Respuesta :
Answer:
(a) Steel rod: [tex]1.1 * 10^{-4}[/tex]
Copper rod: [tex]1.88 * 10^{-4}[/tex]
(b) Steel rod: [tex]8.3 * 10^{-5} m[/tex]
Copper rod: [tex]1.41 * 10^{-4} m[/tex]
Explanation:
Length of each rod = 0.75 m
Diameter of each rod = 1.50 cm = 0.015 m
Tensile force exerted = 4000 N
(a) Strain is given as the ratio of change in length to the original length of a body. Mathematically, it is given as
Strain = [tex]\frac{1}{Y} * \frac{F}{A}[/tex]
where Y = Young modulus
F = Fore applied
A = Cross sectional area
For the steel rod:
Y = 200 000 000 000 [tex]N/m^{2}[/tex]
F = 4000N
A = [tex]\pi r^{2}[/tex] (r = d/2 = 0.015/2 = 0.0075 m)
=> A = [tex]\pi * (0.0075)^{2}[/tex]
=> A = 0.000177 [tex]m^{2}[/tex]
∴ [tex]Strain = \frac{4000}{200000000000 * 0.000177} \\\\Strain = \frac{4000}{35400000}\\ \\Strain = 0.000113 = 1.13 * 10^{-4}[/tex]
For the copper rod:
Y = 120 000 000 000 N/m²
F = 4000N
A = [tex]\pi r^{2}[/tex] (r = d/2 = 0.015/2 = 0.0075 m)
=> A = [tex]\pi * (0.0075)^{2}[/tex]
=> A = 0.000177 [tex]m^{2}[/tex]
[tex]Strain = \frac{4000}{120 000 000 000 * 0.000177} \\\\Strain = \frac{4000}{21240000}\\ \\Strain = = 1.88 * 10^{-4}[/tex]
(b) We can find the elongation by multiplying the Strain by the original length of the rods:
Elongation = Strain * Length
For the steel rod:
Elongation = [tex]1.1 * 10^{-4} * 0.75 = 8.3 * 10^{-5} m[/tex]
For the copper rod:
Elongation = [tex]1.88 * 10^{-4} * 0.75 = 1.41 * 10^{-4} m[/tex]
