Answer:
e = -0.00031 ( the -ve sign is due to the increase in length)
The error depends on the distance measured
Explanation:
Cross Sectional Area of the tape, A = 0.0625 in²
Length of the steel tape, L = 3600 in
Normal room temperature, T₁ = 68°F
Temperature of the hot day, T₂ = 130°F
ΔT = T₂ - T₁ = 130 - 68
ΔT = 62°F
Coefficient of Linear expansion [tex]\alpha = 5 * 10^{-6} F^{-1}[/tex]
The coefficient of linear expansion is given by the formula:
[tex]\alpha = \frac{\triangle L}{L* \triangle T} \\\triangle L = \alpha L \triangle T\\\triangle L = 5* 10^{-6} * 3.6* 10^3 * 62\\\triangle L = 1.11 6 in[/tex]
Since the length is increased, the error will be given by the formula:
[tex]e = \frac{-\triangle L}{L} \\\\e = \frac{-1.116}{3600}[/tex]
e = -0.00031 ( the -ve sign is due to the increase in length)
Since the error is a function of length and change in length, it depends on the distance measured
