Final answer:
The maximum length by which a 10.5-m-long glass optical fiber can be stretched before breaking is 9.93 mm when rounded to two decimal places.
Step-by-step explanation:
Calculating the Maximum Stretch of the Optical Fiber
To determine by how many millimeters a 10.5-m-long glass optical fiber can be stretched before it snaps, we need to use the tensile stress and Young's modulus given in the question. The tensile strength represents the maximum stress the material can withstand without breaking, while Young's modulus (E) relates to the stiffness of the material and is defined as the ratio of tensile stress (σ) to tensile strain (ε). The tensile strain is calculated as the change in length (ΔL) divided by the original length (L0).
The formula to calculate the change in length before the fiber breaks is given by:
- σ = E × ε
- ε = ΔL / L0
- σmax = Tensile Strength
- ΔL = σmax × L0 / E
Plugging in the given values, we have:
- σmax = 67.0 × 106 N/m2
- E = 7.1 × 1010 N/m2
- L0 = 10.5 m
ΔL = (67.0 × 106 N/m2 × 10.5 m) / (7.1 × 1010 N/m2)
ΔL = 9.92957746 mm
Rounded to two decimal places, the fiber can be stretched before it snaps by 9.93 mm.