We know
Maximum Stress without plastic deformation = 3.45X10^{8 }Nm^{-2
}Young's Modulus of Elasticity = 1.03X10^{11 }Nm^{-2}
Radius of wire = 6.43X10^{-3} m
Cross Sectional Area = πr^{2} m^{2}
Cross Sectional Area = 1.30X10^{-4 }m^{2}
Original Specimen Length = 5.00X10^{-2} ^{ }m
Stress = [^{[Force]} / _{[Cross Sectional Area]}]
Young's Modulus = [^{[Stress]} / _{[Strain]}]
Strain = [^{[ΔL]} / _{[L]}]
(a) Stress = { ^{[Force]} / _{[Cross Sectional Area]}}
(3.45X10^{8 }Nm^{-2}) = Force / (1.30X10^{-4 }m^{2})
Force = (3.45X10^{8 }Nm^{-2}) X (1.30X10^{-4 }m^{2})
Maximum Force without plastic deformation= 6.49X10^{4 }N
(b) Young's Modulus = [^{[Stress]} / _{[Strain]}]
(1.03X10^{11 }Nm^{-2}) = (3.45X10^{11 }Nm^{-2}) / Strain
Strain = (3.45X10^{8 }Nm^{-2}) / (1.03X10^{11 }Nm^{-2})
Strain = 3.35X10^{-3}
Strain = [^{[ΔL]} / _{[L]}]
3.35X10^{-3} = ΔL / 5.00X10^{-2} m
ΔL = 3.35 X10^{-3} X 5.00X10^{-2} m
ΔL = 1.68 X10^{-4} m.
L + ΔL = 5.00X10^{-2} m + 1.68 X10^{-4} m.
Maximum Length without Plastic Deformation = 5.02X10^{-2} m.
Maximum Length without Plastic Deformation = 5.02 cm. |