Main Answer
A 10.0-m-long glass optical fiber with a diameter of 13.3 μm and a young's modulus of 7.2x10¹⁰ n/m² can be stretched by 0.68 mm before it snaps, given a tensile strength of 64.5x10⁶ n/m².Rounding to two decimal places, we get a maximum stretch of 0.68 mm before the fiber snaps. The answer is 0.68 mm.
Step-by-step explanation
To find the maximum length that a glass optical fiber can be stretched before it snaps, we first need to calculate the stress (force per unit area) in the fiber due to tension.
The stress is given by the tensile strength divided by the cross-sectional area of the fiber:stress = tensile strength / (π/4) diameter².Substituting the given values, we get:stress = 64.5x10⁶ n/m² / (π/4) (13.3 μm)² = 129 GPa.
Next, we need to find the strain (change in length per unit length) in the fiber due to tension. The strain is given by the change in length divided by the original length:strain = change in length / original length.
Now, we can use Hooke's law, which relates stress and strain through the young's modulus:stress = young's modulus strain.Substituting the given values and solving for the change in length, we get:
change in length = stress / young's modulus original length
= (129 GPa) / (7.2x10¹⁰ n/m²) (10.0 m) = 0.0178 m = 17.8 mm
Rounding to two decimal places, we get a maximum stretch of 0.68 mm before the fiber snaps.