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A copper rod with length 1.4 mand area of cross-section of 2 cm^2 is fastenedto a steel rod with length L and cross-sectional area 1 cm^2. The compound rod is subjected to equal and opposite pulls to magnitude6.00xx10^4 N at its ends .(a) Find the length L of the steel rod if the elongation of the two rods are equal . (b) What is stress in each rod ? (c ) What is the strain in each rod ? [Y_"steel"=2xx10^11 Pa , Y_(Cu)=1.1xx10^11 Pa] |
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Answer» SOLUTION :`Deltal_(CU)=Deltal_(steel)` `(Fl_C)/(A_CY_C)=(Fl_S)/(A_S Y_S)RARR l_S=(A_S/A_C)(Y_S/Y_C)l_C` or `L=(1.0/2.0)((2XX10^11)/(1.1xx10^11))1.40` =1.27 m (B) `sigma_C=F/A_C=(6xx10^4)/(2xx10^(-4))=3xx10^8 N//m^2` and `sigma_S=F/A_S=(6xx10^(4))/(1xx10^(-4))=6xx10^6 N//m^2` (c ) `epsilon_c=sigma_c/Y_c=2.7xx10^(-3)` `epsilon_s=sigma_S/Y_s=3.0xx10^(-3)` |
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