Lab 12: Hooke's Law and Young's Modulus

Learning Objectives

  • Verify Hooke's Law for a spring within its elastic limit.
  • Determine the spring constant from a force-extension graph.
  • Relate stress, strain, and Young's modulus for elastic materials.
  • Identify the elastic limit and sources of measurement error.

This placeholder is prepared for a complete laboratory experiment on elasticity. It can be completed as a spring-extension activity, wire-stretching activity, or combined elastic behavior experiment depending on available apparatus.

Hooke's Law

For small deformations within the elastic limit, restoring force is proportional to extension.

F=kxF = kx

Variables

SymbolDescriptionUnit
FFapplied forceN
kkspring constantN/m
xxextension from natural lengthm

Young's modulus

Young's modulus is the ratio of normal stress to normal strain in the elastic region.

E=σε=F/AΔL/LE = \frac{\sigma}{\varepsilon} = \frac{F/A}{\Delta L/L}

Variables

SymbolDescriptionUnit
EEYoung's modulusPa
σ\sigmanormal stressPa
ε\varepsilonnormal straindimensionless
AAcross-sectional aream2m^2
LLoriginal lengthm
ΔL\Delta Lchange in lengthm

Suggested Apparatus

ApparatusPurpose
Spring or test wireElastic body under investigation.
Mass hanger and slotted massesApplies known force.
Meterstick or pointer scaleMeasures extension.
Clamp standSupports the system.
Vernier caliper or micrometerMeasures wire diameter if Young's modulus is included.

Placeholder procedure outline

  1. Measure the natural length of the spring or wire.
  2. Add masses gradually and record the extension after each load.
  3. Convert mass to force using F=mgF = mg.
  4. Plot force versus extension.
  5. Determine the spring constant from the graph slope.
  6. If using a wire, compute stress, strain, and Young's modulus.
  7. Remove loads gradually and observe whether the material returns to its original length.

Data Table Placeholder

TrialLoad mass, kgForce, NLength, mExtension, mStressStrain
1
2
3
4

Loading safety

Add masses gradually and keep feet clear of falling weights. Do not load the spring or wire beyond the safe elastic range specified by the instructor.

To complete this lab

Add graphing instructions, spring constant or Young's modulus sample calculation, elastic-limit discussion, and post-lab questions connecting elasticity to structural materials.

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