Mechanical Properties of Solids – Quick Student Notes
1 Elasticity vs. Plasticity
• Elasticity is a material’s built-in “memory.” Stretch it, squeeze it, or bend it a little and, once the push stops, it snaps back to its original shape :contentReference[oaicite:0]{index=0}.
• Plasticity means the opposite: after the force is removed, the new shape stays. Putty and mud are handy day-to-day examples :contentReference[oaicite:1]{index=1}.
Why it matters: Designing bridges, artificial limbs, or even the I-shaped rails under a train all starts with knowing how elastic (or plastic) the chosen material is :contentReference[oaicite:2]{index=2}.
2 Stress (“push” per area)
When you press or pull on something that is still in equilibrium, every bit of its cross-section feels a restoring push. The numerical measure of that push is called stress: \[ \text{stress} \;=\; \frac{F}{A} \] where \(F\) is the applied force and \(A\) the area it acts on :contentReference[oaicite:3]{index=3}.
- Unit: pascal (Pa) = N m-2 — exactly the same unit used for air pressure :contentReference[oaicite:4]{index=4}.
- Types of stress :contentReference[oaicite:5]{index=5}:
- Tensile (pulls and lengthens).
- Compressive (squeezes and shortens).
- Shearing (slides layers sideways).
- Hydraulic or bulk (equal squeeze from all directions, like deep-sea pressure).
3 Strain (“how far it deforms”)
3.1 Longitudinal strain
A stretch or compression changes length by \(\Delta L\). Longitudinal strain is the “fractional” change: \[ \text{longitudinal strain} \;=\; \frac{\Delta L}{L} \tag{8.2} \] This number has no units :contentReference[oaicite:6]{index=6}.
3.2 Shearing strain
If opposite faces slide by \(\Delta x\) while the length is \(L\), or the block tilts by a small angle \(\theta\): \[ \text{shearing strain} \;=\; \frac{\Delta x}{L} \;=\; \tan\theta \;\approx\; \theta \quad(\text{in radians}) \tag{8.3} \] When the angle is just a few degrees, \(\tan\theta\) and \(\theta\) are practically identical :contentReference[oaicite:7]{index=7}.
3.3 Volumetric (bulk) strain
A uniform squeeze changes the volume by \(\Delta V\). Volumetric strain is \[ \text{volumetric strain} \;=\; \frac{\Delta V}{V} \] Again, it is a pure number with no units :contentReference[oaicite:8]{index=8}.
4 Stress–Strain Pairs
Every stress type teams up with its own strain type (tensile with longitudinal, shearing with shearing, hydraulic with volumetric). Later sections of the chapter introduce the idea that, for small deformations, stress is directly proportional to the matching strain (that principle is called Hooke’s law).
5 Snapshot of Key Numbers
| Quantity | Symbol | Expression | Unit |
|---|---|---|---|
| Stress | — | \(F/A\) | Pa |
| Longitudinal strain | — | \(\Delta L/L\) | dimensionless |
| Shearing strain | — | \(\Delta x/L \approx \theta\) | dimensionless |
| Volumetric strain | — | \(\Delta V/V\) | dimensionless |
High-Yield Ideas for NEET Practice
- Stress formula \( \displaystyle \text{stress} =\frac{F}{A} \) and its unit (Pa).
- Longitudinal strain expression \( \Delta L/L \) and its unit-less nature.
- Relation \(\text{shearing strain} \approx \theta\) (radians) for tiny angles.
- Clear distinction among tensile, compressive, shearing and hydraulic stresses/strains.
- Everyday contrast between perfectly elastic bodies (like a steel spring) and plastic substances (putty, mud).
You’ve got this — small, steady practice with these definitions is the fastest path to NEET confidence!
