How taking a bath led to Archimedes' principle - Mark Salata

Kako je kupanje dovelo do Arhimedovog principa - Mark Salata

Prevodilac: Mile Živković Lektor: Tatjana Jevdjic

Some of the best opportunities to learn

Neke od najboljih prilika za učenje

are the moments in which we are perplexed.

su trenuci kada smo zbunjeni.

Those moments in which you begin to wonder and question.

Oni trenuci kada se pitate i zapitkujete.

These moments have happened throughout history.

Ovi trenuci dešavali su se tokom cele istorije

and have led to some truly amazing discoveries.

i doveli su do nekih zaista zapanjujućih otkrića.

Take this story, for example.

Na primer, uzmite ovu priču.

There once was a fellow named Archimedes.

Jednom je postojao čovek zvani Arhimed.

He was born in 287 B.C. in the city of Syracuse in Sicily.

Rodio se 287. godine pre nove ere, u Sirakuzi na Siciliji.

He was a Greek mathematician, physicist, engineer,

Bio je grčki matematičar, fizičar, inženjer

inventor, and astronomer.

izumitelj i astronom.

One day, Archimedes was summoned by the king of Sicily

Jednog dana, Arhimeda je zvao kralj Sicilije

to investigate if he had been cheated by a goldsmith.

da ispita da li ga je prevario zlatar.

The king said he had given a goldsmith the exact amount of gold

Kralj je rekao da je zlataru dao tačnu količinu zlata

needed to make a crown.

koja je potrebna da se napravi kruna.

However, when the crown was ready, the king suspected that the goldsmith cheated

Ipak, kada je kruna bila gotova, kralj je posumnjao da ga je zlatar prevario

and slipped some silver into the crown,

i u krunu ubacio malo srebra,

keeping some of the gold for himself.

tako zadržavši nešto zlata za sebe.

The king asked Archimedes to solve the problem.

Kralj je pitao Arhimeda da reši problem.

But there was a catch: he couldn't do any damage to the crown.

Ali postojala je kvaka - nije smeo da ošteti krunu.

One day, while taking his bath,

Jednog dana, dok se kupao,

Archimedes noticed that the water level in the bathtub rose

Arhimed je primetio da se nivo vode u kadi dizao

and overflowed as he immersed himself into the tub.

i da se kada prelivala kada bi uronio u nju.

He suddenly realized that how much water was displaced

Iznenada je shvatio da to koliko vode izađe

depended on how much of his body was immersed.

zavisi od toga koji deo njegovog tela je uronjen.

This discovery excited him so much that he jumped out of the tub

Ovo otkriće toliko ga je uzbudilo da je iskočio iz kade

and ran through the streets naked, shouting "Eureka!"

i go potrčao kroz ulice vičući: "Eureka!"

Which comes from the ancient Greek meaning "I found it."

Što na starogrčkom znači: "Pronašao sam."

What did he find?

Šta je on to pronašao?

Well, he found a way to solve the king's problem.

Pa, pronašao je način da reši kraljev problem.

You see, Archimedes needed to check the crown's density

Vidite, Arhimed je trebalo da proveri gustinu krune

to see if it was the same as the density of pure gold.

kako bi video da li je iste gustine kao čisto zlato.

Density is a measure of an object's mass divided by its volume.

Gustina je mera mase objekta podeljena se njegovom zapreminom.

Pure gold is very dense, while silver is less dense.

Čisto zlato je veoma gusto, dok je srebro manje gusto.

So if there was silver in the crown, it would be less dense than if it were made of pure gold.

Ako je u kruni bilo srebra, ona bila manje gusta nego da je sačinjena od čistog zlata.

But no matter what it was made of, the crown would be the same shape,

Ali bez obzira od čega je napravljena, kruna bi imala isti oblik,

which means the same volume.

što znači istu zapreminu.

So if Archimedes could measure the mass of the crown first,

Dakle, ako bi Arhimed prvo izmerio masu krune,

and then measure its volume,

i onda izmerio njenu zapreminu,

he could find out how dense it was.

mogao bi da otkrije koliko je bila gusta.

But it is not easy to measure a crown's volume - it has an irregular shape,

Ali nije lako izmeriti zapreminu krune - ona ima nepravilan oblik,

that's different from a simple box or ball.

koji je drugačiji od jednostavne kutije ili lopte.

You can't measure its size and multiply like you might for other shapes.

Ne možete joj izmeriti veličinu i to samo pomnožiti, kao kod drugih oblika.

The solution, Archimedes realized,

Arhimed je shvatio da je rešenje u tome

was to give the crown a bath.

da se kruna okupa.

by placing it in water and seeing how much water was displaced,

Tako što bi je stavio u vodu i video koliko vode izlazi,

he could measure the volume,

mogao bi da izmeri zapreminu

and he'd calculate the density of the crown.

i izračunao bi gustinu krune.

If the crown was less dense than pure gold,

Ako je kruna manje gustine nego čisto zlato,

then the goldsmith most definitely cheated the king.

onda je zlatar sasvim sigurno prevario kralja.

When Archimedes went back to the king and did his test,

Kada se Arhimed vratio kod kralja i uradio ovaj test,

the story says, he found that the goldsmith had indeed cheated the king,

po priči, otkrio je da je zlatar zaista prevario kralja,

and slipped some silver in. These days,

i ubacio nešto srebra. U današnje vreme,

using the way an object displaces water to measure volume is called

merenje zapremine pomoću količine vode koju objekat izbaci

Archimedes' principle. The next time you take a bath,

zove se Arhimedov princip. Sledeći put kada se budete kupali

you can see Archimedes' principle in action,

možete videti Arhimedov princip na delu

and maybe you'll have a genius idea of your own.

i možda se i vama javi neka genijalna ideja.