Key relationship
σ=F/A; ε=ΔL/L₀; σ=Yε; elastic energy density u=½Yε².
Physics · Class 11
Stretch within the elastic range
Mechanical Properties of Solids
Stress is force per area; strain is extension divided by original length. Within the linear elastic region the stress-strain slope is Young modulus. Releasing the load recovers the original length in this model.
Open the interactive experiment →Stretch within the elastic range
தகைவு என்பது ஓரலகு பரப்புக்கான விசை; திரிபு நீள மாற்றத்தின் விகிதம். மீள்தன்மை வரம்பில் தகைவு திரிபுக்கு நேர்விகிதம்.
Key notes, relationships and model limits
Remember
Stress is force per area; strain is extension divided by original length. Within the linear elastic region the stress-strain slope is Young modulus. Releasing the load recovers the original length in this model.
Common trap
Hooke law applies only within the proportional elastic range.
Model limits
Ideal linear elastic tensile response below the material’s proportional limit. Plasticity and failure are excluded; the selected modulus does not determine a real yield limit.
What you will learn
Read modulus as graph slope and connect stress, strain and stored energy.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
At strain 0.0005, σ=100 MPa and stored energy density=½×200×10⁹×(0.0005)²=25000 J/m³.
Why this matters
The model connects stretch within the elastic range with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
For Y=200 GPa and strain 0.001, what stress results?
- 200 kPa
- 200 MPa
- 200 GPa
Read the explanation
σ=200×10⁹×0.001=200×10⁶ Pa.
Course connection: Class XI Chapter 8. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.