a. Define strain energy.
b. Write an expression for the energy stored, E, in a stretched wire of original length, l , cross-sectional area, A, extension, e, and Young’s modulus, Y, of the material of the wire.
Explanation
a. Strain energy is the potential energy stored within an elastic material as a result of its deformation caused by external forces.
b. Energy stored E = \(\frac{1}{2}Fe\)
Young Modulus = \(\frac{ Stress}{ Strain}\) = Y
Stress = \(\frac{Force}{Area} = \frac{(F)}{(A)}\)
Strain = \(\frac{ Extension}{Original Length} = \frac{(e)}{(l)}\)
Y = \(\frac{F}{A}\div \frac{e}{l}\)
Y = \(\frac{F}{A} \times \frac{l}{e}\)
F = \(\frac{YAe}{l}\)
Therefore, Energy stored E = \(\frac{1}{2}\frac{YAe}{l}\times e\)
E = \(\frac{YAe^2}{2l}\)