SUMMARY
The discussion focuses on calculating the Elastic Modulus (E) of a metal cable subjected to a load. A mass of 225 kg causes a stretch of 0.668 mm in a cable of length 1.60 m and diameter 8.20 mm. The formula used is E = (F/A) / (ΔL / L₀), where F is the force (2205 N), A is the cross-sectional area (5.28 x 10^-5 m²), and ΔL / L₀ is the strain (4.18 x 10^-5). The calculated Elastic Modulus is 5.26 x 10^11 N/m², which is significantly higher than the expected value of 100 x 10^9 N/m², indicating a potential error in the calculations.
PREREQUISITES
- Understanding of basic physics concepts such as force, area, and stress.
- Familiarity with the formula for Elastic Modulus.
- Knowledge of unit conversions, particularly between mm and m.
- Ability to perform calculations involving significant figures and decimal points.
NEXT STEPS
- Review the calculation of cross-sectional area for circular objects using A = π(r²).
- Learn about the significance of strain and how to accurately calculate it.
- Study common errors in mathematical calculations, especially with decimals.
- Explore the properties of materials and their Elastic Modulus values for comparison.
USEFUL FOR
Students in physics or engineering courses, particularly those studying material properties and mechanics, as well as anyone involved in practical applications of material stress and strain calculations.
