A STEEL ROD OF LENGHT L, YOUNG MODULUS Y AND LINEAR COEFFICIENT OF EXPANSION A IS HEATEDTHROUGH IDEGREEC. WHAT IS THE WORK THAT THE ROD CAN PERFORM WHEN HEATED?
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Length of rod = L
Young modulus = Y
Linear coefficient of expansion = A
temperature difference (dT) = 1° C
we know,
strain = ∆L/L
from linear expansion concept ,
∆L = LAdT
so, strain = LAdT/L = AdT
if wire slowly stretched by ∆L on applying force F , then work done during stretching
W = 1/2 × F × ∆L
we know,
young's modulus = Stress/strain
so, W = 1/2 × Young's modulus × (strain)²
= 1/2 × Y × (AdT)²
= 1/2 × Y(A× 1)²
= YA²/2
hence,
workdone = YA²/2
Young modulus = Y
Linear coefficient of expansion = A
temperature difference (dT) = 1° C
we know,
strain = ∆L/L
from linear expansion concept ,
∆L = LAdT
so, strain = LAdT/L = AdT
if wire slowly stretched by ∆L on applying force F , then work done during stretching
W = 1/2 × F × ∆L
we know,
young's modulus = Stress/strain
so, W = 1/2 × Young's modulus × (strain)²
= 1/2 × Y × (AdT)²
= 1/2 × Y(A× 1)²
= YA²/2
hence,
workdone = YA²/2
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