A copper rod of cross sectional area 0.500 cm^2 and and length 1.00 m is elongated by 2 x 10^-2 mm and a steel rod of the same cross-sectional area but 0.100 m in length is elongated by 2 x 10^-3 mm. Which rod has greater tensile strain?
Answers
Answer:
A brass rod with a length of and a cross-sectional area of is fastened end to end to a nickel rod with length and crosssectional area . The compound rod is subjected to equal and opposite pulls of magnitude at its ends. (a) Find the length of the nickel rod if the elongations of the two rods are equal. (b) What is the stress in each rod? (c) What is the strain in each rod?
Answer:
They have the same tensile strain
Explanation:
Strain of a material is the ratio of its extension to its original length.
strain = e/lo
e is the extension
lo is the original length
For a copper rod;
e = 2.00 * 10^-2mm
lo = 1.00m
convert 1.00m to mm
1.00m = 1*10^-3mm
get the strain
Strain = 2.00 * 10^-2mm/1*10^-3mm
Strain = 2 * 10^{-2+3}
Strain = 2*10^1 = 20
For the steel
e = 2.00 * 10^-3mm
lo = 0.100m
convert 0.100m to mm
0.1m = 0.1*10^-3mm
0.1m = 10^-4mm
get the strain
Strain = 2.00 * 10^-3mm/10^-4mm
Strain = 2 * 10^{-3+4}
Strain = 2*10^1 = 20
Since the value of their strain are the same, this means that they a re under the SAME tensile strain. No one is greater that the other.
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