Elastic Potential Energy
U = ½σε·V — area under σ–ε curve fills as the wire stretches; energy bar grows live.
Key Notes
Elastic potential energy is the energy stored in a deformed elastic body — recoverable when the body returns to its natural shape.
For a spring or wire obeying Hooke's law: U = ½kx² (spring) or U = ½·F·ΔL (wire under tension F, extension ΔL).
Energy per unit volume (energy density): u = ½·σ·ε = ½·Y·ε² = σ²/(2Y).
All this is recovered when stress is released — provided you stay in the elastic region.
Beyond the elastic limit, some energy goes into permanent (plastic) deformation, heat, or fracture.
Springs in series and parallel: in series, k decreases (1/k_eq = Σ 1/k_i); in parallel, k increases (k_eq = Σ k_i).
Application: bow-and-arrow stores elastic energy in the bow, transferred to KE of arrow.
Earthquake faults store enormous elastic energy in stressed rocks — released suddenly during slip.
Formulas
Spring/wire stored energy
Average force × distance — factor of ½ because F ramps up linearly.
Elastic energy density
Per unit volume; valid in linear regime.
Total energy in stretched wire
Energy = (F²L)/(2YA).
Springs (series / parallel)
Series gentle, parallel stiff (opposite of capacitors!).
Important Points
Always factor of ½ — because force varies linearly from 0 to F during elongation.
Energy density u = σ²/(2Y): high stress + low Y stores lots of energy per unit volume (rubber, archery bows).
Beyond elastic limit, NOT all stored energy is recoverable — some heats the material, some causes plastic deformation.
Springs in series: like resistors in PARALLEL (k_eq < k_min).
Springs in parallel: like resistors in SERIES (k_eq = sum).
Stored elastic energy can be enormous — earthquake faults release built-up strain energy in seconds.
Elastic Potential Energy notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.