PhysSandbox

Young’s Modulus from the Elastic Line

Unknown metal, elastic strains only. Measure stress at several strains and recover E from the slope of σ versus ε.

Kids· 20 min·Related simulator: EngineeringStress–Strain & Hooke’s Law

Goal

Determine Young’s modulus from Hooke’s law σ = E ε. The slope of σ (MPa) versus ε is E in MPa; report E in GPa.

Equipment

  • Tensile specimen
  • Extensometer (ε)
  • Load cell (σ)

Experiment

Theory

In the elastic region engineering stress is proportional to engineering strain. The bench hides E and never enters yield. You apply strain; a load cell reports σ only after you record.

Procedure

  1. The specimen is an unknown metal. E is hidden. You only change tensile strain ε, kept well below yield.
  2. Record. The load cell logs σ with small noise. There is no live E or σ while you drag.
  3. Repeat for at least 6 strains from about 0.0003 to 0.0022.
  4. Fit σ versus ε; E (GPa) = slope (MPa) / 1000. Compare with the reference.

Conclusion

The fitted modulus agrees with the hidden E. Main uncertainties: load-cell noise and staying strictly in the linear elastic region.