All Problems Elastic deformations
Problem 1.310
A steel cylindrical rod of length \(l\) and radius \(r\) is suspended by its end from the ceiling. (a) Find the elastic deformation energy \(U\) of the rod. (b) Define \(U\) in terms of tensile strain \(\Delta l / l\) of the rod.
1.310. (a) \(U=1 /{ }_{6} \pi r^{2} l^{3} \rho^{2} g^{2} / E\) (b) \(U=2 / 3 \pi r^{2} l E(\Delta l / l)^{2} .\) Here \(\rho\) is the density of steel.