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