Answer:
length of the Steel beam = 39.00327 m
Explanation:
Linear expansivity(∝) of a metal : Is defined as an increase in length per unit length for one degree rise in temperature.
It is express mathematically as
∝= (L₁-L₂)/(L₁ΔT)........................ Equation 1
∴ L₂ = L₁ + (1 + ∝ΔT)....................... Equation 2
Where ∝ = linear expansivity of the metal ( K⁻¹), L₁ = Initial length (m), L₂ = Final length ( m )
L₁- L₂ = ΔL = Change in length of the metal ( m )
ΔT = T₂ - T₁ ( K )
∴ L₂ = L₁ + (1 + ∝ΔT)....................... Equation 2
The linear expansivity of steel = 11 × 10⁻⁶ ( K⁻¹),
L₁ = 38.00 m , ΔT = 87 - 11 = 76 °F
Conversion
°F to Kelvin = K = 5/9 (° F - 32) + 273
T(K) = 5/9 (76-32) + 273
T(K) = 5/9(44) + 273
T (K) = 297.44 K
substituting these values into equation 2
L₂ = 38 + (1 + {11×10⁻⁶× 297.44})
L₂ = 38 + (1 + 0.00327)
L₂ = 38 + (1.00327)
L₂ = 39.00327 m.
Therefore, length of the Steel beam = 39.00327 m
