Question

Two ends of a steel wire of length 8m and 2mm radius are fixed to two rigid supports. Calculate the increase in tension when the temperature falls by 10°C. Given linear expansivity of steels = 12x10^_6 per kelvin and Young's modules for steel =2x10^11 n/m^2 ​

Answer 1

The increase in tension on the steel wire is 8,484.75 N.

The given parameters;

• original length of the wire, l = 8 m
• radius of the wire, r = 2 mm

The area of the steel wire is calculated as follows;

$A = \pi r^2\\\\A = \pi \times (2\times 10^{-3})^2\\\\A = 1.257 \times 10^{-5} \ m^2$

The extension of the steel wire is calculated as follows;

$\Delta l = \alpha \times l\times \Delta T\\\\\Delta l = (12\times 10^{-6}) \times (8) \times (10 + 273)\\\\\Delta l = 0.027 \ m$

The increase in tension on the steel wire is calculated as follows;

$E = \frac{stress}{strain } = \frac{\ F/A}{\Delta l/l} \\\\E = \frac{F\times l}{A \times \Delta l} \\\\F = \frac{E\times A \times \Delta l }{l} \\\\F = \frac{(2\times 10^{11}) \times (1.257\times 10^{-5})\times 0.027}{8} \\\\F = 8,484.75 \ N$

Thus, the increase in tension on the steel wire is 8,484.75 N.

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