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A metallic rod 1 cm long with a square cross-section is heated through 1°C. If Young's modulus of elasticity of the metal is E and the mean coefficient of linear expansion is alpha per degree Celsius, then the compressional force required to prevent the rod from expanding along its length is : (Neglect the change of cross sectional area)
Thermal expansion in form of change in length l2 = l1(1+alpha*t)Young’s modulus = E E = (F/A)/(l/L)E = FL/AlL = l + del l E = F (l+del l )/A* del l Find the value of F F = EA(alpha *t)/(1+ alpha *t)
Thermal expansion in form of change in length (Linear expansion) l 2 = l 1 ( 1 + α t ) l2=l1(1+αt) c h a n g e i n l e n g t h = ( l Δ t ) change in length=(lΔt) Δ t = ( t 2 − t 1 ) Δt=(t2−t1) Y o u n g ′ s M o d u l u s = E Young′s Modulus=E E = F A / l L E=FA/lL E = F L / A l E=FL/Al L = ( l + Δ l ) L=(l+Δl) L = l + Δ l L=l+Δl E = F A / l L E=FA/lL E = F L / A l E=FL/Al E = F ( l + Δ l ) A Δ l E=F(l+Δl)AΔl F = E A Δ l / ( l + Δ l ) F=EAΔl/(l+Δl) F = E A ( α t ) 1 + α t F=EA(αt)1+αt
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