A steel rod with a length of l = 1.55 m and a cross section of A = 4.89 cm2 is held fixed at the end points of the rod. What is the size of the force developing inside the steel rod when its temperature is raised by ∆T = 28.0 K? The coefficient of linear expansion for steel is α = 1.17×10-5 1/K, and the Young modulus of steel is E = 200.0 GPa.

The size of the force developing inside the steel rod is 32039.28 N

Explanation:

Given;

length of the steel rod, L =  1.55 m

cross sectional area of the steel, A = 4.89 cm²

temperature change, ∆T = 28.0 K

coefficient of linear expansion for steel, α = 1.17 × 10⁻⁵ 1/K

Young modulus of steel,  E = 200.0 GPa.

Extension of the steel is given as;

α ∆T L = FL / AE

α ∆T = F/AE

F = AEα ∆T

F = ( 4.89 x 10⁻⁴)(200 x 10⁹)(1.17 × 10⁻⁵)(28.0 K)

F = 32039.28 N

Therefore, the size of the force developing inside the steel rod when its temperature is raised, is 32039.28 N

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