The mighty mathematics of the lever - Andy Peterson and Zack Patterson

Moćna matematika poluge - Endi Piterson (Andy Peterson) i Zek Paterson (Zack Patterson)

Prevodilac: Milana Stojadinov Lektor: Mile Živković

A famous Ancient Greek once said,

Jednom je jedan poznati stari Grk rekao:

"Give me a place to stand, and I shall move the Earth."

"Dajte mi oslonac i pomeriću Zemlju."

But this wasn't some wizard claiming to perform impossible feats.

Ovo nisu bile reči nekog čarobnjaka koji je tvrdio da može da uradi nemoguće.

It was the mathematician Archimedes

To je rekao matematičar Arhimed

describing the fundamental principle behind the lever.

opisujući osnovne principe poluge.

The idea of a person moving such a huge mass on their own

Ideja da čovek sam pomeri toliko veliku masu

might sound like magic,

može zvučati magično,

but chances are you've seen it in your everyday life.

ali verovatno ste već videli nešto slično u svakodnevnom životu.

One of the best examples is something you might recognize

Najbolji primer kojeg se možete setiti

from a childhood playground:

je primer sa dečjeg igrališta:

a teeter-totter, or seesaw.

klackalica.

Let's say you and a friend decide to hop on.

Recimo da drug i ti odlučite da uskočite.

If you both weigh about the same,

Ako ste otprilike jednake težine,

you can totter back and forth pretty easily.

klackanje vam neće biti problem.

But what happens if your friend weighs more?

Šta se događa ako je vaš drugar teži?

Suddenly, you're stuck up in the air.

Iznenada, ostaćete u vazduhu.

Fortunately, you probably know what to do.

Srećom, verovatno znate šta treba uraditi.

Just move back on the seesaw, and down you go.

Samo se malo odmaknite, i spustićete se dole.

This may seem simple and intuitive,

Ovo možda deluje jednostavno i intuitivno,

but what you're actually doing is using a lever to lift a weight

ali zapravo koristite polugu da biste podigli nešto

that would otherwise be too heavy.

što bi inače bilo jako teško.

This lever is one type of what we call simple machines,

Poluga je jedna od takozvanih jednostavnih mašina.

basic devices that reduce the amount of energy required for a task

Osnovni uređaj koji smanjuje potrebnu količinu energije

by cleverly applying the basic laws of physics.

mudrom primenom osnovnih zakona fizike.

Let's take a look at how it works.

Pogledajmo kako funkcioniše.

Every lever consists of three main components:

Poluga se sastoji od tri glavna dela:

the effort arm, the resistance arm, and the fulcrum.

krak aktivne sile, krak sile tereta i oslonac.

In this case, your weight is the effort force,

U ovom slučaju, tvoja težina je aktivna sila,

while your friend's weight provides the resistance force.

a težina tvog druga je sila tereta.

What Archimedes learned was that there is an important relationship

Arhimed je zapazio da postoji čvrsta veza

between the magnitudes of these forces and their distances from the fulcrum.

između intenziteta ovih sila i njihovog rastojanja od oslonca.

The lever is balanced when

Poluga je u ravnoteži kada je

the product of the effort force and the length of the effort arm

proizvod aktivne sile i dužine kraka te sile

equals the product of the resistance force and the length of the resistance arm.

jednak proizvodu sile tereta i dužine kraka tereta.

This relies on one of the basic laws of physics,

To sledi iz osnovnog zakona fizike,

which states that work measured in joules is equal to force applied over a distance.

koji kaže da je rad izražen u džulima srazmeran sili i dužini pređenog puta.

A lever can't reduce the amount of work needed to lift something,

Poluga ne može smanjiti potrebnu silu za podizanje nečega,

but it does give you a trade-off.

ali nudi kompromis.

Increase the distance and you can apply less force.

Povećaj rastojanje i možeš upotrebiti manju silu.

Rather than trying to lift an object directly,

Umesto da diže predmet direktno,

the lever makes the job easier by dispersing its weight

poluga olakšava posao širenjem njegove težine

across the entire length of the effort and resistance arms.

preko cele dužine kraka aktivne sile i kraka sile tereta.

So if your friend weighs twice as much as you,

Tako da, ako je tvoj prijatelj duplo teži od tebe,

you'd need to sit twice as far from the center as him in order to lift him.

sedi dva puta dalje u odnosu na oslonac i podići ćeš ga.

By the same token, his little sister, whose weight is only a quarter of yours,

Isto tako, njegova mlađa sestra, koja je četiri puta lakša od tebe,

could lift you by sitting four times as far as you.

može da podigne tebe ako sedi četiri puta dalje.

Seesaws may be fun, but the implications and possible uses of levers

Klackalica je zabavna, ali značaj i moguće primene poluge

get much more impressive than that.

su mnogo čudesnije od toga.

With a big enough lever, you can lift some pretty heavy things.

Sa dovoljno velikom polugom, možete podići poprilično teške stvari.

A person weighing 150 pounds, or 68 kilograms,

Čovek koji teži 150 funti, odnosno 68 kilograma,

could use a lever just 3.7 meters long to balance a smart car,

pomoću poluge dugačke 3,7 metara može da balansira kolima marke "Smart",

or a ten meter lever to lift a 2.5 ton stone block,

ili da pomoću poluge od 10 metara podigne kameni blok od 2,5 tone,

like the ones used to build the Pyramids.

sličan onima od kojih su gradjene Piramide.

If you wanted to lift the Eiffel Tower, your lever would have to be a bit longer,

Ako želiš da podigneš Ajfelov toranj, poluga treba da bude malo duža,

about 40.6 kilometers.

otprilike oko 40,6 kilometara.

And what about Archimedes' famous boast?

Šta je sa Arhimedovim hvalisanjem?

Sure, it's hypothetically possible.

Naravno da je to u teoriji moguće.

The Earth weighs 6 x 10^24 kilograms,

Zemlja je teška 6 x 10^24 kilograma,

and the Moon that's about 384,400 kilometers away

i Mesec koji je udaljen oko 384 400 kilometara

bio bi odlična tačka oslonca.

would make a great fulcrum.

So all you'd need to lift the Earth

Sve što je potrebno za pomeranje Zemlje

is a lever with a length of about a quadrillion light years,

jeste poluga dugačka oko kvadrilion svetlosnih godina,

1.5 billion times the distance to the Andromeda Galaxy.

1,5 milijardi puta više od udaljenosti do galaksije Andromeda.

And of course a place to stand so you can use it.

I naravno, mesto na kome ćeš stajati da bi je iskoristio.

So for such a simple machine,

Iako je toliko jednostavna mašina,

the lever is capable of some pretty amazing things.

poluga je podobna za velike stvari.

And the basic elements of levers and other simple machines

Osnovni delovi poluge, kao i drugih jednostavnih mašina,

are found all around us in the various instruments and tools

mogu se naći svuda oko nas, na raznim instrumentima i na alatima

that we, and even some other animals, use to increase our chances of survival,

koje mi, kao i neke životinje, koristimo da bi povećali šanse za opstanak,

or just make our lives easier.

ili samo da bi olakšali život.

After all, it's the mathematical principles behind these devices

Uostalom, glavni krivci su matematički principi iza ovih uređaja

that make the world go round.

koji pokreću svet.