# Physics Q&A Game

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Just like the Astronomy Q&A game in the Astronomy forum, let's play a physics Q&A game here. The astronomy game has certainly taught me some very neat facts -- maybe this one will do the same.

I'm going to post one question posed by marcus:

"A favorite version of the question chroot just answered is the one about the airplane flying the polar route. It is going 200 meters per second and its wingspan is 30 meters----what is the voltage difference between the two wingtips? I am not asking this question because it is a cousin of the one asked by Ivan, just recalling it. the plane is in a region where the Earth's magn. field is roughly vertical and of such and such a strength etc etc."

It seems that there should be no voltage. Faraday's law dictates that

E = -N d[phi]/dt

Since [phi] is defined as the flux: [phi] = B * A, where B is the magnitude of the magnetic field and A is the area enclosed by the loop. In this problem, neither A nor B is changing -- so the induced voltage should be zero.

Am I right? Was it really just a trick question?

- Warren

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-[30X200][50X10^-6][+-30]= +-9 volts

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Tyger

When the plane takes off a voltage will be induced across the wings, and it will be sustained in flight. But you can't measure it with a voltmeter across the wingtips because the very same induction will occur with the meter leads. However, if the plane can land with the charge on the wingtips remaining, it can be measured on the ground with an electrometer, which is a very sensitive voltmeter.

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Originally posted by Tyger
When the plane takes off a voltage will be induced across the wings, and it will be sustained in flight. But you can't measure it with a voltmeter across the wingtips because the very same induction will occur with the meter leads. However, if the plane can land with the charge on the wingtips remaining, it can be measured on the ground with an electrometer, which is a very sensitive voltmeter.

I bought perfect test leads for my perfect voltmeter. They have them down at the gedunken supply house.

Re: "There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."

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Originally posted by Ivan Seeking
-[30X200][50X10^-6][+-30]= +-9 volts

30 meter wingspan x 200 meter/sec speed
x 50 microTesla (the vertical component of the geomagn. field)

let's see how that multiplies out

it comes to 0.3 volts

but you have an extra factor of 30 you multiplied in
which brings it to 9.0

You are permitted to edit your answer if it is a typo!

If it is not a typo then explain please the factor of "[+-30]"
You may certainly be right to have it. I am often forgetting
details and there may be some obvious thing I am missing.
I got this problem from an old edition of Halliday Resnick
but don't remember the exact numbers

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Originally posted by marcus
30 meter wingspan x 200 meter/sec speed
x 50 microTesla (the vertical component of the geomagn. field)

let's see how that multiplies out

it comes to 0.3 volts

but you have an extra factor of 30 you multiplied in
which brings it to 9.0

You are permitted to edit your answer if it is a typo!

If it is not a typo then explain please the factor of "[+-30]"
You may certainly be right to have it. I am often forgetting
details and there may be some obvious thing I am missing.
I got this problem from an old edition of Halliday Resnick
but don't remember the exact numbers

Shoot no. I was integrating the emf over the length of the wings. twas thinking E and not &epsilon;

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Originally posted by Ivan Seeking

sorry I got preoccupied with something else and just got
back

(this game was partly your idea----the teaser problem---which chroot generalized, you and chroot make the rules I think)

It's the Hall effect, Warren. :) Actually a real-life voltmeter should work fine, I think -- just stretch the leads out, doesn't matter if you even touch the wing or not.

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I'm still not sure how this answer was arrived at.

- Warren

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Ohhh.. the Hall effect. Hmph.

- Warren

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Originally posted by marcus

sorry I got preoccupied with something else and just got
back

(this game was partly your idea----the teaser problem---which chroot generalized, you and chroot make the rules I think)

yippie!

The dA/dt was just the width of the wings multiplied by the speed of the plane.

Ok. I don't know if this will be really easy, or really hard, or somewhere in between. A True Story.

The answer to a very complex physics or mathematics problem [I don't remember the exact nature of the problems] was to be calculated on one of the world's top supercomputers of the time; circa 1975. Two approaches were considered. The first and preferred approach was to calculate an extremely precise answer, and next was to approximate the answer. The best answer would require about a year of CPU time. The approximation could be calculated in relatively short order: in a matter of days.

The cost of CPU time caused this issue to be scrutinized very closely. It was decided that in spite of the money, the approximate answer was the best choice. What is the physical motivation [the physics] for their choice?

Originally posted by Tyger
... However, if the plane can land with the charge on the wingtips remaining, it can be measured on the ground with an electrometer, which is a very sensitive voltmeter.

Charge can't remain (separated when plane is on the ground) because plane is made of metal.

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Originally posted by damgo
It's the Hall effect, Warren. :) Actually a real-life voltmeter should work fine, I think -- just stretch the leads out, doesn't matter if you even touch the wing or not.

No, voltmeter won't show anything (because emf [vB]l is evenly distributed along a wire l).

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Originally posted by Alexander
No, voltmeter won't show anything (because emf [vB]l is evenly distributed along a wire l).

I often disagree with you Alexander or else am put off by your argumentatitive tone of voice (I do not remember which it is) but here I must commend you and voice agreement.

This is not normally considered an example of the Hall effect.

It is a standard textbook example that comes in right after the Faraday law. Halliday Resnick has it as an antenna of a car driving where the field is horizontal and the vertical antenna is cutting across field lines.
Giancoli has it with airplane wings cutting across vertical field lines.

The basic law (as in so many things) is the Lorentz force.
(Which also explains the classical Hall effect! but the problem is elementary and appears long before the Hall effect is discussed.)

A voltmeter could not be used, I reckon, to measure the voltage difference between the wingtips in flight (for the reason Alexander gave----no current would flow thru the meter altho the voltage difference would be there)
A conductor is not necessarily a constant potential thing when it is moving thru a B field as someone said, maybe Alexander.

Lorentz force is so basic, almost the F=ma of E/M
Lorentz force law is really the definition of the E and B fields, it is part of the groundwork.

dropping out the electrostatic part of the law it just says
F = qv X B

The B arrows near the north geomagnetic pole, which is a "south" pole---paradoxically---point DOWN.

So conduction electrons in the wing feel a force to the right

The voltage is higher on the left wingtip, where positive charge carriers would concentrate if there were some.

In Giancoli the problem comes right after the example of the bar sliding along two parallel rails, in a uniform vertical field

The rails merely permit the voltage difference between the ends of the bar to be measured (it is a Faraday law loop including the rails)

The airplane wing is the bar with the two rails removed.

You could put rails in the sky and have the airplane swoop down and fly along them with its wingtips touching them so that the voltage could be measured but the FAA and the Airline's Pilots Association would not allow this so one must trust in Faraday and believe on grounds of faith.

^^^ Well, you would need 'leads' with a great deal of capacitance; then charges will build up at the ends and cause a voltage difference across the voltmeter inputs. emfs in 'series' along each lead act just like one big emf, remember.

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Originally posted by damgo
^^^ Well, you would need 'leads' with a great deal of capacitance; then charges will build up at the ends and cause a voltage difference across the voltmeter inputs. emfs in 'series' along each lead act just like one big emf, remember.

not a bad idea. As I picture your idea it involves remote switches that can be used to isolate parts of a conductor running the length of the wing
one might even "freeze" the voltage differerence in carefully insulated elements inside the airplane wing and keep
the difference "on hold" so to speak until the plane could
land and have it measured.

the humble textbook writers did not bother to discuss how the voltage could be measured!

Tyger

Originally posted by Alexander
Charge can't remain (separated when plane is on the ground) because plane is made of metal.

So let's make the plane out of fiberglass with metal wingtips and have a wire and a switch between them. We can close the switch when the plane takes off and open it before it lands, keeping the charge on the wingtips. And I see marcus thought of this too.

Originally posted by marcus
I often disagree with you Alexander or else am put off by your argumentatitive tone of voice (I do not remember which it is) but here I must commend you and voice agreement... (blah blah blah)...

Markus, why this long post? Any relevance to a voltmeter reading? Looking across this long post I could not find what you state about voltmeter. Can you be concrete in you posts, without mentioning all what textbooks have cover-to-cover?

Voltmeter with its leads span as airplane wings will show zero reading despite that there may be quite high potential between tips of leads. (And I can prove that if needs be.)

From you post I understood that you claim opposite. Well, then prove it.

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Originally posted by Alexander

Voltmeter with its leads span as airplane wings will show zero reading despite that there may be quite high potential between tips of leads. (And I can prove that if needs be.)
.

Me too, this is what I was saying. You did not understand.

Originally posted by Alexander

From you post I understood that you claim opposite. Well, then prove it.

Then you REALLY misunderstood me---180 degrees. Well that happens. Better luck next time.

My post was opposed to using the Hall effect (which damgo referred to) as an explanation. Sorry it confused you!

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Well, I see we've all been very busy while I was away.

If you are all ready to get back to the next question? I'm asking not pushing:

The answer to a very complex physics or mathematics problem [I don't remember the exact nature of the problems] was to be calculated on one of the world's top supercomputers of the time; circa 1975. Two approaches were considered. The first and preferred approach was to calculate an extremely precise answer, and next was to approximate the answer. The best answer would require about a year of CPU time. The approximation could be calculated in relatively short order: in a matter of days.

The cost of CPU time caused this issue to be scrutinized very closely. It was decided that in spite of the money, the approximate answer was the best choice. What is the physical motivation [the physics] for their choice?

Too vague or have you just been too busy?

Tyger

Machine reliability. The machine would have a high chance of breaking down and losing all the data in a year.

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Originally posted by Ivan Seeking
It was decided that in spite of the money, the approximate answer was the best choice.
I'm not sure I understand. The approximate answer is cheap, right? Why then would they decide to do it "in spite of the money," if it's the cheap solution?

- Warren

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Originally posted by chroot
I'm not sure I understand. The approximate answer is cheap, right? Why then would they decide to do it "in spite of the money," if it's the cheap solution?

- Warren

Another motivation was realized.

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Originally posted by Tyger
Machine reliability. The machine would have a high chance of breaking down and losing all the data in a year.

No one was concerned about the machine breaking down. But I did respond to your post.

Originally posted by marcus
...

Lorentz force law is really the definition of the E and B fields, it is part of the groundwork.

No, Lorents force is not definition of electric nor nagnetic field. Electric field is defined as a force on a static charge (which, is derived in QED to actually be a result of creation- of virtual photons around one electric charge and disappearance of virtual photon around another charge), and magnetic field is defined as the specific term arizing from Lorents transformation of electric field from one reference system to another (namely - B is just the vector product of electric field with velocity of reference system [vxE]/c2[/).

Lorentz force is so basic, almost the F=ma of E/M

Really?

Here is a simple problem on understanding of Lorents force. Two protons move in perpendicular direction. At some moment of time vector of velocity of one of them is directed toward another one. Imagine L letter, first proton is in upper point and its velocity is directed down, second is in lower point right under it, and its velocity is directed to the right). What is the Lorents force F = q[vxB] of the lower proton on the upper one? Well, lower proton creates magnetic field B directed (in the vicinity of the upper electron) "out of the screen", which when vectorly multiplied by the velocity vector of upper proton gives the Lorents force on upper proton directed to the left.

Now, upper proton also creates a magnetic field. The magnitude of this magnetic field is non-zero everywhere except on the axis of motion of the upper proton (= on the line of its velocity vector). Therefore, lower proton happens to be in ZERO megnetic field (because this proton is located directly on the path of the upper proton) and therefore the magnitude of Lorents force on it is ZERO.

But we have a contradiction here: One objects (lower proton) exert force on another one, but gets no reaction force back.

How so? Momentum can't conserve if one objects exerts force on another and is not subjected by the same but oppositely directed force.

Can you resolve this apparent paradox (taking into consideration that Lorents force is "so basic" for you)?

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Originally posted by Ivan Seeking
No one was concerned about the machine breaking down. But I did respond to your post.
Uh maybe because they wanted the answer fast so they could publish their papers before the other guys and get their PhD's...

- Warren

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Originally posted by chroot
Uh maybe because they wanted the answer fast so they could publish their papers before the other guys and get their PhD's...

- Warren

Hee hee. No. There was a physical reason for their choice.

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No offense, Ivan, but there's really not enough information here to make a guess. And this sort of "riddle" really isn't the sort of question I was hoping to see here.

- Warren

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Originally posted by chroot
No offense, Ivan, but there's really not enough information here to make a guess. And this sort of "riddle" really isn't the sort of question I was hoping to see here.

- Warren

Yes. Perhaps I failed at formulate a good question out of this. I really didn't mean to make a riddle as much as to provide hints. Oh well, I will fess up and punt to you chroot. The answer is:

It was found that over the period of one year, the chance of an error due to bombardment by cosmic rays was nearly 1. As a result, this error would have made the exact answer less reliable than the approximation. Actually Tyger was getting close. Also, I would think that the chances for other errors could also be significant.

Here's to you chroot.

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Well, hell, Ivan, machine reliability clearly includes this.

In fact, cosmic ray strikes are the most common cause of single-bit errors in modern computer memories -- hence the common SECDED technology -- "single error correction, double error detection." I was thinking "cosmic rays" the entire time, but thought that "machine reliability" included it!

When you said a "physical reason," I thought you meant something about the problem being solved -- not something about the physical machine. :)

In any event, it is certainly an interesting thing!

Why don't you ask another question?

- Warren

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Originally posted by chroot
Well, hell, Ivan, machine reliability clearly includes this.

In fact, cosmic ray strikes are the most common cause of single-bit errors in modern computer memories -- hence the common SECDED technology -- "single error correction, double error detection." I was thinking "cosmic rays" the entire time, but thought that "machine reliability" included it!

When you said a "physical reason," I thought you meant something about the problem being solved -- not something about the physical machine. :)

In any event, it is certainly an interesting thing!

Why don't you ask another question?

- Warren

Since Tyger included the specific reference to breakdowns, I tried to point to his answer but felt that he was otherwise off course.

Darn. That may be the only other interesting thing I have ever learned. O.K. How about this, I should say up front that I have an answer, but my confidence in this answer is not quite 100% [comes from a so-so professor]. So I will play this one by ear. At some appropriate point I will interject my two cents worth.

The total force due to friction between two materials is calculated as the normal force times the coefficient of friction between the materials. Why do racing cars use wide tires?

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Originally posted by chroot

This is what I was not sure about. Since I have heard little discussion about this topic outside of NASA, I feared this could be an extremely obscure argument, or that this proof may have been a cosmic error! I was waiting to get run up the flag pole after giving my answer!

Why do racing cars use wide tires?

that easy!? greater surface area ensures that it is harder to reach the static coefficiant of friction.

am i right?

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