Njutnovo klatno
Njutnova kolevka u kretanju; kao postolje iskorišćena je knjiga Ser Isaka Njutna, “Matematički principi filozofije prirode”
Njutnova kolevka, (engl. Newton’s cradle) ili, kako se još naziva, Njutnovo klatno (engl. Newton’s pendulum), je sprava koja demonstrira zakone održanja impulsa i energije. Konstruisana je pomoću serije klatana (obično 5) koja se oslanjaju jedno na drugo. Svako klatno je zakačeno za okvir ljuljaške pomoću dve niti jednake dužine koje se udaljavaju pod kosim uglom jedna od druge. Ovakav raspored niti ograničava klatna da se kreću samo u jednoj, istoj, ravni. Kada je jedna na kraju otklonjena i puštena da osciluje, rezultujuća sila putuje duž linije u kojoj su postavljene i otklanja poslednju u redu na suprotnom kraju. Ovaj proces se ponavlja sve dok se sistem potpuno ne umiri zbog dejstvujućih sila. Ukoliko u otklon stavimo nekoliko loptica, to će rezultirati otklanjanjem jednakog broja kuglica na suprotnoj strani. Kada je na samom kraju kuglica podignuta na visinu h, i puštena da osciluje kao klatno, ona udara prvu susednu lopticu. Energija i impuls dobijene od te lopte se prenosi kroz tri preostale kuglice do poslednje na kraju. Poslednja lopta na kraju ima istu brzinu i isti otklon kao i prva.

Prva kuglica otklonjena na visinu h, spremna da se sudari sa prvom susednom i da joj prenese impuls.
Mada deluje da se kuglice dodiruju, one su razdvojene za manje od debljine ljudske dlake. Zanimljiva činjenica je da ukoliko podignemo u otklon dve ili više kuglica, puštanjem one će otkloniti jednak broj kuglica na drugom kraju. Sudari kuglica će se nastaviti i zatim će sistem početi da usporava, pri čemu je usporenje uslovljeno trenjem i elastičnošću kuglica. Iz navedenog dešavanja sledi da je najbolji efekat otklona postignut ako su kuglice od čelika. Čelične kuglice se veoma malo deformišu pod udarom i mala vrednost energije se gubi prilikom sudara (oko 2%). Sudari između kuglica su elastični, a otpor vazduha je zanemarljiv. Prva otklonjena kuglica neposredno pre sudara ima brzinu v. Ako je kuglica puštena sa visine h, prema zakonu održanja energije važi:
odnosno .
Kako su to kuglice istih masa, a sudar je centralni, a druga kuglica će preuzeti celokupnu njenu brzinu. Potom se sudaraju druga i treća kuglica, posle čega se druga kuglica zaustavi a treća kuglica se kreće istom brzinom v. Isto će se desiti i pri sudaru treće i četvrte kuglice, treća će posle sudara stati, a četvrta kuglica će krenuti takođe brzinom v, a zatim udariti petu kuglicu. Prema zakonu održanja energije, stići će do visine h, potom će padati i proces će se periodično ponavljati: videćemo samo kretanje krajnjih kuglica prve i pete, a zbog inertnosti oka, kretanje kuglica dva, tri i četiri neće se ni primetiti.
ISTORIJAT NjUTNOVE KOLEVKE
Christiaan Huygens koristio je klatna da bi proučavao sudare. Njegov rad De Motu Corporum ex Percussione („O kretanju tela prilikom sudara“) koje je štampano posthumno 1703. sadrži verziju prvog Njutnovog zakona i razmatra sudare izbačenih tela uključujući i dva tela iste veličine u kretanju pri čemu prilikom sudara jedno telo predaje energiju drugom telu. Njutnova kolevka postala je popularna igračka (ukras sa kancelarijskih i radnih stolova) od trenutka kada je engleski glumac Simon Prebl (Simon Prebble) izumeo, dao joj naziv i počeo sa njenom proizvodnjom, 1967. godine. U početku, drvenu verziju kolevke prodavao je londonski Herods (Harrods of London) da bi kasnije kolevku u hromiranom dizajnu stvorio vajar i budući filmski režiser Ričard Lonkrein (Richard Loncraine).
Zanimljivosti:

Najveće Njutnovo klatno je izloženo u Milwaukee, Wisconsin u prodavnici „American Science and Surplus“.
Ova kolevka predstavlja konstrukciju sa najvećim kuglama, prečnika 26 inča izloženih na javnom mestu. Sam sistem je pričvršćen za plafon uz podršku veoma jakih magneta. Zbog problema sa održavanjem sistem je rastavljen u avgustu 2010.
Jednu od najinteresantnijih verzija Njutnove kolevke napravio je u 2012. godine student umetnosti iz Japana pod imenom Asobi (Lighbulb Version of Newton s Cradle.



Newton’s pendulum

 

Newton’s cradle in motion; a book by Sir Isaac Newton, “Mathematical principles of natural philosophy” is used as a stand.

Newton’s cradle, also called Newton’s pendulum, is a device that demonstrates the law of conservation of momentum and energy. It was constructed by using a series of pendulums (typically 5) that lean on each other. Each pendulum is attached to the frame of the swing by two cords equal in length which move apart from each other at an acute angle. Such an arrangement of cords allows the pendulums to move along only one and the same plane. When a pendulum at the one end is displaced from its resting equilibrium position and then released, it oscillates whereby the resulting force travels through the line and causes the swinging of the pendulum at the opposite end. This process repeats itself until the system comes to rest due to acting forces. If we set several balls in motion, it will result in the swinging of an equal number of balls on the opposite side. When the ball at the very end of the line is raised to the height h, and then released, it oscillates like a pendulum and it strikes the first ball in the series. The energy and momentum acquired from that ball pass through the remaining three balls to the last one at the end. The last ball in the end has the same velocity and the same deflection as the first one.

The first ball raised to the height h, ready to collide with the first one in series and to transmit momentum to it.

Although it seems as though the balls are touching, they are actually separated by less than the thickness of a human hair. An interesting fact is that if we lift two or more balls, after releasing them, they will cause the lifting of an equal number of balls at the opposite end.  The balls will continue to collide, but then the system will start to slow down, whereby the slowdown is determined by friction and elasticity of the balls. What follows from the above-mentioned course of events is the fact that the best effect can be achieved if the balls are made of steel. Steel balls deform insignificantly during the impact and only a small amount of energy is lost during the collision (about 2%). Collisions between balls are elastic, and air resistance is negligible. The first lifted ball has the velocity v just before the collision. If the ball is released from the height h, according to the law of conservation of energy, the following applies:

that is .

Since the balls are equal in mass, and the collision is central, the second ball will take over its entire velocity. Then, the second and the third ball collide, after which the second ball stops and the third ball moves at the same velocity v. The same will happen during the collision of the third and the fourth ball, the third one will stop after the collision, and the fourth ball will also move at the velocity v, and then hit the fifth ball. According to the law of conservation of energy, it will reach the height h, then it will fall down and this process will repeat itself periodically: we will be able to see only the movements of the balls that are at the ends of the line, the first and the fifth one, and due to the inertia of the eye, the movements of the balls two, three and four will not even be noticed.

HISTORY OF NEWTON CRADLE

Christiaan Huygens used pendulum to study collision. His paper “De Motu corporum ex percussion” (“The Motion of Colliding Bodies”), which was published posthumously in 1703, contains a version of Newton’s first law, and considers the collisions of ejected bodies including two equal bodies in motion whereby, during a collision, one body transmits the energy to another body. Newton’s Cradle became a popular toy (decoration on desks in offices) when an English actor, Simon Prebble, invented it, named it and started its production in 1967. Initially, the wooden version of the cradle was on sale at Harrods of London and later the chrome cradle was created by a sculptor and future film director Richard Loncraine.

Interesting:

The largest Newton’s pendulum was on display in Milwaukee, Wisconsin, in the store “American Science and Surplus“.

This cradle represented the structure with the largest balls, 26 inches in diameter, on public display. The system itself was fixed to the ceiling by means of very strong magnets. Due to maintenance problems, the system was dismantled in August 2010.

One of the most interesting versions of Newton’s cradle, Asobi, was made in 2012 by an art student from Japan (Lightbulb Version of Newton s Cradle).