Using the force constant in equations

nightcleaner · Feb 13, 2005

marcus said:

Frog was out driving his vintage Morgan.
This car is great! said Frog. It can really take the curves.
Suddenly, coming around a bend in the road, he saw a sign BRIDGE OUT.

Frog jammed on the brakes and locked the wheels. The sporty vehicle skidded to a stop.

Toad emerged from the bushes beside the road and told Frog to wait while he measured the skidmarks. If you were speeding, said Toad, I will give you a ticket.

Toad paced out the skidmarks. They were 50 paces long (50E34).
He applied the formula that assumes a friction coefficient of one for rubber on pavement:
v² = 2gL = 2 x E-50 x 50E34 = E-14
v = E-7

You were going right at the speed limit, said Toad, E-7 is 67 miles per hour. I will not write you a ticket. You may proceed on your merry way!

But the bridge is out, said Frog.

No, said Toad, the sign is just part of our Emergency Preparedness program, in case terrorists blow up the bridge. We are testing the sign to see if it works. The bridge is passable. Do not make me tell you again to proceed on your merry way.

Frog drove the Morgan along the winding country roads. As dusk approached, a thin crescent moon appeared in the west. Ah, said Frog, the moon is curved just like the bends in the road

What about the mass of the Morgan? What if Froggy had a ton of gold bars in the bonnet?

marcus · Feb 13, 2005

Hi nc,

some odds and ends. You know all thru this thread I've been using the number 2.6E18 (for masses and weights of atoms and molecules)

well I sometimes think of that number as "Wilczek's number" because he wrote a series of 3 articles in "physics today" about that number, how interesting it is and how to explain its large size (or the small size of its reciprocal)

today Wilczek's Nobel acceptance speech posted on arxiv
http://arxiv.org/abs/hep-ph/0502113

this speech is NOT about the number 2.6E18, it is about "asymptotic freedom" and quarks etc. that Wilczek and two others got prize for.
but probably in the end the size of that number will be explained out of the same fundamental ground as QCD-----the reciprocal is the proton mass expressed in natural units.
Wilczek is a good writer so i think anybody might like to try reading his speech, even tho about difficult stuff.

About that gold in the Morgan
putting gold bars in Morgan would have no net effect (at least to first approx.)
because it has two opposite effects that cancel
heavier makes the car have more traction
more massive makes it have more momentum (at given speed)
and so it needs more force to make it stop

double the mass and you double the stopping force of tires on pavement, but also double the need for stopping force, so it cancels and get same result.
therefore the simple formula they teach which relates speed to length of skidmarks does not have the mass of the car in it as a factor.
(at least this is how I remember, please correct me if you have better info)

marcus · Feb 13, 2005

...today Wilczek's Nobel acceptance speech posted on arxiv
http://arxiv.org/abs/hep-ph/0502113
this speech is NOT about the number 2.6E18,...

well he does mention it after all (a bit vaguely using more popularly recognizable h instead of hbar and leaving out 8pi) on page 21,

nontechnically, but mentions it anyway-----it is the paper's equation #2
which says that mass of proton is approx 10^-18 of Planck mass.

nightcleaner · Feb 13, 2005

marcus said:

Hi nc,
double the mass and you double the stopping force of tires on pavement, but also double the need for stopping force, so it cancels and get same result.
therefore the simple formula they teach which relates speed to length of skidmarks does not have the mass of the car in it as a factor.
(at least this is how I remember, please correct me if you have better info)

Hi Marcus

I don't have better info, just curiosity and a vague memory from a defensive driving course many years ago. The instructor said you have to watch out for motorcycles because they can accelerate very fast, and also can stop very fast, due to their light weight. Give them extra following space, was his advice, but he was no physicist.

Even more vague, it takes something like half a mile of screeching to stop a freight train.

Here, near The Lake, it has begun to snow. I am on my way to work in a few minutes. The forcast was rain, freezing rain, then snow, so I expect it to be slippery. There is zero traffic on the highway, so I suspect the forcast was correct, and I will have to be very careful walking up the little hill to the truck. When it is icy, sensible people drive very slowly or better, not at all. You can be very surprised how long it takes to stop. I once skidded half a block after rounding a corner onto an icy side street. I didn't think I was going fast at all.

I think you are right about the traction thing, though, but there are probably mass effects on the coefficient of friction that are neglected in the formula. I used to drive a semi truck and I do know it takes a lot longer to stop a loaded truck than an empty one, but I never had to lock up the brakes. Tapping the brakes repeatedly is better than jamming them on, because once the tires break free of the pavement, as in a skid, the friction goes way down.

Be safe,

nc

marcus · Feb 13, 2005

nightcleaner said:

Here, near The Lake, it has begun to snow. I am on my way to work in a few minutes. The forcast was rain, freezing rain, then snow, so I expect it to be slippery. There is zero traffic on the highway, so I suspect the forcast was correct, and I will have to be very careful walking up the little hill to the truck. When it is icy, sensible people drive very slowly or better, not at all. You can be very surprised how long it takes to stop. I once skidded half a block after rounding a corner onto an icy side street. I didn't think I was going fast at all.

I think you are right about the traction thing, though, but there are probably mass effects on the coefficient of friction that are neglected in the formula. I used to drive a semi truck and I do know it takes a lot longer to stop a loaded truck than an empty one, but I never had to lock up the brakes. Tapping the brakes repeatedly is better than jamming them on, because once the tires break free of the pavement, as in a skid, the friction goes way down.

I think you are right, pumping the brakes is better. I do that whenever I think there is a danger of tires breaking free and have avoided skids thank heaven so far, except (as you mention) on ice.
one time near NYC the hutchinson river parkway was iced and we and all the other cars were going slow. I remember turning around 360 degrees and sort of waltzing down a gentle slope. it was better than turning around 180 degrees and coasting down backwards

roads can ice suddenly and nobody have chains. at times we had to push on that trip, fortunately there were several of us in the car.

However there is this classic freshman physics problem where the driver (Frog in this case) actually does lock the wheels and does the whole skid thing, EVEN THOUGH it is the wrong way to stop.
and then the textbook usually assumes some value like one for the kinetic friction of rubber on pavement. It may not be altogether realistic (especially modern cars have automatic anti-locking so you can't do it even if you want) but firstyear physics problems often have a slight unreality anyway.

BTW Wilczek says in that nobel acceptance talk that 90 percent of the mass of a proton is due to the kinetic energy of the quarks buzzing around inside it. Curious thought. the protons mass is owing to the speed of its constituent parts which sitting still would not weigh much.

marcus · Feb 15, 2005

marcus · Feb 15, 2005

The cyclotron frequency of the cat

On a planet famous for its potato pancakes, they have special cats which are highly tolerant of electric charge. It is possible to charge one of these cats up to E19 a truly amazing charge equal, in conventional terms, to 1.6 metric Coulombs!

A large magnetic room has been built to discover the cycloton frequency of fully charged cats.

A cat of charge E19 and mass E9 (about 10 pounds) is launched into a uniform vertical field of strength E-53 (in conventional terms one Tesla). The cat is observed to travel in a circle with a fixed constant angular frequency determined by its mass m, charge q, and the strength B of the field

frequency = qB/m = E19 x E-53/E9 = E10 x E-53 = E-43.

This constant frequency is called the "cyclotron frequency of the cat"

A modest vertical electric field cancels the cat's weight, so it is effectively in zero gravity. It follows a large horizontal circular path which eventually spirals inwards as the animal slows down (due to aerodynamic drag).
The reason for spiraling is that it has to keep circling with constant frequency E-43, so as it slows down it must go in smaller and smaller circles to maintain the same frequency.

question If the cat is launched into the room at a speed of E-8 (in familiar terms 6.7 mph), what is the radius of its circular path?

answer We have shown that the cat takes time E43 to go one radian, if it is traveling at speed E-8 then the distance traveled in that time is E-8 x E43 = E35. this is the radius of the cat's path. In traditional terms it is 10E34 or 10 paces.

marcus · Feb 16, 2005

Quantum Hall Resistance

the quantum hall resistance (also called "von Klitzing's constant") is a certain definite ratio of voltage to current built into nature

in terms of these natural units it is simply 2pi

if you want to know the metric value (adopted in 1990 to standardize current measurement) you probably have to look it up:

the NIST website gives it as exactly 25,812.807 volts per amp, in other words as 25,812.807 Ohms.

we encountered this kind of thing earlier with the StefanBoltzmann radiation law constant which in natural units is pi²/60
but if you want to know it in metric you look it up and it is about
5.6704 x 10^-8 watts per sq meter per Kelvin⁴

--------------
I found some stuff about QHE (quantum hall effect) on google. I'm not an expert about this---just know that the effect exists and is used to base the current standard on at various countries' national labs
http://www.warwick.ac.uk/~phsbm/qhe.htm
-----------------

so you have a cold horizontal rectangle placed in a vertical magnetic field and you send a certain current down the length of the rectangle and a crossways voltage is induced across the width, which depends on the current in a fixed ratio (you can even vary the magnetic field some and as long as you don't change the field too much the ratio of voltage to current stays the same). See for example the picture and graph at that link.

In natural terms the ratio is 2pi. So like if you make the current E-28 then the transverse voltage across the width of the thing will be 2piE-28

(in familiar terms voltage E-28 is a "quartervolt" so we are talking 6.28 quartervolts or about one and half volt)

At national labs they use the Quantum Hall effect to standardize current measurement. Voltage can be measured using the atomic clock and the Josephson effect, and then once one has a voltage standard (based on atomic clock) then one standardizes current using the ratio 25,812.807 volt per amp adopted by the CIPM in 1990.

Richard, I went googling for QHE references in response to your questions in next post. Will edit in some links

I tried Wikipedia but it had no pictures or diagrams.
this JohnHopkinsUniv. page has pictures but also a huge amount of formulas so you have to go searching for the pictures:
http://www.pha.jhu.edu/~qiuym/qhe/qhe.html
It does give the dimensions and materials of an actual QHE device.

nightcleaner · Feb 16, 2005

Hi Marcus.

This is very interesting, and gets at a point which I have always found confusing. I hope you will entertain some questions here.

First the magnetic field. We know the field lines by looking at iron filings near a magnet, which line up in the familiar way, joining north to south poles in loops. But you can shove the iron filings over to the right or left a bit with no problem, until you come to the limit where the filings need to touch each other. The "lines" therefore are artifacts brought about by the presense of the iron filings. The field lines are not really lines through empty space at all, but need the presense of material particles for definition, correct? In the absense of magnetizable particulate matter the field is continuous, undivided, perhaps more like a density cloud than a lattice.

We might imagine that there is a density cloud of photons or even of virtual particles which exists even in non-material space, and that these particles line up in their own scale in a manner analogous to the way the iron filings behave. So the "lines" may be present down to the Planck scale, even in a vacuum. Then when a charged or magnetized particle enters the region affected by the magnet, it encounters these microscopic particles, which are arranged in lines due to the effect of the magnet, and so is deflected in predictable ways.

Something about this field idea bothers me.

Then there is the rectangular conductor. If one places an electrode in one place and an annode in another place, does the current go directly from one diode to the other, in a straight line, or does it fill the conductor? Or at least, does it cover the surface of the conductor? Or do we need to apply a path integral approach and say that the current is everywhere on the conductor but cancels itself out mostly except for along the line between the diodes?

Cats! I am out of time. As you can see I still have more points of confusion to consider. I hope to return to this tonight. Meanwhile, chores.

Be well,

nc

marcus · Feb 16, 2005

hi Richard,
the best I found in a quick search was
http://www.warwick.ac.uk/~phsbm/qhe.htm

and this shows that in our units the QHE "resistance" i.e. the voltage/current ratio can take on several values. It has several plateaux it can be on depending on the strength of the field.

2pi, but for a weaker field 2pi/2, and for even weaker field 2pi/3, and I also see a plateau at 2pi/4,...etc.

So if you put in a current of E-28 (roughly a tenthousandth of an amp)
then it will create a transverse voltage (helped by magetic field) of
either 2piE-28, or (2pi/2)E-28, or (2pi/3)E-28, and so on...
You can see the plateaux in the diagram.

the strongest voltage, 2piE-28, is when the field is strongest. According to the diagram it happens when the field is 10 Tesla, or more. Say 11 Tesla to be safe.
In our units a tesla is 1.00E-53, by accident it was really close. So I can
translate that to say the field has to be 11E-53 or more.

marcus · Feb 16, 2005

nightcleaner said:

... The "lines" therefore are artifacts brought about by the presence of the iron filings. The field lines are not really lines through empty space at all, but need the presense of material particles for definition, correct? ...

I agree.
field lines are a mathematical tool for drawing a field. they are not really there as material objects.

there are alternative ways to draw a field. those do not use field lines but they use other mathematical tools to depict or represent. these are also not there in material reality.

one can depict a field by first imagining the framework of Euclidean 3D space (like 3D graph paper) and at each point one imagines a little arrow.

the direction and length of the arrows gives the needed information about the field.

some fields are harder to imagine because you can't capture the information about the field simply by drawing field lines or bunches of little arrows. but why worry about that?

to understand QHE you just must picture the magnetic field as a thick bunch of arrows pointing straight up sticking thru the rectangular planar semiconductor sample----see the picture.

they make the electrons of the current going down the length of the sample want to "swerve" or veer over to one side-----so voltage builds up on one side versus the other.

nightcleaner · Feb 17, 2005

Superconductivity? Resistance falls to zero at some values of magnetic field.

The unit, h/e^2 n, uses h instead of h-bar? And why is it not presented as
n e^2/h? An integer number of squared charges per Planck? And on the other side of the graph, what is P_xx? and what is that unit, k omega per sq? Would that be square as in an area? So a ratio, of resistance to area? But xx isn't an area. So would it be a curve, the curve of the current j_x? So the resistance is the resistance to the curve? Curve means acceleration, and naturally charges resist acceleration.

nightcleaner · Feb 17, 2005

QH effect looks like it is geometric. I am playing with the numbers. Seems like mag field and amplitude of effect are roughly equivalent, with a factor of ten.

can QH effect be used to turn superconductivity on and off? Application in quantum computing? i am going to go play with the numbers some more. Magnetic resonance? What is sweeping? Is it like herding electrons with magnetic pulses?

I'll be back soon, if the dish doesn't run away with the spoon. Marcus, do you remember the Uncle Wiggley stories?

Be well, and many thanks

Richard

marcus · Feb 17, 2005

nightcleaner said:

... And why is it not presented as
n e^2/h? An integer number of squared charges per Planck? ...

It IS presented that way sometimes. For example in the Wikipedia article.

In conventional physics talk and electrical engineering, the reciprocal of a resistance (a voltage-over-current ratio) is called a "conductance" (the word for a current per voltage, or current-over-voltage ratio)
So if it is to the author's liking to present it as you suggest, then he will talk about "Quantum Hall Conductance" which will be various values
e^2/h, or 2e^2/h, or 3e^2/h, or...

I think maybe aesthetically this is better.

However the NIST website lists the constant as 25,812.807 Ohm resistance.

If I want to be aesthetically better I have to talk about a constant which is
1/25812.807 "siemens" conductance.
many people have heard of Ohms of resistance but may not have heard of siemens of conductance. So I run the risk of losing them.

But I do not care all that much.
Ohm is just the metric name for "volt per amp" or volt/amp ratio.
and Siemens is the metric name for "amp per volt" or amp/volt ratio.
You prefer to talk about amp/volt ratio and you are reading this thread and the other people arent, so if you like to talk in terms of conductance, that is entirely to my liking.

You mentioned the h versus hbar thing.
Yes, this is a case where h is the preferred form of Planck constant. Physicists use hbar a lot (it has become pretty much the rule in the things I read) but whenever convenient they occasionally write h instead! It means you don't have to write 2pi

So e^2/h acts like a quantum of conductance in this situation
and you get multiples of this basic current-to-voltage ratio.

I will get the link to the Wiki article that discusses it that way.
http://en.wikipedia.org/wiki/Quantum_Hall_effect

marcus · Feb 17, 2005

nightcleaner said:

I'll be back soon, if the dish doesn't run away with the spoon. Marcus, do you remember the Uncle Wiggley stories?

I can remember reading an Uncle Wiggley book, or books, when I was about 7 years old but I cannot remember any of the content. I remember a picture of a river and a riverboat and Uncle Wiggley, the rabbit, who was the hero, was on board the boat. Maybe he was steering, or maybe he was just riding passenger.

My memory of Uncle wiggley has faded. I know he was a rabbit though.

what about you, do YOU remember the uncle wiggley stories?

the dish running away with the spoon has nothing to do with it. I am sure you are aware that the dish-spoon escapade belongs to Mother Gooserhyme about cow jumped over the moon and is entirely extraneous (or so I believe) to stories about rabbits.

the metric unit of conductance (amps per volt) used to be the "mho"
which is Ohm spelled backwards, but the official body which governs the metric system renamed it "siemens". they play politics of honoring various national science role-models by naming units after them. they have great power over this department of our language. they are called CIPM "comité international des poids et mesures" or something like that: international committee on weights and measures If they decide to honor a German edison then even if you like Mho, Mho dies.
Eventually everyone goes along with decisions of the CIPM.

marcus · Feb 17, 2005

just to recall the short summary in post #121
https://www.physicsforums.com/showthread.php?p=457767#post457767

now what I want to condense into a post or so is a sampling of how the formulas look, which this thread has been illustrating

1. for a satellite in circular orbit
mass = 4 x period x speed³

e.g. a planet's year is E50 and its speed is E-4 (both very like Earth's)
how massive is its star?
4 E(50-12) = 4E38

e.g. a planet's mass is E33, its year is E50 and the speed of a synchronous satellite circling it is E-5 (similar to Earth case as well)
how many of this planet's days to a year?
4 period E-15 = E33, 4 period =E48, 400 days in a year.

e.g. you are orbiting a small planet at the speed of a run, 6.7 mph, and find that full circuit takes 1 and 7/8 hours. What is the planet's mass?
speed = E-8, 4 x period = 450 minutes = E47, E47 E-24 = E23

2. for black hole radius, area, temperature, evaporation time

radius = (1/4pi) mass
area = (1/4pi) mass²
temp = mass^-1
evaporation time = (80/pi) mass³

3. radiant energy density and brightness
(energy per unit volume, power per unit area)

energy density = (pi²/15) temp⁴
brightness = (pi²/60) temp⁴
...

that is the first three of the 8 items.

John Baez is skimming around a planet of pure gold. How long does it take him to make one complete orbit?

marcus · Feb 17, 2005

Over centuries, the planet's generations of craftsmen have carved ornamental figures on its surface. Mostly they are figures of naked women, as do often occupy the artistic mind, but there are also those of monkeys and elephants engaged in sportive activity. The entire surface of the planet has been worked ornamentally in this way and Baez admires it as he skims along in low orbit.

By diligent study Baez has acquired the ability to judge brightness in the infrared (which the unenlightened cannot see) and he notices that the planet's surface glows with brightness 2E-117

what is the temperature of the planet?

marcus · Feb 17, 2005

marcus said:

just to recall the short summary in post #121
https://www.physicsforums.com/showthread.php?p=457767#post457767
...
John Baez is skimming around a planet of pure gold. How long does it take him to make one complete orbit?

item 6 of that list mentioned that in low orbit, limiting case,
radiantime² = 6/density

our densities of materials are on the E-91 scale and gold is 23 some.
Call it 23E-91.
radiantime² = 6/(23E-91) = 2.6E90
radiantime = 1.6E45
multiply by 2pi to get time for full orbit, remember E45 = 4.5 minutes
it seems that one circles a solid gold planet very quickly regardless of whether (within reason) it is large or small.

item 3 said
brightness = (pi²/60) temp⁴
so if the brightness is 2E-117 all one needs do is multiply 2E-117 by 60/pi² and take fourth root.

as a humanscale handle on it 2E-117 is like two 160 watt litebulbs on a square pace area: one litebulb power is E-49 and the area is E68, and the ratio of that power to area is E-49/E68 = E-117. Two bulbs is twice.

(60/pi²)2E-117 = 1.21E-116

(1.21E-116)^1/4 = 1.05E-29

nightcleaner · Feb 17, 2005

Hi Marcus

Does a cyclotronic cat rotate?

marcus · Feb 17, 2005

the cyclotron frequency of the proton

this is partly in reply to richard. the cyclotron frequency of basic particles like electron and proton has been an important frequency to know in experimental physics over the years, especially in the design of ring accelerators (like cyclotrons) and detectors (like cloud and bubble chambers). the spiral paths one sees in detector photographs are due to there being a vertical magn field so the particles come in and go splat and the pieces that are charged go in spirals.

however I have introduced this idea using charged cats instead of charged particles because more people are cat-conscious than proton-conscious

marcus said:

... they have special cats which are highly tolerant of electric charge. It is possible to charge one of these cats up to E19 a truly amazing charge equal, in conventional terms, to 1.6 metric Coulombs!

A large magnetic room has been built to discover the cycloton frequency of fully charged cats.

A cat of charge E19 and mass E9 (about 10 pounds) is launched into a uniform vertical field of strength E-53 (in conventional terms one Tesla). The cat is observed to travel in a circle with a fixed constant angular frequency determined by its mass m, charge q, and the strength B of the field

frequency = qB/m = E19 x E-53/E9 = E10 x E-53 = E-43.

This constant frequency is called the "cyclotron frequency of the cat"
...

However let us now calculate the cyclotron frequency of the proton in a 1 Tesla magnetic field

It is very easy to do in natural units because the field B = E-53, the charge q=1 and the reciprocal mass 1/m= 2.6E18 (this is a number you have already seen dozens of times in this thread)

frequency = qB/m = 1 x E-53 x 2.6E18 = 2.6E-35

to get a humanscale handle on this frequency, recall that the musical pitch D on the treble clef (a note that sopranos and altos sing) is E-39.

so we are talking something that is 10,000 times higher frequency---which would be E-35----and then some, a little factor of 2.6.

[edit: Note about the previous post. One can easily determine that cats are stable with regard to rotation. Simply drop a cat from a convenient height. You will observe that the cat only rotates as much as it has to so that it lands rightside up. The question is not relevant to the problem but no, the cats in the cyclotron do not rotate.]

[edit: NOTE about next post. It is on the round number planet where gravity is a neat E-50 instead of around 0.9E-50 the way it is here. the air, which is a comfortable temperature and good to breathe, offers no resistance to motion]

marcus · Feb 18, 2005

Batman is in his batbed, sipping a cup of warm batmilk.
It is his sleepytime and he has a hard day of fighting injustice tomorrow.
King Kong reaches in through the window and, seizing Batman, hurls
him upwards at angle 45 degrees from the horizontal at a speed
of 7E-8.
How far does Batman travel before he goes bump on his batbottom?

marcus · Feb 18, 2005

In 1873 the two poets Verlaine and Rimbaud went to Belgium. They were 29 and 19 years old.
Verlaine shot Rimbaud with his pistol, giving him a non-fatal wound.
The mass of the bullet which Verlaine shot at Rimbaud was E7
and the speed was E-6.

As a consequence Verlaine had to sit in jail for 2 years during which time he wrote this poem:

Le ciel est, par-dessus le toit,
Si beau, si calme!
Un arbre, par-dessus le toit,
Berce sa palme.

La cloche, dans le ciel qu'on voit,
Doucement tinte,
Un oiseau sur l'arbre qu'on voit,
Chante sa plainte.

Mon Dieu, mon Dieu, la vie est là,
Simple et tranquille.
Cette paisible rumeur-là
Vient de la ville.

-Qu'as-tu fait, ô toi que voilà
Pleurant sans cesse,
Dis, qu'as-tu fait, toi que voilà,
De ta jeunesse?

What was the momentum of the bullet?

marcus · Feb 18, 2005

I just made this rhymed translation of the Verlaine poem:

The sky above the roofs,
so clear and calm!
And higher than the roofs,
there sways a palm.

From steeples on that sky
a chime comes faint,
and from the tree outside
a bird's complaint.

My god that's Life out there:
so settled down--
the peaceful noise I hear
comes from the town.

"Hey you down there! the one
with all the tears:
Say, what have you done
with your young years?"

Le ciel est, par-dessus le toit,
Si beau, si calme!
Un arbre, par-dessus le toit,
Berce sa palme.

La cloche, dans le ciel qu'on voit,
Doucement tinte,
Un oiseau sur l'arbre qu'on voit,
Chante sa plainte.

Mon Dieu, mon Dieu, la vie est là,
Simple et tranquille.
Cette paisible rumeur-là
Vient de la ville.

-Qu'as-tu fait, ô toi que voilà
Pleurant sans cesse,
Dis, qu'as-tu fait, toi que voilà,
De ta jeunesse?

this poem is about looking out of the jailhouse window
and regretting one's lost youth.
we've all had this experience, or will sometime.

marcus · Feb 18, 2005

Verlaine carves a wooden cat

Verlaine carves a wooden cat.
He inserts a screw-eye so he can tie a string to the cat
and suspend it like a pendulum from the ceiling.

Then he shoots the cat with his pistol.

The famous poet has aimed precisely at the cat's center of mass, the slug buries itself deep in the heart of the wooden carving. This causes the cat to swing.

How much momentum does the cat acquire at impact?

marcus · Feb 18, 2005

marcus said:

Batman is in his batbed, sipping a cup of warm batmilk.
It is his sleepytime and he has a hard day of fighting injustice tomorrow.
King Kong reaches in through the window and, seizing Batman, hurls
him upwards at angle 45 degrees from the horizontal at a speed
of 7E-8.
How far does Batman travel before he goes bump on his batbottom?

Batman flies 50 paces, that is a distance of 50E34 = 5E35 natural.
solution: vertical speed = horizontal speed = 5E-8,
gee = E-50
time of flight = 2 x 5E-8/E-50 = E43
distance of flight = E43 x 5E-8 = 5E35

as a rough estimate, a pace is 2 and 1/2 feet, so 50 paces is about 125 feet.

marcus · Feb 18, 2005

Rimbaud measures the angle of deflection of the cat

Verlaine carves a wooden cat.
He inserts a screw-eye so he can tie a string to the cat
and suspend it like a pendulum from the ceiling.

Then he shoots the cat with his pistol.

The famous poet has aimed precisely at the cat's center of mass, the slug buries itself deep in the heart of the wooden carving. This causes the cat to swing.

How much momentum does the cat acquire?

The carved wooden cat is suspended by a string from the ceiling at a distance of 2 paces, or 2E34 natural.
the mass of the slug is a tenth of a pound----E7 mass units----and the muzzle velocity of Verlaine's pistol is E-6, roughly the speed of sound.
Therefore the slug's momentum is 10 natural units of momentum.

the mass of the cat is about 10 pounds----E9 mass units----so for it to acquire 10 units of momentum it must have the speed E-8 (in familiar terms 6.7 mph).

What is the kinetic energy of the cat immediately after impact?

KE = (1/2) m v² = (1/2)E9 x (E-8)² = (1/2)E-7 natural energy units.

Rimbaud, who is the lab assistant, measures the maximum angle of deflection from the verticle attained by the pendulum.

What swing angle does Rimbaud measure?

marcus · Feb 18, 2005

How the Gypsies stole the Moon (revised)

How the Gypsies stole the Moon

Some gypsies were roaming this part of the galaxy. On their way thru the solar system they stole the moon and replaced it by a black hole of the same mass

Dont worry, said the gypsies (when the people complained) you will still have tides and everything will be the same because the black hole we put in has the same mass----1.7E31 units---as the moon.

The people appointed John Baez the noted explorer to negotiate.

Give us back our moon, Baez told the gypsies, this black hole you gave us will eventually evaporate. It is not a fair exchange, you have cheated us.

The gypsies thought about it some. then they said "All right, we will give you one chance. If you can tell us how long the black hole will take to evaporate we will swap the moon in for the black hole and take our black hole away with us!"

John baez cubed 1.7E31 to get 4.9E93

then he multiplied by 80/pi to get 125E93

he knew gypsies like to use units based on the Force, so he said "Evaporation will take 1.25E95 natural."

Very good, said the gypsies, but you are from Earth and measure time in years. Tell us the time in years so we can know you really understand.

John Baez knew that a year is close to E50 natural units of time, so that the answer would be close to 1.25E45 years. In fact a year is 1.17E50 natural, so he divided 1.25 by 1.17 to get 1.07 and said
"1.07E45 years"

All right said the gypsies and they swapped their black hole out and the real moon back into orbit.

nightcleaner · Feb 18, 2005

marcus said:

The carved wooden cat is suspended by a string from the ceiling at a distance of 2 paces, or 2E34 natural.
the mass of the slug is a tenth of a pound----E7 mass units----and the muzzle velocity of Verlaine's pistol is E-6, roughly the speed of sound.
Therefore the slug's momentum is 10 natural units of momentum.

the mass of the cat is about 10 pounds----E9 mass units----so for it to acquire 10 units of momentum it must have the speed E-8 (in familiar terms 6.7 mph).

What is the kinetic energy of the cat immediately after impact?

KE = (1/2) m v² = (1/2)E9 x (E-8)² = (1/2)E-7 natural energy units.

Rimbaud, who is the lab assistant, measures the maximum angle of deflection from the verticle attained by the pendulum.

What swing angle does Rimbaud measure?

5E-8 ML2T-2 E50t2L-1=5E42ML;
5E42ML E-9M = 5E33L

The cat is lifted 5E33, the rest is trig.

secant theta = 20E33 1/15 E-33 = 20/15 = 1.5
cos theta = .75
theta= about 41 degrees

marcus · Feb 18, 2005

nightcleaner said:

The cat is lifted 5E33, the rest is trig.

right on target nightcleaner!
the pendulum swing is just enough to lift the cat a distance 5E33
exactly as you say

one way to do the trig (for anybody reading the thread who likes trig)
is to say (since the length Richard calculated, 5E33, is a quarter of the length of the pendulum) we want to find angle A such that:
1- cos A = 1/4
cos A = 3/4
A = 41.4 degrees angle

so the pendulum swings some 41 degrees converting KE to PE and then it stops and turns around and swings back.

nightcleaner · Feb 18, 2005

Hi Marcus

Some gypsies were traveling through Switzerland and they lost a trinket. A goat boy found it and tried to pry it open but couldn't. He took it to his grandmother, who was a wise woman, and she said he shouldn't play with it.

But she was very curious about what was inside the trinket and so she took it along with her to a meeting of her friends at Solstice. They always had a good time at Solstice and the old woman drank quite a bit of blackberry cordial. When she got home again, she had a good sleep, and after a few days she unpacked her bags, discovering that the trinket was gone.

Then she began to worry. Those darn Gypsies. They were always going to far places and bringing strange things back with them. What if what was in the trinket were dangerous? Some of her friends might be silly enough and yet smart enough to open the trinket. Then what might happen?

She went deep into a cave and had a long think. Now, wise women have certain mystical abilities, and one of them is to be able to see things and places that their eyes can't ordinarily visit. She should have used this before, but she was busy getting ready for the Solstice gathering and hadn't had time, before, to sit in a cave.

Now she used her mystical ability and found that things with the trinket were worse than she first imagined. Inside the trinket was a very very hungry worm. If it were released from it's magical case, it would fall to the center of the earth, swallowing everything in its path. Then, it would keep on going through the center, and come out almost all the way to the other side. Then it would fall back again, swallowing everything in its path. Eventually, given enough time, it would swallow up everything in the earth, leaving only a hollow shell. She didn't think this was a good idea.

She was about to set out to retrace her steps to search for the trinket, and had just put on her coat and hat, when she saw a gypsy caravan passing by on the road just beyond her gate. A young girl was sitting in the window of the caravan. She was wearing the trinket on a chain around her neck, and she held it up to show it to the old woman, giving her a dirty look.

She might have felt much better that the gypsies had recovered their trinket on their own, but she didn't trust gypsies. She spit three times on the path and turned around twice before going back in her cottage. The whole episode left her with an uneasy feeling. Next time she saw the goat boy, she gave him a good swat to the back of the head.

And if the dish doesn't run away with the spoon, or the teacup fall into the soup kettle, I will be back tomorrow for another bedtime story.

Thanks for being here,

nc

marcus · Feb 18, 2005

nightcleaner said:

And if the dish doesn't run away with the spoon, or the teacup fall into the soup kettle, I will be back tomorrow for another bedtime story.

so will I, and i will expect another story from you!

marcus · Feb 19, 2005

we could try utilizing the Josephson effect, in a story or problem.
Here is the Wiki article:
http://en.wikipedia.org/wiki/Josephson_effect

it explains that there are several effects, or several parts to the Jos. eff.
1.The AC Jos. effect amounts to a perfect voltage to frequency converter
(Wiki says) in other words you put a constant voltage across the junction and a current flows but the current RIPPLES and the frequency of the ripple is propor'nl to the voltage. In our units the constant is simply the number 2.

if the voltage put across the junction is E-31 (in conventional terms, a quarter of a millivolt)
then the ripple frequency resulting will be 2E-31 (remember that soprano D is E-39 so we are talking something a hundred million times higher than a soprano)
the impressive thing to me is not that it is a high frequency but that the ratio is just the number 2 regardless of how you build the device---it is an absolute universal proportion between voltage and frequency

every voltage has a particular "pitch"

2. The Inverse Jos. Effect this is a perfect frequency-to-voltage converter (Wiki says).
If you have a known frequency microwave source you can set the junction up someway that allows you to "shine" the microwave signal on the junction and GET A VOLTAGE produced which is proportional to the frequency.
Here the constant is just the inverse of 2, namely 1/2.

Wiki says that the Inverse Jo. is used by the metric system people to standardize the volt.

Maybe it used to be that if you wanted to know what a volt was you called them on the phone and they would come over with a standard one volt chemical battery (or something equally ridiculous) and show it to you and say "DAS IST VUN FOLT!" and they would let you hook up things to it and callibrate your volt gauges and so on. But now they don't do that.

Now I suppose if you call them the metric people will still come to your house but they don't bring their old chemical battery (which wasnt very reliable) instead they bring a superstable microwave zinger. They come in and immediately ask "WO IST DER CHUNKTSHUN??" and you show them your Jo. junction and they point their zinger at it and zap it with their precise standardized frequency and it gives a little squeak and makes a perfect one volt potential. And they say "Das ist vun folt," and go away.

In other words WHAT HAS NOW BEEN STANDARDIZED IS NOT THE VOLT ANYMORE BUT THE FREQUENCY THAT PRODUCES ONE VOLT in a Josephson junction.

Or so it seems to me anyway. Maybe someone has more detailed knowledge of contemporary standards.

marcus · Feb 19, 2005

when I discuss frequencies I prefer to consistently use angular format (radians per unit time) instead of cyclic format (cycles per unit time) to talk about them.
Ordinarily physicists don't stick to one format and switch easily back and forth.

the letter they use for frequency (in angular format) is small omega looking like a small rounded w.

the letter for the other format could be a nu sometimes or an f.

in the Wiki article you can see both formats being used
----------------

when you put a steady voltage across a Jo junction it is a little bit like blowing a whistle
(except it is a special whistle where the harder you blow the higher the pitch gets, proportional to the pressure)

with a whistle blowing makes the air stream thru the whistle but it is a steady stream with a flutter or ripple superimposed on it. there is a basic "DC" current of air but on top of that there is an AC flutter.
-----------
a commercial company Theva also has stuff on web about Jo junction
http://www.theva.com/super/josephson.html
http://www.theva.com/super/ac_josephson.html

they seem to use omega angular format frequency more consistently than Wiki but I haven't looked it over enough to recommend it. they have several related pages. talk a little about SQUIDs and such.

if anyone has a good link for Josephson effect please share it!

marcus · Feb 19, 2005

Astronuc just posted about a bright flash witnessed in December 2004
http://www.everything-science.com/index.php?option=com_content&task=view&id=111&Itemid=2
see his post "brightest explosion ever observed"
https://www.physicsforums.com/showthread.php?t=64274

some co-authors of the Nature article are
Bryan Gaensler (Harvard-Smithsonian Center for Astrophysics)
Rob Fender
Maura McLaughlin

“This is a once-in-a-lifetime event. We have observed an object only 20 kilometres across, on the other side of our Galaxy, releasing more energy in a tenth of a second than the Sun emits in 100,000 years,”

"The next biggest flare ever seen from any soft gamma repeater was peanuts compared to this incredible December 27 event. Had this happened within 10 light years of us, it would have severely damaged our atmosphere and possibly have triggered a mass extinction. Fortunately there are no magnetars anywhere near us."
-----------
Let's estimate the energy release in natural units of energy, and also gauge the power output during that tenth of a second.
A year is E50 and 100,000 years is E55.
I looked up the power output of the sun and it seems to be 2.7E-25 (have to double check this)
So the energy the sun puts out in 100,000 years is 2.7E-25 x E55 = 2.7E30.
A tenth of a second is about 4E41. So the power of the flash during that tenth of a second was 27E29/4E41 = 6E-13. Just preliminary estimates that we can check when their paper comes out. I'm having a bad arithmetic day, will double check this after coffee.

Yes, I need to double check more. Back a ways I was trying to get a humanscale handle on the natural unit of power and made a rough calculation that E-49 was like a 160 watt litebulb. Just checked that and it came out to 144 watts instead. Embarrassment :redface:

Fortunately not very much later stuff depended on that, it was a rough calculation to provide a way to visualize the solar constant or brightness of direct sunlight.

marcus · Feb 19, 2005

the solar constant is 6.2E-117
instead of the 5.7E-117 which I reckoned earlier
and I still visualize it as around 6 litebulbs in a square pace area
but they are 6.2 bulbs which are 144 watts each
instead of 5.7 bulbs which are 160 watts each.
drat. nothing to do but check more carefully

Using the force constant in equations

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