Young’s Modulus & Elastic Potential Energy — A/L Physics

What must I remember about Young’s Modulus & Elastic Potential Energy?

• Young's Modulus (Y): Ratio of longitudinal tensile stress to longitudinal tensile strain within Hooke's proportional limit: Y = (F / A) / (ΔL / L0) = (F L0) / (A ΔL) (units N/m² or Pa); an intrinsic material property independent of dimensions.
• Elastic Force Constant (Spring Constant k of wire): From Y = (F L0)/(A ΔL) => F = (Y A / L0) ΔL = k ΔL, where stiffness k = (Y A) / L0.
• Elastic Potential Energy (Strain Energy U): Work done in stretching a wire within elastic limit: U = ∫ F dx = (1/2) F ΔL = (1/2) k (ΔL)² = (1/2) [ (Y A) / L0 ] (ΔL)².
• Strain Energy Density (u): Elastic energy stored per unit volume of material: u = U / (A L0) = (1/2) * Stress * Strain = (1/2) Y * (Strain)² = (Stress)² / (2Y) (units J/m³).

Test yourself (1 minute)

1. Searle's Apparatus for Young's Modulus

   Employs two identical parallel wires (Experimental wire and Reference/Dummy wire) suspended from the same rigid support; eliminates errors due to support yielding and thermal expansion.

2. Work done in breaking vs storing

   Area under entire F-ΔL curve up to fracture represents total work done to break the wire; area under unloading curve represents recoverable elastic potential energy; difference is dissipated permanently as heat.

3. Dependence on dimensions

   Young's Modulus Y depends ONLY on the material and temperature; doubling wire length L or area A does NOT change Y, but changes elongation ΔL and stiffness k.

Practise Young’s Modulus & Elastic Potential Energy questions today

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 10: Mechanical Properties of Matter

What should I study first?

What comes next?

Next in the syllabus

Where does Young’s Modulus & Elastic Potential Energy fit in the syllabus?

Unit 10.2 · Year 2 · Term 3