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Alt 03.09.08, 00:08   Yukarı Git #1
facia
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Post Arşimet Prensibi


SIVILARIN KALDIRMA KUVVETİ

Sıvı içinde bulunan bir cisim sıvı tarafından yukarıya doğru itilir. Bu itme kuvveti, sıvının kaldırma kuvveti olup cismin sıvı içinde kapladığı hacim kadar hacimdeki sıvının ağırlığıdır.

F=Vbatanhacim.r=Vbatanhacim.d. g

Sıvı içine bırakılan bir cisme aynı anda iki kuvvet etki eder:
G=Cismin ağırlığı G=V.dcisim.g
F=Sıvının kaldırma kuvveti F=V.dsıvı.g

Yüzme Ve Batma Koşulları

I) G>F ise; dc>ds olur. Bu durumda cisim batar.
II) G=F ise; dc=ds olur. Bu durumda cisim sıvı içinde nereye bırakılırsa orada kalır.
III) G Bu durumda: G=F olur.
V.dc.g=Vbatan.ds.g
dc/ds=Vbatan/V=batma miktarı olur.
Örneğin, eğer cismin özkütlesi 1g/cm3 , sıvının özkütlesi 3g/cm3 ise cismin hacminin 1/3 ü sıvı içine girer.
Bir cismin bir kısmı veya tamamı sıvı içinde ise ancak cisim batmamışsa daima cismin ağırlığı sıvının kaldırma kuvvetine eşit alınır.
Aynı cisim farklı sıvılarda şekillerdeki konumlarda dengede ise farklı sıvılar cismi daima aynı kuvvetle kaldırır.
İki cisim bir sıvıda dengede ise GX+GY=F olur.
Bir cisim, birbirine karışmayan X ev Y gibi iki sıvı içinde dengede ise G=FX+FY olur.
Cismin hacminin yarısı X,diğer yarısı Y sıvısı içinde ise dcisim=(dX+dY)/2 olur.
Serbest bırakıldığında sıvıda batabilecek olan bir cisim iple bağlanarak sıvıya daldırılmış olsun. İpteki T gerilme kuvveti T=G-F olur. Bu durumda kap G-T=F kadar ağırlaşmış olur.
Esnek olmayan cisimler iple şekildeki gibi bağlanmış olsun.
T1=G-F ve T2=F-G olur.
T
ip gerilmesini değiştirmek için F kaldırma kuvvetini değiştirmek gerekir. F?yi değiştirmek için
1.Kaptan biraz sıvı dökerek cisimlerin bir kısmının sıvı dışına çıkmasını sağlamak gerekir.Bu durumda cismin sıvı içindeki hacmi azaltılmış olur.Veya;
2.Kaptaki sıvının özkütlesini değiştirmek gerekir.

İçi hava dolu esnek balon iple kabın tabanına bağlı olsun. Bu durumda T=F-G olur. İpteki gerilme kuvvetini değiştirmek için F kaldırma kuvvetini değiştirmek gerekir. F?yi değiştirmek için;
1.Sıvının özkütlesini değiştirilmelidir.Veya;
2.Sıvının balona yaptığı basınç değiştirilmelidir.Basın artarsa,balonda içindeki havanın basıncını artırma için hacmini azaltmak zorunda kalır.



SIVILARIN KALDIRMA KUVVETİ
VE
KULLANILDIĞI YERLER




? Sıvıların Kaldırma Kuvveti Nedir?
Sıvıların içine batırılan cisimler,yukarıya doğru itilirler ve ağırlıklarından kaybederler.Bunun nedeni sıvıların kaldırma kuvvetidir.Kaldırma kuvvetinin varlığı ,Arşimet adlı bilim adamı
tarafından bulunmuştur.

(şekil-1-Kaldırma kuvvetinin cisme etkisi)
---------------------- -------------------------------
Bütün sıvılar içlerinde bulunan maddeye kaldırma kuvveti uygularlar. Bu kuvvet cismin akışkan içindeki hacmine ve akışkanın yoğunluğuna bağlıdır. Sıvı ne kadar yoğunsa uygulanan kaldırma kuvveti de o kadar fazladır. Bu yüzden suyun kaldırma kuvvetini suya girdiğimizde hissederiz ama havanın bize herzaman uyguladığı kaldırma kuvvetini ,çok az olduğundan dolayı hissedemeyiz. Bu bağlamda da sıvıların kaldırma kuvvetinin yoğunluğa da bağlı olduğunu söyleyebiliriz.
------------------------------------------------------------------------
? Arşimet Prensibi:
Bir sıvı içindeki katı cisim,taşırdığı sıvının ağırlığına eşit bir kuvvet ile yukarıya itilir.Ünlü bir deneyde Arşimet,aynı kütledeki altın bir taç ile bir altın külçesinin taşıracakalrı su miktarlarının aynı olması gerektiğini ileri sürmüş ve dediği çıkmayınca tacın altın olup olmadığını anlamıştır.
? Kullanıldığı Yerler:
Arşimet prensibi,cisimlerin kendi ağırlıklarının bulunmasında kullanılır.
Parmaklarımızı bitiştirip içi su dolu bir kaba batıralım.Elimizi aşağıdan yukarıya doğru iten bir kuvvet hissederiz.Denizde yüzerken de bizi suyun yüzeyine iten bir kuvvet vardır.Çok büyük kütleli ve boyutlu gemiler bile suda Arşimet prensibi sayesinde yüzerler.Bütün bu örnekler bizlere,sıvıların bir kaldırma kuvveti olduğunu gösterir.Bu kaldırma kuvvetinin kullanıldığı alanlar ise oldukça fazladır.
İnsanların yiyecek ihtiyacından tutun da,turistik faaliyetler için bile şu anda suyun kaldırma kuvvetinden yararlanılmaktadır:
Bazı bölgelerde bulunan baraj gölleri,balık bakımından zengindirler.Kayık,kaldırma kuvvetinden yararlanılarak yapılmış olduğu için kayık kullanan bir kısım balıkçılar hem geçimlerini sağlamak hem de insanların besin ihitiyacını karşılamak için bu yola başvurular.Yine aynı şekilde, kaldırma kuvvetinden yararlanılarak yapılan bir spor da raftingdir.Her yıl binlerce turist ülkemize gelerek bu sporla ilgilenirler.Turistlerin bu konudaki ilgi alanları bununla sınırlı kalmaz.Günümüzün yaygın sporlarından Jet-Ski,Sörf,Yelkenli ; turistlerin ilgi odağı olmuştur.
Kaldırma kuvvetini kullanıldığı bir diğer alan ise taşımacılıktır.Kıbrıs'ın bir ada olması bakımından oraya yapılan gezilerde su yolu kullanılmaktadır.Ülkemizde bulunan Keban Gölü'nde bile iki köy arasında gidip gelmek için kayıkla veya sallar ile ulaşım gerçekleşir.Her gün binlerce İstanbullu öğrenci Anadolu ve Avrupa yakasına varabilmek,okullarına ulaşabilmek için(köprü olmasına rağmen)ucuz ve rahat olduğu için deniz yolunu tercih etmektedirler.
Toprakları deniz kıyısında bulunan ülkeler için su ve su yolları savunma bakımından büyük önem taşır.Kaldırma kuvveti ile su üzerinde durabilen binlerce tonluk savaş gemileri yapılarak ülkeler arası güvenlik sağlanır.
Osmanlı Devleti zamanında bir çok devlet sıcak denizlere açılıp ticaret yapmak istemişlerdir.Bunun için de su yolunu kullanmışlar ,dolayısıyla da suyun kaldırma kuvvetinden yararlanmışlardır.Bu şekilde ticaretlerini geliştirerek dünyanın sayılı ülkeleri haline gelmek istemişlerdir.İşte Arşimet'in bulduğu kaldırma kuvvetinden birçok devlet belki de bu prensibi bilmeden ondan yararlanmışlardır.
Sonuç olarak;suyun böyle bir özelliğinin farkında olmasaydık hayat bizim için belki de çok zor
olacaktı.Unutmayalım ki,şu anda yüzüp,denizde seyahat ediyorsak, bunlarArşimet'in sayesinde olmuştur.Bu yüzden bu bilim adamının kıymetini bilmeli,prenisibini en iyi şekilde kullanarak onu geliştirmeye çalışmalıyız

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Alt 03.09.08, 00:36   Yukarı Git #2
facia
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79 mesajına 121 kere teşekkür edildi.

Standart


Sıvı içine daldırılan bir cisim, yerini değiştirdiği sıvının ağırlığına eşit bir kuvvetle aşağıdan yukarıya doğru itilir.

F= V?.d

V? : Yer değiştiren sıvının hacmi = Cismin batan kısmının hacmi

d : Yer değiştiren sıvının özgül ağırlığı

F : Yer değiştiren sıvının ağırlığı yani sıvının kaldırma kuvveti.

Archimedes prensibinin deneysel olarak gerçekleştirilmesi

İç içe girebilen biri dolu diğeri boş olan ¤¤¤¤l silindirden dolu olan altta olmak üzere aşağıdaki şekilde görüldüğü gibi bir terazinin kefesinin altına asılır. Diğer kefeye konan dara ile terazinin dengesi sağlanır. Dolu silindir sıvıya batırılırsa denge bozulur. Dengeyi bozan sıvının kaldırma kuvvetidir. Hacmi, dolu silindire eşit olan boş silindir sivi ile doldurulursa, terazi tekrar dengeye gelir. Burada kaldırma kuvveti, silindire konan sıvı (cismin batan kısmının hacmi kadar sıvı) tarafından dengelenmiş oluyor. Şu halde sıvının kaldırma kuvveti , yer değiştiren sıvının hacmine eşittir.



Archimedes prensibinin teorik olarak gerçeklenmesi

Silindir şeklindeki bir blokun , sıvı içinde düşey olarak tutulduğunu düşünelim. Silindirin taban alanı S, yüksekliği h ve sıvının özgül ağırlığı d olsun. Silindirin üst tabanının sıvı yüzeyine mesafesini h1 , alt tabanın sıvı yüzeyine mesafesini h2 , ile gösterelim. Silindirin üst tabanındaki basınç p1=h1.d ve dolayısıyla tabana etki eden basınç kuvveti,

F1=p1.s=h1.d.S



Silindirin alt tabanındaki basınç p2.h2.d ve tabana etki eden basınç kuvveti, F2=p2.S=h2.d.S dir.Bu iki kuvvet aynı doğrultuda, zıt yönde ve F2>F1 dir. Yan yüzlere etki eden basınç kuvvetleri; karşılıklı olarak ikişer ikişer düşünülürse, eşit şiddette, aynı doğrultuda olduklarından bileşkeleri sıfırdır. Şu halde silindire etki eden basınç kuvvetlerinin bileşkesinin şiddeti F1 ile F2 kuvvetlerinin farkına eşit ve yönü yukarıya doğrudur. F=F2-F1=h2.d.S-h1.d.S=d.S.(h2-h1) dir.Halbuki h2-h1 silindirin h yüksekliğine eşittir h2-h1=h yazılırsa ,F=d.S.h ve S.h ise silindirinV hacmine eşit olduğundan,F=d.V=yer değiştiren sıvının ağırlığıBu sonuç, Archimedes prensibinin doğruluğunu gerçekler.

ÖRNEK PROBLEMLER

1. Kenarı 10 cm ve yoğunluğu 7,8 g/cm3 olan küp biçiminde bir cisim, yarısı yoğunluğu 0,8 g/cm3 olan sıvı içinde iken tartılırsa kaç gram gelir?

Çözüm: Cismin havadaki ağırlığı,

G=V.d =1000.7,8=7800 g. dır.

Cisim suya batırıldığı için, itme kuvveti kadar ağırlığından kaybeder. Sıvı içindeki ağırlık G? ve sıvının kaldırma kuvveti F ise;

G?=G-F dir.

F=V?.d=0,8.1000/2=400g.

G?=7800-400=7400 g.

2. ¾?ü su içinde iken tartılan bir cisim, havadaki ağırlığına nazaran 600 g hafiflediğine göre, cismin hacmi kaç cm3 tür?

Çözüm: Cisim, itme kuvveti kadar ağırlığından kaybettiğine göre itme kuvveti 600 g dır.

V?=3/4.V olur. F=V?.d 600=3/4V.1 ; V=800 cm3 bulunur.

3. Havada 500g, suda 400 g gelen cismin yoğunluğunu bulunuz.

Çözüm:Bir cismin havadaki ağırlığı G1, sudaki ağırlığı G2 olsun, suyun itme kuvveti ,

F=G1-G2

Cismin hepsi suya daldırıldığı için V?=V=cismin hacmi

F=V?.d

G1-G2=V.1 V=G1-G2

Buradan şu netice çıkıyor:

Bir cismin, havadaki ağırlığı - sudaki ağırlığı = cismin hacmi, cismin yoğunluğu = d ise ;

d=G/V =G1/(G1-G2)= 500/(500-400)= 5 g/cm3 bulunur.

4. Bir cisim havada 200 g, suda 150 g ve başka bir sıvıda 160 g geliyor. İkinci sıvının yoğunluğunu bulunuz. Cevap:0,8g/cm3

5. Yoğunluğu 2 olan bir cisim suda 40 g geliyor. Cismin hacmi kaç cm3 tür?

Cevap:40 cm3

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