Levers and Buoyancy
Year of Dis cov ery: 260 B.C.
What Is It? The two fundamental principles un der ly ing all phys ics and en gi neer ing.
Who Discov ered It? Archimedes
Why Is This One of the 100 Great est?
The con cepts of buoy ancy (wa ter pushes up on an ob ject with a force equal to the
weight of wa ter that the ob ject dis places) and of le vers (a force push ing down on one side of
a le ver cre ates a lift ing force on the other side that is pro por tional to the lengths of the two
sides of the le ver) lie at the foun da tion of all quan ti ta tive sci ence and en gi neer ing. They rep –
re sent hu man ity’s ear li est break throughs in un der stand ing the re la tion ships in the phys i cal
world around us and in de vis ing math e mat i cal ways to de scribe the phys i cal phe nom ena of
the world. Count less en gi neer ing and sci en tific advances have depended on those two
How Was It Dis cov ered?
In 260 B.C. 26-year-old Ar chi me des stud ied the two known sci ences—as tron omy and
ge om e try—in Syr a cuse, Sic ily. One day Ar chi me des was dis tracted by four boys play ing
on the beach with a drift wood plank. They bal anced the board over a waist-high rock. One
boy strad dled one end while his three friends jumped hard onto the other. The lone boy was
tossed into the air.
The boys slid the board off-cen ter along their bal anc ing rock so that only one-quar ter
of it re mained on the short side. Three of the boys climbed onto the short, top end. The
fourth boy bounded onto the ris ing long end, crash ing it back down to the sand and cat a pult –
ing his three friends into the air.
Ar chi me des was fas ci nated. And he de ter mined to un der stand the prin ci ples that so
eas ily al lowed a small weight (one boy) to lift a large weight (three boys).
Ar chi me des used a strip of wood and small wooden blocks to model the boys and their
drift wood. He made a tri an gu lar block to model their rock. By mea sur ing as he bal anced
dif fer ent com bi na tions of weights on each end of the le ver (lever came from the Latin word
mean ing “to lift”), Ar chi me des re al ized that le vers were an ex am ple of one of Eu clid’s pro –
por tions at work. The force (weight) push ing down on each side of the le ver had to be pro –
por tional to the lengths of board on each side of the bal ance point. He had dis cov ered the
math e mat i cal con cept of le vers, the most com mon and basic lifting system ever devised.
Fif teen years later, in 245 B.C., Ar chi me des was or dered by King Hieron to find out
whether a gold smith had cheated the king. Hieron had given the smith a weight of gold and
asked him to fash ion a solid-gold crown. Even though the crown weighed ex actly the same
as the orig i nal gold, the king sus pected that the gold smith had wrapped a thin layer of gold
around some other, cheaper metal in side. Ar chi me des was or dered to dis cover whether the
crown was solid gold with out dam ag ing the crown itself.
It seemed like an im pos si ble task. In a pub lic bath house Ar chi me des no ticed his arm
float ing on the wa ter’s sur face. A vague idea be gan to form in his mind. He pulled his arm
com pletely un der the sur face. Then he re laxed and it floated back up.
He stood up in the tub. The wa ter level dropped around the tub’s sides. He sat back
down. The wa ter level rose.
He lay down. The wa ter rose higher, and he re al ized that he felt lighter. He stood up.
The wa ter level fell and he felt heavier. Wa ter had to be push ing up on his sub merged body
to make it feel lighter.
He car ried a stone and a block of wood of about the same size into the tub and sub merged
them both. The stone sank, but felt lighter. He had to push the wood down to sub merge it. That
meant that wa ter pushed up with a force re lated to the amount of wa ter dis placed by the ob ject
(the ob ject’s size) rather than to the ob ject’s weight. How heavy the ob ject felt in the wa ter
had to re late to the ob ject’s density (how much each unit vol ume of it weighed).
That showed Ar chi me des how to an swer the king’s ques tion. He re turned to the king.
The key was den sity. If the crown was made of some other metal than gold, it could weigh
the same but would have a dif fer ent den sity and thus oc cupy a dif fer ent volume.
The crown and an equal weight of gold were dunked into a bowl of wa ter. The crown
dis placed more wa ter and was thus shown to be a fake.
More im por tant, Ar chi me des dis cov ered the prin ci ple of buoy ancy: Wa ter pushes up
on ob jects with a force equal to the amount of wa ter the ob jects displace.
Fun Facts: When Ar chi me des dis cov ered the con cept of buoy ancy, he
leapt form the bath and shouted the word he made fa mous: “Eu reka!”
which means “I found it!” That word be came the motto of the state of Cal i –
for nia af ter the first gold rush min ers shouted that they had found gold.
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