Dimensional formula of Strain energy

How to get the dimensional formula of strain energy

1. Start from the definition: strain energy = work.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. displacement = length, so displacement is [L] = [L].
6. work = force × displacement, so work is [M L T^-2] × [L] = [M L² T^-2].
7. Put in the dimension of each part: [M L² T^-2].
8. Add the powers of each base quantity: [M L² T^-2].

Quantities with the dimensions [M L² T⁻²]

• Work
• Energy
• Kinetic energy
• Potential energy
• Torque
• Torsional constant
• Gravitational potential energy
• Heat
• Internal energy
• Electric potential energy
• Work function
• Photon energy
• Binding energy

Equal dimensions do not make them the same quantity. Compare strain energy with the others in the full grid.

Three questions on strain energy

Related quantities

• P Pressure [M L⁻¹ T⁻²]
• dP/dx Pressure gradient [M L⁻² T⁻²]
• σ Stress [M L⁻¹ T⁻²]
• u Strain energy density [M L⁻¹ T⁻²]
• ε Strain [M⁰ L⁰ T⁰]
• Y Young's modulus [M L⁻¹ T⁻²]