Question

Calculate the force required to prevent a steel wire of 1 mm" cross-section fromcontracting when it cools from 60°C to 15°C, if Young's modulus for steel is2 10 Nm and its coefficient of linear expansion is 0.000011ºC

Answer 1

Force required will be 5.5*10^6 N.

Young's modulus is given by the formula - (F/A)/(∆L/L)

We have to calculate F in the given equation.

Given values are-

F= ?

Y = 210 Nm.

A = 1 mm² = 1*10^-6 m²

∆L = aL∆T

a= 0.000011 °C = 11*10^6

∆T = 60-15 °C = 45 °C

Now, formula -

F = YAa∆T(since l will be cancelled by l present in ∆L)

F = 210*10^-6*45*11*10^6

F= 5.5*10^6 N.