using the force constant in equations

marcus

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

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:


What was the momentum of the bullet?

marcus

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?"


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

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

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

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

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

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

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

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

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

marcus

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 dont do that.

Now I suppose if you call them the metric people will still come to your house but they dont 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

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.
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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 havent 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

Astronuc just posted about a bright flash witnessed in December 2004
http://www.everything-science.com/in...d=111&Itemid=2
see his post "brightest explosion ever observed"
http://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
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

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

marcus

Here's a nasa link that goes with that. It has an animation of the flare and some photographs of the aftermath taken in the optical range.
http://www.nasa.gov/vision/universe/..._nsu_0205.html

It says that for a tenth of a second the power of the explosion was E40 watts.
the natural unit of power is 1.444E51 watts, so roughly 100 billion time brighter still.
In case anyone is curious and wants to calculate the natural power unit for themselves it is really easy, you just need to know c and G
the power unit is just c⁵/(8piG)

so you put in 299792458, raise it to the fifth,
then you divide by 8pi,
then you divide by 6.6742E-11 (what NIST gives for G)
and that's it

at this point I believe you have 1.444E51 watts.

this is the number that I somehow goofed with and got 1.6E51
in a rough calculation a couple of weeks ago. too much in a hurry
or just careless