A steel wire of uniform cross-section of 1 m 2 is heated to 70 ° ° C and stretched by tying its two ends rigidly. What is the change in the tension of the wire when the temperature falls from 70 ° ° C to 35 ° ° C? Coefficient of linear expansion of steel is 1.1 ´ ´ 10 -5 / ° ° C and Young’s modulus is 2.0 ´ ´ 10 11 N/m 2 .
Text Solution
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The tension produced in a stretched wire due to fall in
temperature by Δ Δ t is.
F = YA α α Δ Δ t
Where Y and α α are the Young’s modulus and coefficient of
linear expansion of the material of the wire and A is the cross-
sectional area.
Here Y = 2.0 ´ ´ 10 11 N/m 2
A = 1.0 mm 2 = 1.0 ´ ´ 10 -6 m 2
α α = 1.1 ´ ´ 10 -5 / 0 C
Δ Δ t = (70 – 35) = 35 0 C
∴ ∴ F = 2.0 ´ ´ 10 11 ´ ´ (1.0 ´ ´ 10 -6 ) ´ ´ (1.1 ´ ´ 10 -6 ) ´ ´ 35 = 77N
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