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Alt 11.01.08, 16:45   Yukarı Git #1
karamelek
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Standart MOMENT DENGE


İki noktası ya da en az bir noktası sabit olan cisimlere bir kuvvet uygulandığında, cisim sabit bir nokta veya eksen etrafında dönme hareketi yapar.
Kapı ve pencereleri açıp kaparken, musluğu çevirirken, kapı anahtarını ve vidayı tornavida ile çevirirken kuvvetin döndürme etkisinden faydalanırız. Bir kuvvetin döndürücü etkisine moment denir. M sembolü ile gösterilir ve vektörel bir büyüklüktür.

Momentin büyüklüğü, uygulanan kuvvet ile, kuvvetin sabit nokta ya da eksene olan dik uzaklığının çarpımına eşittir. Å~ekildeki çubuk, O noktasından sabitlenmiş olup, O dan geçen dik eksen etrafında dönebilmektedir. F kuvvetinin O noktasına göre momenti

M = F . d bağıntısı ile hesaplanır.

O noktasından sabitlenmiş çubuğa F1 ve F2 kuvvetleri uygulandığında, kuvvetlerin etkime doğrultusu şekildeki gibi O noktasından geçiyorsa


M = F . d bağıntısına göre, her iki kuvvet için de d dik uzaklıkları sıfır olduğundan, bu kuvvetlerin döndürücü etkisi yoktur. Yani F1 ve F2 kuvvetlerinin O noktasına göre momentleri sıfırdır


O noktasından sabitlenmiş çubuğa F kuvveti şekildeki gibi uygulanırsa, kuvvetin O noktasına göre momenti iki yoldan bulunur.


I. Yol : F kuvveti, biri çubuğa paralel, diğeri ise çubuğa dik iki bileşenine ayrılır. Çubuğa paralel olan Fx bileşeninin uygulama doğrultusu O noktasından geçtiği için döndürücü etkisi yoktur. Yani momenti sıfırdır. Fy bileşeni çubuğa dik olduğundan O noktasına göre momenti,


M = Fy . l olur. (Fy = F . sina dır.)

II. Yol : F kuvvetinin Onoktasına göre momenti bulunurken dik uzaklık olarak, kuvvetin etkime doğrultusuna dönme noktasından çizilen dik uzaklık kullanılır. O ya göre moment M = F . d dir.

Bileşke Moment
Moment vektörel bir büyüklük olduğundan, birden fazla kuvvetin etkisinde kalan cismin hangi yönde döndüğünü bulabilmek için momentlerin vektörel toplamını yani bileşke momenti bulmak gerekir.

Ağırlığı önemsiz şekildeki çubuk O noktasından sabitlenmiştir. F1, F2, F3 kuvvetlerinin O noktasına göre bileşke momentini bulmak için önce kuvvetlerin çubuğa hangi yönde döndürücü etki yaptıkları tespit edilir. Herhangi bir yön (+), zıt yön ise (?) seçilir. F1 ve F2 kuvvetleri çubuğu O noktasına göre (?) kabul edilen yönde döndürücü etki yaparken, F3 kuvveti (+) yönde döndürücü etki yapar. O noktasına göre kuvvetlerin toplam momenti, kuvvetlerin ayrı ayrı momentlerinin cebirsel topl***** eşittir.

SM = F3 . d3 ? (F1 . d1 + F2 . d2)

Kuvvetlerin şiddetine ve O noktasına olan dik uzaklık değerlerine göre, bu işlemin üç sonucu vardır. Sonuç (+) ve (?) değerde çıkabildiği gibi sıfır da çıkabilir. Sonucun (+) değerde çıkması, çubuğun (+) kabul edilen yönde ve çıkan değer kadar bir momentle döndüğünü ifade eder.

Sonucun (?) değerli çıkması da, benzer şekilde çubuğun (?) yönde çıkan değer kadar bir momentle döndüğünü ifade eder.

Sonucun sıfır çıkması yani bileşke momentin sıfır olması çubuğun dengede kalması demektir. Bu durumda çubuk duruyor ya da sabit hızla dönüyordur.


Kuvvet Çifti

2d uzunluğundaki çubuk O noktasından geçen dik eksen etrafında dönebilmektedir. Aynı düzlemde, eşit büyüklükteki kuvvetler şekildeki gibi zıt yönlü uygulandıklarında çubuk ok yönünde döner.

Bu sisteme kuvvet çifti denir. Kuvvet çiftinin denge noktası yoktur. Çubuk 2F . d kadarlık toplam momentle döner. Arabanın direksiyonu çevrilirken, musluklar açılıp kapanırken, anahtar döndürülürken kuvvet çifti uygulanır.

Denge

Üzerine kuvvet etkiyen bir cismin ya da sistemin kesin olarak dengede kalabilmesi için iki şartın gerçekleşmesi gerekir.

Dengenin 1. şartı

Bir cismin dengede kalabilmesi için üzerine etkiyen kuvvetlerin bileşkesi sıfır olmalıdır.

SF = 0 => SFx = 0, SFy = 0 olmalıdır.

Dengenin 2. şartı

Bir cismin dengede kalabilmesi için üzerine etkiyen kuvvetlerin dönme noktasına ya da eksenine göre momentlerinin toplamı sıfır olmalıdır.


SM = 0 olmalıdır.


Eğer bir sistemin dengede olduğu söyleniyorsa, yukarıdaki iki şartın sağlandığı söyleniyor demektir.

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Alt 25.10.08, 18:10   Yukarı Git #2
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denge, moment

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