SUMMARY
The effective stiffness of the interatomic bond in iron can be calculated using the Young's modulus formula, where Y represents the modulus, F is the force applied, A is the cross-sectional area, dL is the change in length, and L is the original length. In this case, with a 151 kg mass causing a 1.03 cm elongation in a 2.0 m long iron rod with a square cross-section of 0.12 cm, the calculation yields a specific stiffness value. The formula used is Y = (F/A)/(dL/L), which simplifies to Y = [(151 kg * 9.8 m/s²)/(0.12e-2 m)²]/[(1.03e-2 m)/2].
PREREQUISITES
- Understanding of Young's modulus and its application in material science.
- Basic knowledge of force, area, and elongation in physics.
- Familiarity with unit conversions, particularly between grams, kilograms, and centimeters.
- Ability to perform algebraic manipulations to solve equations.
NEXT STEPS
- Study the principles of elasticity and how they relate to material properties.
- Learn about the calculation of stress and strain in materials.
- Explore the concept of interatomic forces and their implications in solid mechanics.
- Investigate advanced topics in material science, such as the effects of temperature on stiffness.
USEFUL FOR
Students in physics or engineering, material scientists, and anyone interested in the mechanical properties of metals, particularly iron.