JAMB / WAEC Physics: Elasticity Explained — Hooke’s Law & Young’s Modulus
Elasticity is the property of a material that allows it to return to its original shape and size after a deforming force is removed. This topic, covering Hooke’s Law, stress, strain, and Young’s modulus, is a regular feature in JAMB and WAEC Physics, usually tested through calculations involving springs and wires. This lesson explains each idea step by step, with worked examples.
Quick takeaways
- Elasticity is a material’s ability to return to its original shape and size once a deforming force is removed.
- Hooke’s Law states that, within the elastic limit, the extension of a spring or wire is directly proportional to the applied force: F = ke.
- The elastic limit is the maximum force beyond which a material no longer returns to its original shape and becomes permanently deformed.
- Stress is force per unit cross-sectional area (F/A), and strain is the ratio of extension to original length (e/L).
- Young’s modulus is the ratio of stress to strain (E = stress/strain), a constant that describes how stiff a material is.
Timestamps
- 0:00 Introduction
- 0:42 Definition and Examples of Elasticity
- 3:13 Elastic Limit, Yield Point & Breaking Point
- 4:10 Stress-Strain Graph
- 7:00 Hooke’s Law
- 9:06 Hooke’s Law — Worked Example
- 11:25 Young’s Modulus — Formula
- 12:33 Stress and Strain (Formulas)
- 13:30 Young’s Modulus — Worked Example
- 17:57 Extension of a Spring
- 18:55 Energy Stored in a Spring (Formula)
- 20:11 Spring Extension & Energy — Worked Example
- 22:26 Applications of Elasticity
What is elasticity?
Elasticity is the property of a material that allows it to return to its original shape and size after the force deforming it is removed. A rubber band, a steel spring, and a metal wire all show elasticity to different degrees. Materials that stay deformed after the force is removed are called plastic materials, and the boundary between these two behaviours is the elastic limit.
What is Hooke’s Law?
Hooke’s Law states that, within the elastic limit, the extension of a spring (or wire) is directly proportional to the force applied to it:
F = ke
Where F is the applied force (in newtons), e is the extension (in metres), and k is the force constant or spring constant (in N/m), which measures how stiff the spring is. A larger k means a stiffer spring that needs more force to stretch by the same amount.
For example, a spring with k = 200 N/m is pulled by a force of 10 N. Its extension is e = F/k = 10/200 = 0.05 m (5 cm).
What is the elastic limit?
The elastic limit is the maximum force (or extension) up to which a material will still return to its original length when the force is removed. Beyond this point, Hooke’s Law no longer applies, and the material is permanently stretched. When you plot extension against force, the graph is a straight line through the origin up to the elastic limit, then curves.
What are stress and strain?
Hooke’s Law for a spring depends on the particular spring, but stress and strain describe the material itself, independent of its size:
- Stress = Force / Cross-sectional area = F/A (unit: N/m², or pascal)
- Strain = Extension / Original length = e/L (no unit, since it’s a ratio of two lengths)
What is Young’s modulus?
Young’s modulus (E) is the ratio of stress to strain for a material within its elastic limit:
E = Stress / Strain = (F/A) / (e/L) = FL / Ae
It measures the stiffness of a material, independent of its shape or size. A high Young’s modulus (like steel) means the material is very stiff, while a low one (like rubber) means it stretches easily. Its unit is N/m² (pascal).
Worked example: finding Young’s modulus
A wire 2 m long with a cross-sectional area of 1 × 10⁻⁶ m² is stretched by a force of 100 N, producing an extension of 1 mm (0.001 m). Find Young’s modulus.
- Stress = F/A = 100 / (1 × 10⁻⁶) = 1 × 10⁸ N/m²
- Strain = e/L = 0.001 / 2 = 5 × 10⁻⁴
- E = Stress / Strain = (1 × 10⁸) / (5 × 10⁻⁴) = 2 × 10¹¹ N/m²
What is the energy stored in a stretched spring?
Work is done in stretching a spring, and this is stored as elastic potential energy:
Energy = ½Fe = ½ke²
For the spring above (k = 200 N/m, e = 0.05 m): Energy = ½ × 200 × (0.05)² = ½ × 200 × 0.0025 = 0.25 J.
Common mistakes students make with elasticity
- Using Hooke’s Law beyond the elastic limit, where force and extension are no longer proportional
- Confusing extension (the increase in length) with the total stretched length of the spring or wire
- Forgetting to convert units, such as millimetres to metres or cm² to m², before substituting into formulas
- Mixing up stress (force per area) with strain (a ratio of lengths with no unit)
Frequently asked questions
Q: What does Hooke’s Law state? Hooke’s Law states that, within the elastic limit, the extension of a spring or wire is directly proportional to the force applied to it, written as F = ke.
Q: What is the elastic limit? The elastic limit is the maximum force or extension up to which a material returns to its original shape once the force is removed; beyond it, the material is permanently deformed.
Q: How is Young’s modulus calculated? Young’s modulus is calculated as stress divided by strain, which equals FL/Ae, where F is the force, L the original length, A the cross-sectional area, and e the extension.
Q: What is the difference between stress and strain? Stress is the force applied per unit cross-sectional area, measured in N/m², while strain is the ratio of extension to original length and has no unit.
Want to see another Mechanics topic? Read our Friction lessons → or Gravitational Field →
This is one topic from our full JAMB & WAEC Physics course — see everything covered →
