A force stretches a wire by 1.8mm A) A second wire of the same material has the

Question

A force stretches a wire by 1.8mm A) A second wire of the same material has the same crosssection and twice the length. How far will it be stretched bythe same force? B) A third wire of the same material has the same length andtwice the diameter as the first. How far will it be stretchedby the same force? A force stretches a wire by 1.8mm A) A second wire of the same material has the same crosssection and twice the length. How far will it be stretched bythe same force? B) A third wire of the same material has the same length andtwice the diameter as the first. How far will it be stretchedby the same force?

Explanation / Answer

we know Young's modulus Y = stress / strain                                                = ( F / A ) / ( e/L )                                                 =FL / Ae Same material .So, young's modulus is same. So, FL = Ae (A).Given same crosssectional area and force from above  L e   ( L ' / L ) = ( e ' / e)    ( 2L / L ) = ( e ' / e )      e ' / e = 2            e' = 2e               = 2* 1.8 mm = 3.6 mm (B). Y , L , F are constant .    Ae = consatnt ( A ' / A ) = ( e / e' ) ( d' / d) ^ 2 = ( e/ e' )     Sincearea A = d 2 / 4 Given d ' = 2d    2^ 2 = ( e/ e' )          4 = e/e'         e ' = e / 4             = 1.8 mm / 4              =0.45 mm       

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