm's Law is like the perfect gas laws, it is idealistic, and it does not 'translate' well to gravity and inclines. A much better analogy is water pressure and current. Current is the pipe diameter, pressure is the voltage, and resistance is the function of a valve in the pipe, The amount of current is the pipe diameter times the pressure, divided by the resistance of the valve. Few valves are actually linear, but likewise it takes special care to make a truly linear resistor.

BTW, if you do come up with a real unification theory between gravity and electricity, you will will all of the prizes. (Nearly) every one of the theoretical physicists out there have been trying to do this for decades. You just may have accidentally picked the hardest problem ever. Of course all of their work is way too complex for us to understand; way, way, way beyond classical physics.

It is interesting that there is a measurable voltage differential that is function of the derivative of the altitude. I know a model airplane enthusiast who built an altitude control that depended upon the voltage differential between the top and the bottom of the plane, and it worked quite will.

 

[sophiecentaur]

resistance is the function of a valve in the pipe,

Interesting that you use a valve and not a hydraulic motor - which will actually transfer some useful and measurable energy. Sharing a common mathematical form doesn't indicate any significant analogous physics. The hunt for the analogy seems to occupy a lot of some peoples' time. We have Maths for this sort of thing.

 

[DaveE]

Interesting that you use a valve and not a hydraulic motor - which will actually transfer some useful and measurable energy. Sharing a common mathematical form doesn't indicate any significant analogous physics. The hunt for the analogy seems to occupy a lot of some peoples' time. We have Maths for this sort of thing.

Yes. Analogies are always wrong. Useful in many ways, but ultimately wrong. That's why they're called analogies.

IMO, after analogies are use to teach a concept, the instructor should point out (as soon as they can) how they break down, just so they don't leave students with a misleading model.

 

[Fredbonyea]

Interesting that you use a valve and not a hydraulic motor - which will actually transfer some useful and measurable energy. Sharing a common mathematical form doesn't indicate any significant analogous physics. The hunt for the analogy seems to occupy a lot of some peoples' time. We have Maths for this sort of thing.

Yes, that is a better analog because a hydraulic motor or water wheel does work. The valve analogy works if you are fighting a fire: The height of the column of water is closely related to the pressure (voltage) and the volume (current) of water that you can push though the nozzle is dependent upon the diameter of the pipe.

 

[sophiecentaur]

the instructor should point out (as soon as they can) how they break down

But they never hear that bit. Water going through pipes is a much more powerful picture than abstract Amps and Volts so it's the water that sticks. Also, the instructor often doesn't realize the shortcomings of his analogy and both he and the student go away thinking that the message has got across.

 

[DaveE]

But they never hear that bit. Water going through pipes is a much more powerful picture than abstract Amps and Volts so it's the water that sticks. Also, the instructor often doesn't realize the shortcomings of his analogy and both he and the student go away thinking that the message has got across.

Yes, but I think you have to use analogies anyway. You can't teach physical sciences without simplification.

It is a fundamental, unavoidable, dilemma: what should you teach given that you can't teach the whole thing at once, and that students may leave school before they have learned everything that's possible to teach? I claim there is no simple answer, we just have to muddle through. Education is always incomplete.

I'm reminded of that old joke; every physics class begins with "What we taught you last year was wrong."

 

[A.T.]

Yes, but I think you have to use analogies anyway. You can't teach physical sciences without simplification.

General concepts like energy and potential apply to both cases, and should very much be related using analogies. But when you try to analogize all of it, you might find that the resulting contrived mechanical systems are not necessarily much simpler or intuitive to students, than the electric ones.

 

[cmb]

Summary:: Is there an gravity equivalent of Ohm's law?

Conceptually I have never really understood Ohm's law, other than using it in calculations. My brain just cannot understand why this equation works.

I was wondering if there is some sort of gravity equivalent to perhaps conceptualise it a bit better.

Voltage: would be the acceleration due to gravity: 9.81 m/s/s.

Resistance: Perhaps the slope of something falling down, like down an incline ramp?

Any help would be much appreciated

To the OP; don't feel negative about it. Whenever someone looks for an analogy to Ohm's Law one can expect resistance. I am sure a gravity analogy will have potential.

;)

 

[vanhees71]

Interesting that you use a valve and not a hydraulic motor - which will actually transfer some useful and measurable energy. Sharing a common mathematical form doesn't indicate any significant analogous physics. The hunt for the analogy seems to occupy a lot of some peoples' time. We have Maths for this sort of thing.

And I don't understand this hype about this "hydro-em analogy" at all. Hydrodynamics, as a set of non-linear partial differential equations, is more complicated than electromagnetism as long as you stick to the usual linear-response theory of the constitutive equations in the introductory E&M lecture.

 

[anorlunda]

And I don't understand this hype about this "hydro-em analogy" at all. Hydrodynamics, as a set of non-linear partial differential equations, is more complicated than electromagnetism as long as you stick to the usual linear-response theory of the constitutive equations in the introductory E&M lecture.

Surely your joking Mr. vanhees. Analogies appeal to people trying to avoid thinking about equations.

 

[sophiecentaur]

Surely your joking Mr. vanhees. It appeals to people trying to avoid thinking about equations.

. . . . and I'm not sure that's not written with tongue in cheek.
"10% inspiration and 90% perspiration" is the quote, I believe.

 

[DaveE]

And I don't understand this hype about this "hydro-em analogy" at all. Hydrodynamics, as a set of non-linear partial differential equations, is more complicated than electromagnetism as long as you stick to the usual linear-response theory of the constitutive equations in the introductory E&M lecture.

Yes, it's not great. But it is something that people have some real world experience with. They think they understand water flow, so it's a place to start. If you feel you need an analogy to something people have experienced, I'm not sure there's a better one. At that level no one knows about non-linear PDEs or how either water or electricity really works.

 

[Swastik Majumder]

There is a thermodynamics equivalent. Heat and ohms law can be compared. Resistance can be compared to conductivity of material and current as rate of flow of heat. Heat flow rate = Difference in temperature on ends/ (l/kA)
A is area and l is length of the metal. k is a constant for the metal. Change in tempuerature can be compared to voltage. Even flow of heat follow laws like resistors.

 

[cmb]

I think there are a lot of analogies one can use to illustrate Ohm's law, but more interestingly are there any analogies for gravity?

The only way to describe gravity is to describe gravity, it seems! It is just not obvious it is even there, until it is pointed out to someone! Hence the mocking of Newton when he famously 'noticed' it (for the first time? Can that be argued at a scientific POV?) and 'set things in motion' (pun intended) in the field of mathematical dynamics.

 

[sophiecentaur]

The only way to describe gravity is to describe gravity,

Agreed. Any Analogy needs to include a whole list of caveats. People don't read caveats. They very often get things wrong, as a result. The only 'analogy' that's respected is Maths. Even then, the limits (caveats) still apply.
Anyone who says that they 'get' the Maths but still want a 'Physical Explanation' has not really 'got' the Maths and they probably can't be bothered. The understanding process halts there.

 

[vanhees71]

The only analogy coming to my mind is the fact that the Newtonian gravitational-field potential is described by Poisson's equation,
$$\Delta \phi=-4 \pi G \rho,$$
where $\rho$ is the mass density as a source of the gravitational field $\phi$, as is the electrostatic potential in electrodynamics.

 

[anorlunda]

Don't forget that Ohm's Law V=IR expresses simple proportionality. Quantity A is proportional to quantity B scaled by a constant. The value of the constant depends on the units of measurement.

That must be the simplest of all nonzero kinds of relationships. Using Occam's Razor, we should expect more analogies of that than any other kind of relationship.

 

[vanhees71]

I still don't understand, where there should be an analogy between Ohm's Law and Newtonian gravitation. Maybe, if you consider the simple Drude model of conductivity, it's the fall of a not too fast body including linear friction, but what does this analogy help in any way. At the end you have to solve the (not too complicated) equation of motion
$$\ddot{x}=g-\gamma \dot{x}.$$
Where $g=q E/m$ for a charge in a homoegeneous electric field within a conductor or $g=9.81 \, \text{m}/\text{s}^2$ and $\gamma$ some friction coefficient.

 

[sophiecentaur]

I still don't understand, where there should be an analogy between Ohm's Law and Newtonian gravitation.

Shared maths formulae is not 'analogy'. If that's all that's needed then any straight line would do. We are chasing our tails here. As I commented further up, analogies are best kept as a personal secret or between two people who really are on the same hymn sheet. Trying an analogy with a class of kids can guarantee some of them will get it wrong - if your criterion is other than to make them vaguely familiar with an idea.
Also, this hymn sheet must include shared class, social culture and generations. Try to use the water analogy with someone who uses a pump for their water supply, for instance. They may be far more familiar with the electrical circuit of their solar panels than a non-existent running water supply. Other non-parallels may be much more subtle.

If God had intended us to use analogies, he would never have given us MATHS.

 

[anorlunda]

Shared maths formulae is not 'analogy'.

What he said.