recall and use Hooke’s law

📐 Stress and Strain

In physics, stress is the force applied per unit area, while strain is the resulting deformation relative to the original length. When a material is stretched or compressed, it responds according to its elastic properties.

🔧 Hooke’s Law

Hooke’s Law describes how a material behaves within its elastic limit:

\$F = -kx\$

where:

  • \$F\$ = restoring force (N)

  • \$k\$ = spring constant (N m⁻¹)

  • \$x\$ = displacement from equilibrium (m)

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Key point: Hooke’s Law only holds while the material remains elastic; beyond the elastic limit it deforms permanently.

📏 Stress–Strain Relationship

Stress (σ) [Pa]Strain (ε) [dimensionless]Hooke’s Law (σ = Eε)
5 0000.001\$E = 5\,000/0.001 = 5\,000\,000\$ Pa
10 0000.002\$E = 10\,000/0.002 = 5\,000\,000\$ Pa

🧪 Example Problem

Imagine a spring with a spring constant \$k = 200\$ N m⁻¹. If you stretch it by \$x = 0.05\$ m:

  1. Calculate the force: \$F = kx = 200 \times 0.05 = 10\$ N.

  2. Check the elastic limit: If the material’s elastic limit is \$15\$ N, you are safely within it.

💡 Exam Tips

Remember:

  • Hooke’s Law is linear: plot of stress vs. strain is a straight line with slope \$E\$ (Young’s modulus).

  • Always state the elastic limit before applying Hooke’s Law.

  • Units matter: stress in Pa (N m⁻²), strain is dimensionless.

  • Use the symbol \$σ\$ for stress and \$ε\$ for strain.

  • When given a diagram, identify the applied force and the resulting displacement.

🤔 Analogy

Think of a rubber band stretched between your fingers. The more you pull, the more force the band exerts to return to its original length. This is exactly what Hooke’s Law describes for springs and many elastic materials.