Gradiente e pendenza

Adattato dal testo:
Matematica Generale Con Il Calcolatore  By Michele Impedovo

Momento della forza - Qualche volta si sente dire, in modo semplice, che il "momento della forza" è il "braccio" per la "forza". Che dimensioni ha il momento della forza?

Il "braccio" è una lunghezza - Dimensione [L]

La "forza" ha dimensioni [M][L][T^-2]

[momento]= [M][L²][T^-2]

Quali altre grandezze fisiche hanno le stesse dimensioni?

Equazione dimensionale

Lo spostamento S di una particella che si muove con accelerazione costante è funzione di tempo, accelerazione e velocità. Come?

Introduciamo una equazione: S=k a^b t^c + k' v^d t^e + k'' S_o

 k,k',k'' sono costanti di proporzionalità. Numeri senza dimensioni.
Dobbiamo determinare gli esponenti b,c,d,e.

Passo all'eq. dimensionale: [S]= [ a^b t^c] + [ v^d t^e ] + [ S_o ]

[L]= [ a^b t^c] + [ v^d t^e ] + [ L ]

[L]= [ L^b T^-2b T^c] + [ L^d T^-d T^e ] + [ L ]

[L]= [ L^b T^-2b+c ] + [ L^d T^-d+e ] + [ L ]

Deve essere:

b=1, -2b+c=0, d=1, -d+e=0

da cui: b=1, c=2, d=1, e=1.

Lo spostamento S di una particella che si muove con accelerazione costante è una funzione di tempo ed accelerazione.  Scriviamo:

S = k a^b t^c  

dove k è una costante di proporzionalità (un numero). Mostrare che b=1 e c=2. 

[S] = [L] = [k] [a^b] [t^c]  = [a^b] [t^c]

La costante k non ha dimensioni.

[L] = [L^b T^-2b]  [T^c]

[L¹ T^o ] = [L^b T^-2b+c]

b=1, 0=c-2b=c-2 da cui: c=2.

Dimensioni accelerazione centripeta

Quando un oggetto si muove di moto circolare uniforme, esso è soggetto all'accelerazione centripeta v²/R, dove v è la velocità in modulo ed R il raggio. Verificare le dimensioni.

[a _c] = [v²/R] = [v² R^-1] = [L² t^-2 R^-1] =

 [L² T^-2 L^-1] =  [L T ^-2] = [accelerazione]

Nel moto circolare uniforme, la velocità scalare della particella è data dall'equazione v = ω R, dove ω è la velocità angolare ed R il raggio. Che dimensioni ha ω? Che unità di misura?

Energia cinetica, energia potenziale e lavoro hanno le stesse dimensioni?

[Energia]    cinetica, potenziale  [Lavoro]

Energia cinetica, E _c= 1/2 m v²
[E _c]= [ m v²]=[ M L² T^-2 ]

Energia potenziale, E _c= m g h

[E _c]= [ m g h ]=[ M L² T^-2 ] 

Lavoro = L F
[L F] = [ L M L T^-2 ] = [ M L² T^-2 ]

Why is the ocean blue?

"Why is the ocean blue? Speculation about the blue color of the ocean, as seen from above, goes way back. Lord Rayleigh claimed it was simply reflection of the blue sky. The correct explanation required combining the 19th-century ideas of Robert Bunsen, who felt that the color depended on light absorption by water, and Jacques-Louis Soret, who felt that the color was entirely due to scattering. C. V. Raman pointed out the importance of molecular scattering, and in 1923 Vasily Shuleikin combined those ideas to develop a complete explanation of the color of the sea."

In  Physics Today, Shedding new light on light in the ocean
Tommy D. Dickey, George W. Kattawar, and Kenneth J. Voss
April 2011, http://dx.doi.org/10.1063/1.3580492
Recent advances are making it possible for optical oceanographers to solve a host of pressing environmental problems.

More planets than stars

Microlensing suggests that our galaxy has more planets than stars, buBertram M. Schwarzschild
March 2012, http://dx.doi.org/10.1063/PT.3.1463
Gravitational bending of light reveals exoplanets with large orbital radii.
"Most of the more than 600 exoplanets discovered to date have been found through Doppler evidence of periodic host-star motion or photometric evidence of transits across a star’s face. Both methods are strongly biased in favor of planets with orbital radii much smaller than Earth’s, which defines 1 astronomical unit (AU). Gravitational microlensing is an alternative technique that’s most sensitive to planets a few AU from their stars. It favors very distant stars and it’s relatively unbiased as to stellar mass. Though microlensing’s discovery rate is still modest, it appeals to those who seek a representative galactic survey of planets with orbits like those of the solar system."  http://www.physicstoday.org/resource/1/phtoad/v65/i3/p19_s1

Master of the Mint

I read today that Sir Isaac Newton  was a "Master of the Mint." It is quite interesting this activity of the great scientist. But, what is the Mint? It is the "place where money is coined." The term derived from a Latin moneta, that we have, as it is, in Italian.
http://www.etymonline.com/index.php?term=mint
The online etymology dictionary tells that the adjective meaning "perfect" (like a freshly minted coin) is from 1902; hence "mint condition". I like this coin as a fresh mint candy.

Measuring latitude using a pendulum

Question: is it possible to determine the latitude using a pendulum?

Yes. Use the Foucault's pendulum

Form http://en.wikipedia.org/wiki/Foucault_pendulum
At either the North Pole or South Pole, the plane of oscillation of a pendulum remains fixed relative to the distant masses of the universe while Earth rotates underneath it, taking one sidereal day to complete a rotation. So, relative to Earth, the plane of oscillation of a pendulum at the North Pole undergoes a full clockwise rotation during one day; a pendulum at the South Pole rotates counterclockwise.
When a Foucault pendulum is suspended at the equator, the plane of oscillation remains fixed relative to Earth. At other latitudes, the plane of oscillation precesses relative to Earth, but slower than at the pole; the angular speed, ω (measured in clockwise degrees per sidereal day), is proportional to the sine of the latitude, φ:

where latitudes north and south of the equator are defined as positive and negative, respectively. For example, a Foucault pendulum at 30° south latitude, viewed from above by an earthbound observer, rotates counterclockwise 360° in two days.

Newton's apple

"Newton’s apple - the birth of a physics legend", By Hamish Johnston
In 1666 a young Isaac Newton was waiting out the plague in his mother’s garden in Lincolnshire when an apple fell from a tree. Newton wondered why such bodies always moved downwards, rather than sideways or upwards – and the theory of universal gravitation was born. Read more

http://physicsworld.com/blog/2010/01/newtons_apple_-_the_birth_of_a.html

Home to a famous apple tree

http://physicsworld.com/blog/2010/01/newtons_apple_-_the_birth_of_a.html

Graphyne

"Super-strong, highly conducting graphene is the hottest ticket in physics, but new computer simulations suggest that materials called graphynes could be just as impressive."

Physics - Graphyne May Be Better than Graphene

Luna, Venere e Giove

25 Febbraio, ore 20

Congiunzione Venere, Luna e Giove, con Coolpix

Neutrino: only furious

Science Magazine tells
BREAKING NEWS: Error Undoes Faster-Than-Light Neutrino Results - ScienceInsider

See my old posts
http://stretchingtheboundaries.blogspot.com/2011/09/neutrino-fast-and-furious.html
http://stretchingtheboundaries.blogspot.com/2011/09/speed-of-neutrinos-and-cosmic.html

Aurora boreale

Video da Murmansk,  Russia al link
http://www.youtube.com/watch?v=_qWKLobBmPA

Campo con due cariche

Un esempio di campo vettoriale di tipo centrale. Il cursore permette di modificare la distanza fra le due sorgenti del campo.
http://www.ba.infn.it/~palano/chimica/book/it/Chap_4/sec_4/campo_vettoriale.html

Joule Unlimited

Joule Unlimited will build a production plant for turning sunlight and CO2 into liquid fuels.

Photosynthesis Fuel Company Gets a Large Investment - Technology Review

La massa di Gorgio Gaber

Una serie, una somma di numeri
un insieme di punti attaccati, fenomeno strano
fenomeno strano si sono magnetizzati
un ammasso dove ogni molecola vive da sola
a contatto di ogni altra molecola come
una serie, una somma di uomini
un insieme di uomini uniti, fenomeno strano
fenomeno strano ma sono ipnotizzati
un’inerzia caotica e opaca investita da strane correnti
da instabili flussi, da moti sconnessi che lei non rimanda
 o non vuole e poi assorbe, diventa una massa, una grande potenza neutrale
Una morbida spugna che da sola si ingrossa e vive: LA MASSA
la massa è un terreno fangoso
che tutto sprofonda diventa confuso
la massa è passiva e abissale
ingurgita il senso distrugge il sociale
la massa è il silenzio
è il destino neutrale del plagio
la massa è il contagio
la massa interrompe il circuito
la massa è il neutro
la massa fa massa
la massa opacizza la luce
la massa rifiuta la fede, rifiuta anche il male
rifiuta l’attesa il mistero il sociale
Una morbida spugna che da sola si ingrossa e vive: LA MASSA
la massa è una palla informale
è molle e vischiosa
è uno strano animale
che tutto distrugge e disperde
la massa è un computer avaro
un gran buco nero in cui tutto si perde
la massa è l’inerzia
è il corto circuito, l’immobile orgia del rito
la grande energia negativa
la massa è implosiva
la massa fa massa
Una serie, una somma di uomini
un insieme di uomini uniti, fenomeno strano
fenomeno strano si sono neutralizzati
fenomeno strano
fenomeno strano
fenomeno strano...

La Massa (Giorgio Gaber)

Get physical

Michael Quinion (World Wide Words) writes
"Have you noticed how physical has begun to be more popular as one element in retronyms relating to the online world? If you actually go into a store to buy something, instead of ordering online, that’s physical shopping. Similarly, a physical book is one made with ink on dead trees, in contrast to a digital e-book. Both terms have been around for more than a decade but my impression is that they’ve only recently gone mainstream."
http://www.worldwidewords.org/nl/yurg.htm

Gold nano 'ears' set to listen in on cells - health - 13 January 2012 - New Scientist

"MOVE over microphones, nanophones have arrived. A gold sphere just 60 nanometres in diameter is the most sensitive listening device ever created, paving the way for soundtracks to formerly silent movies of bacteria and other single-celled organisms.
Alexander Ohlinger at Ludwig Maximilian University in Munich (LMU), Germany, and colleagues suspended gold nanoparticles in a drop of water. They trapped one sphere in a laser beam and then fired rapid pulses of light from a second laser at others a few micrometres away. The pulses heated the nanoparticles, which disturbed the water around them, generating pressure, or sound, waves."

Gold nano 'ears' set to listen in on cells - health - 13 January 2012 - New Scientist

Google Science Fair

"The Google Science Fair is an online science competition seeking curious minds from the four corners of the globe. Anybody and everybody between 13 and 18 can enter. All you need is an idea.
 Geniuses are not always A grade students. We welcome all mavericks, square-pegs and everybody who likes to ask questions. Simply upload your project here to win some life changing prizes."
http://www.google.com/events/sciencefair/index.html

Ohm's law at atomic scale

"A new technique for embedding atomic-scale wires within crystals of silicon has revealed that Ohm's law can hold true for wires just four atoms thick and one atom tall. The result comes as a surprise because conventional wisdom suggests that quantum effects should cause large deviations from Ohm's law for such tiny wires. Paradoxically, the researchers hope the finding will aid the development of quantum computers."

Ohm's law holds down to atomic scale - physicsworld.com

An Arctic solution to the data storage

Cold storage - an Arctic solution to the data storage cooling problem | In-depth | The Engineer
"We generate a storm of data throughout the day, whether we want to or not ... And the amount of data we generate personally is dwarfed by the numbers generated by government, industry and commerce. All this data has to be stored and this is giving rise to a new form of building, characteristic to the early 21st century: the data centre. Sharing some of the form and characteristics of ages-old strongrooms and more modern hardened bunkers, these are the locations that keep the numbers vital to our lifestyles, and the fortunes of government and industry, safe. But this has also generated a set of problems for civil engineers. The most vital thing that a data centre has to do is to keep its ranks of computer servers running. For that, they need two things: power and cooling..."

Cloaking objects from surface water waves

Viewpoint: Cloaking Comes Out of the Shadows, by Ross McPhedran, Alexander Movchan.
http://physics.aps.org/articles/v5/2
"Cloaking devices made of a composite of soft and hard materials can divert elastic vibrational waves around an object as though it wasn’t there. Though cloaking devices are mainly associated with hiding objects from light, the concept of cloaking is not restricted to electromagnetic waves. Experimentalists have shown they can cloak objects from surface water waves [1] and electron waves on the surface of metals (plasmons) [2]. Now, Nicolas Stenger at the Karlsruhe Institute of Technology in Germany and his colleagues have designed and tested a cloak that makes an object in a flexible medium invisible to elastic vibrational waves [3]; that is, the waves pass by the object as though it wasn’t there. The work, which is presented in Physical Review Letters, describes a cloaking device that is both more efficient and covers a wider bandwidth than any other existing cloak."

2011: The Year of Materials

Vibrant displays head to market, invisibility cloaks become more practical, and batteries store more energy...
The Year in Materials - Technology Review