Caculate the compressionalforce required to prevent the metallic rod of length I cm and cross- sectional area A cm^(2) when heated through t^(@)C, from expanding along lengthwise. The young's modulus of elasticity of the metal is E and mean coeJJ'icient of linear expansion is alphaperdegreecelsius :

Caculate the compressionalforce required to prevent the metallic rod o

1.	Caculate the compressionalforce required to prevent the metallic rod of length I cm and cross- sectional area A cm^(2) when heated through t^(@)C, from expanding along lengthwise. The young's modulus of elasticity of the metal is E and mean coeJJ'icient of linear expansion is alphaperdegreecelsius :
Answer» Solution :The change in natural length = `Delta_(t) = 1 alpha t ` The natural length of rod at temperature `t^(@)` C is 1 + `alpha` t The decrease in natural length due to developed stress ` = Delta ` l But the length of rod remains constant. `THEREFORE Delta l_(t) - Delta l = 0"" therefore Delta l = Delta l_(t) = l alpha t ` `therefore E = ("stess")/("strain") = (((F)/(A))/(-Delta L))/(l + Delta l_(t))` `therefore F = (EA Delta l )/(l + Delta l_(t)) = (- E A l alpha t )/(l + l alpha t ) = - (E A alpha t )/( (1 + alpha t ) )` Here, negative sign indicates that the forces is compressive in NATURE.