It's physics, my dear Watson

"Physics can be like a universal tool kit for solving mysteries. It does not come with instructions, but if you figure out how to use it you’ll find that it comes equipped with everything you need to discover whether or not an ancient pyramid has hidden chambers, how to explain discrepancies in the JFK assassination footage, or find substantial evidence that a meteor impact killed the dinosaurs. And for those who don’t know how to use the tool kit, be sure you get a detective like Luis W. Alvarez." http://physicsbuzz.physicscentral.com/2007/11/its-physics-my-dear-watson-or-pyramids.html

Errore ed incertezza

Discutiamo l’errore e l’incertezza di misura

Quando si procede con un certo strumento alla misura di una grandezza fisica, si può immaginare che questa grandezza sia un’incognita x e che lo strumento dia come risultato dell’operazione di misura un valor noto y.

 Mentre all’ingresso dello strumento abbiamo l’incognita x, rappresentante il valor vero della grandezza fisica, all’uscita abbiamo un valor y perfettamente noto. Si dice errore di misura la differenza tra valor vero e valor misurato:  y-x=e.

Anche l’errore e è incognito come x. Stimo l’errore con l’incertezza U che è invece una grandezza not, come y. Per far questo maggioro l’errore:

|y − x| = |e| < U

Il valor vero sarà compreso allora nell’intervallo [y−U,y+U]. Per definizione:

x=y±U

L’errore quindi non si può conoscere ma si stima con l’incertezza U.

Graficamente

(Per la stima dell’incertezza vedi il testo con approfondimenti sul portale)

Se, per ottenere la misura,  non basta un solo strumento, si deve procedere nel modo seguente. Immaginiamo di avere due strumenti che misurano due grandezze: x_a e x_b.

Gli strumenti danno due valori a e b, noti. Supponiamo di essere stati in grado di stimare le incertezze U_a e U_b. Supponiamo che la misura indiretta sia valutata dalla formula y=f(a,b)=a·b, come per esempio nel prodotto di base per altezza, nell’area del rettangolo. x_a ·x_b sarebbe l’area vera, a·b è l’area misurata.

Siccome:

Si ha che l’errore dell’area è:

 Siccome si suppone che gli errori siano piccoli, il prodotto degli errori è trascurabile rispetto agli altri due termini contente i prodotti errore x misura. Quale sarà allora l’incertezza dell’area?

Essa è data dal seguente procedimento

 Dove abbiamo maggiorato l’errore coi moduli e col successivo uso delle incertezze.

Physics and cathedrals: Flying buttress

"The aim of the Gothic architecture was to achieve light looking, vertical buildings. So they had to invent ways to handle vault pressure without heavy walls. With flying buttress it is possible to keep inner walls thin because: the flying buttress' design provides for an equal and opposite force to be imposed on the wall, thus keeping the wall in balance. This, firstly, enables the vaulted roof and, secondly, by externalising some of the structural elements of the wall, allows the wall so supported to be thinner, which in turn enables the development of large arched window sections to let in light and be filled by stained glass (source: wikipedia)."

More at http://www.opendimension.org/blender_en/arch_pressure.php

Collision Lab 2.01

Per studiare gli urti (collisions) col simulatore

http://phet.colorado.edu/sims/collision-lab/collision-lab_en.html

Poisson and Rutherford, Geiger and Bateman

Poisson distribution
"The Poisson distribution applies when: (1) the event is something that can be counted in whole numbers; (2) occurrences are independent, so that one occurrence neither diminishes nor increases the chance of another; (3) the average frequency of occurrence for the time period in question is known; and (4) it is possible to count how many events have occurred, such as the number of times a firefly lights up in my garden in a given 5 seconds, some evening, but meaningless to ask how many such events have not occurred."
from http://www.umass.edu/wsp/statistics/lessons/poisson/index.html
Dato che lavora sui numeri discreti è la statistica dei decadimenti radioattivi.
La pagina http://www.umass.edu/wsp/statistics/lessons/poisson/problems.html
propone proprio un problema che lavora sui dati del 1910
"Here are the classic 1910 observations of Rutherford, Geiger, and Bateman for the number of alpha particles emitted by a film of polonium, as observed over intervals of one-eighth of a minute (7.5 seconds). "
Here the answer
http://www.umass.edu/wsp/statistics/lessons/poisson/answer03.html

Fai un milione di dollari, col tuo contatore Geiger

"Un nuovo ed entusiasmante gioco per la famiglia. Fai un milione di dollari!
Segui le luci e i ronzii del tuo contatore Geiger" per trovare giacimenti d'uranio...  da una pagina web di Codice Edizioni intitolata "Paura del Piccolo chimico? Allora dovreste provare la radioattività" del 10 gennaio 2013 , che  regala un estratto da "La scienza dal giocattolaio" di Davide Coero Borga, dal capitolo dedicato al Piccolo chimico.

http://www.codiceedizioni.it/paura-del-piccolo-chimico-allora-dovreste-provare-la-radioattivita/

Se volete un Geiger virtuale andate alla pagina

http://www.csupomona.edu/~pbsiegel/Geiger_Counter/Geiger.html

oppure

http://www.geigercounters.com/DownloadDemo.htm

By Toutatis!

"Near-Earth asteroid 4179 Toutatis will be passing within 7 million kilometers of Earth on December 12. It's visited us several times before, with a close pass every four years in December. As near-Earth asteroids go, it's a good-sized one, an elongated and lumpy object about 2 by 2 by 4 kilometers in extent."
http://www.planetary.org/blogs/emily-lakdawalla/2012/12061004-toutatis-preview.html

"Toutatis makes frequent close approaches to Earth, with a currently minimum possible distance (Earth MOID) of just 0.006 AU (2.3 times as far as the Moon). The approach on September 29, 2004, was particularly close, at 0.0104 AU[13] (within 4 lunar distances) from Earth, presenting a good opportunity for observation, with Toutatis shining at magnitude 8.8 when brightest. A more recent close approach of 0.0502 AU (7,510,000 km; 4,670,000 mi) happened on November 9, 2008. The next close approach will be December 12, 2012, at a distance of 0.046 AU (6,900,000 km; 4,300,000 mi), and at magnitude 10.7. ...
Given that Toutatis makes many close approaches the Earth, such as in 1992, 1996, 2000, 2004, 2008, and 2012, it is listed as a potentially hazardous object. ..."
http://en.wikipedia.org/wiki/4179_Toutatis

Toutatis  was a Celtic god worshipped in ancient Gaul and Britain.  Today, he is best known through the Gaulish oath/catchphrase "By Toutatis!", invented for the Asterix comics by Goscinny and Uderzo. The spelling Toutatis, however, is authentic and attested by about ten ancient inscriptions.

Indiana Jones

Vi ricordate il giovane Indiana Jones che salta giù dal treno del circo?

"An especially interesting case arises when a projectile is hurled from the rear of a fast-moving train or other vehicle. Let us suppose that someone throws a stone, horizontally, down the track from the rear platform of a train speeding along at 60 miles per hour. And suppose that the stone is thrown at an initial speed of 60 miles per hour (relative to the train, of course) . Then, to the people on the train, the stone will appear to follow a perfectly normal parabolic path. But how will it seem to a person standing on the ground alongside the track? Remember that velocity is always relative. The forward motion of the train will just cancel the backward motion of the stone. In other words, the stone will plummet straight down to the ground, with no motion at all in the horizontal direction.
A similar situation arises when a bullet is fired from a speeding aeroplane. A revolver bullet, for instance, has a muzzle velocity of only about 500 miles per hour. If such a bullet is fired from the rear of a modern warplane speeding along at 500 miles per hour, the two velocities cancel, and the bullet at first stands still momentarily then falls straight down as though it had been dropped. On the other hand, if the bullet is fired from the front of the plane, the velocities add, and the speed of the bullet relative to the earth is 1,000 miles per hour. Of course, the machine guns used in warfare fire their bullets at speeds much greater than 500 miles per hour. Moreover, if the target is another moving plane, it is the speed of the bullet relative to this moving target that counts in determining the damage done not the speed relative to the earth. It makes no difference at all whether a revolver bullet stands still with respect to the earth and you run into it with a speed of 500 miles per hour, or whether you are standing still with respect to the earth and the revolver bullet strikes you with this speed. In both cases the effect is the same, and unpleasant for you."

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena 

By OVERTON LUHR

the Monkey on the String

Imagine a string passing over a pulley, with a monkey hanging on one end of the string, and an iron bob on the other end balancing the monkey. Monkey and bob are equal in weight, and both are initially at rest. The weight of the string and the friction in the pulley can be neglected.
What happens to the iron bob when the monkey begins to climb up the string? In other words, will the bob rise with the monkey, will it descend, or will it remain stationary?

To solve the problem we must apply Newton's Laws of Motion. When the monkey begins to climb, he is accelerated upward. Therefore, according to Newton's Second Law, the string must not only support the monkey's weight, but it must supply additional force for the acceleration. As a test of this conclusion, you might stand  on bathroom scales sometime when you are going up in an elevator. You will find that as the elevator starts upward, the scales will register several pounds more than your weight. The added push upward on the bottom of your feet serves to accelerate your body. For a simpler experiment, one which can be done less conspicuously, hang a weight on a string, and jerk upward. You will feel a sudden added tension in the string as the mass is accelerated.

Even though the monkey moves upward by his own efforts, there must be an added tension in the string to provide force for the acceleration. By Newton's Third Law the tension in the string must pull equally on the iron bob. Therefore, the bob is accelerated upward just like the monkey. The solution to the problem, then, is this: the monkey and the bob rise together.

When the monkey stops climbing, and thus decelerates, the tension in the string is decreased, and the bob comes to rest at the same time as the monkey. Likewise, if the monkey turns and starts down the string, the bob descends with the monkey.

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena 

By OVERTON LUHR

Does a Flying Bird Weigh Anything?

Does a Flying Bird Weigh Anything? ... Suppose that a bird weighing one pound is flying around in a five-pound cage. If you hung the cage on a spring balance,  would the scales record the weight of the cage alone, or the weight of the cage plus the bird? 

There is a story connected with this problem. Some years ago, a graduate student in physics at a large university decided to have some fun at the expense of two of his professors. A newspaper reporter was made a party to the scheme, and was persuaded to call each of the two professors on the telephone in order to ask his expert opinion on a scientific question.

Professor A was asked the following question: If a one-pound bird is flying in a five-pound cage made of thin wire, how much will the combination weigh? "Five pounds," Professor A told the reporter.

Professor B was then called, and a similar, but slightly different question was put to him: If a one-pound bird is flying in a five-pound cage made entirely of glass, how much will the combination weigh? "Six pounds," replied Professor B without hesitation.

The next day, much to the embarrassment of the two prominent professors, headlines appeared in the local paper: UNIVERSITY PROFS DISAGREE ON SCIENTIFIC QUESTION. A carefully misworded account of the questions and answers followed, with the words wire and glass omitted. No doubt everyone would agree that the bird and cage together would weigh six pounds, provided the bird were sitting stationary on its perch. But which of the professors was right in the case of the flying bird? The answer is that they were both right.  Since the bird is not falling, it must be supported by something. That something is the air. Because of the flapping of the bird's wings, the air pushes up on the bird with a force of one pound. The bird must then push down on the air with an equal and opposite force. This downward force of one pound is transmitted through the air to the first solid surface available. Since the wire cage would not have solid walls or floor, the air would push down, not on the cage, but on the ground below. Therefore, as Professor A said, the wire cage plus bird would weigh only five pounds. On the other hand, the glass cage would be impermeable to air, and in this case the weight of the bird must be borne by the cage. Professor B was absolutely correct when he said that the scales would then read six pounds. There is a moral to this story about the bird in the cage. It illustrates the necessity for precise statement in a scientific problem. 

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena 

By OVERTON LUHR