MediumStrength of materials
What is the longitudinal strain of a 200 m cable whose midpoint sags by 4.5 m?
TL;DR
Approximately 0.001, or 0.1% — option 1.
Question
A cable initially 200 m long is fixed horizontally between two supports. After a load is suspended at its midpoint, that point drops by 4.5 m.
Assume the loaded cable consists of two equal straight segments. What is its longitudinal strain?
Answer choices
- 0.001
- 0.0045
- 0.1
- 0.45
- 4.5
Explanation
Each half has a horizontal projection of 100 m and a vertical displacement of 4.5 m. By Pythagoras, the new length is:
L = 2√(100² + 4.5²) ≈ 200.2024 m.
The extension is ΔL ≈ 0.2024 m. The strain is:
ε = ΔL / L₀ ≈ 0.2024 / 200 ≈ 0.001012.
The matching choice is 0.001. Strain is dimensionless.
