A uniform steel rod of 5 mm^2 cross section is heated from 0°C to 25°C. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain. - Physics

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A uniform steel rod of 5 mm2 cross section is heated from 0°C to 25°C. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain.

(α for steel = 12 x 10-6/°C and γ for steel = 20 x 101ON/m2)

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Solution

Given that α steel = 12 x 10-6 /°C, γ steel = 20 x 1010 N/m2

Area of cross-section of the rod, A = 5 mm2 = 5 × 10−6 m

Change in temperature (ΔT), (T2 − T1) = 25°C

Force exerted by the rod due to heating = Thermal stress × Area

                         Thermal stress = γ x Strain

                                                = γsteel x αsteel x ΔT

Therefore, the force exerted by the rod due to heating is

      = γsteel x αsteel x ΔT x A

      = 20 x 1010 x 12 x 10-6 x 25 x 5 x 10-6

      = 300 N

`"Strain" = "Change in length"/ "Original length"= alphaDelta"T"`

Strain = αsteelΔT

          = 12 x 10-6 x 25

          = 3 x 10-4

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