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The cross section area of a steel rod is 5.40cm^2. What force must be applied to each end of the rod to preven?
The cross section area of a steel rod is 5.40cm^2. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120C to 20C?
1 Answer
- ?Lv 77 years ago
U might have provided the linear expansion coefficient of steel to be used as it varies depending on the type of steel rod is made of. Young's modulus (E) for this steel rod would also have been nice to have :>)
Let's assume α = 13.0E-6 /C°
then with ΔT = 120-20 = 100° and Lo = 1.31 cm = 1.31E-2 m {circular rod}
α(ΔT) = ΔL/Lo
(13.0E-6)(100) = ΔL/Lo = 13E-4
ΔL = (13E-4)(Lo) = (13E-4)(1.31E-2) = 17E-6 m
E = Young's modulus for steel = 200E9 N/m²
E = F/A ÷ ΔL/Lo
2E11 = (F/1.35E-4)(1.31E-2)/17E-6 = (F/1.35E-4)(0.0771E4) = 0.0571FE8
F = 2E11/0.0571E8 = 35.0E3 = 35,000 N ANS
