All Problems

Elastic deformations

Problem 1.310

A steel cylindrical rod of length ll and radius rr is suspended by its end from the ceiling. (a) Find the elastic deformation energy UU of the rod. (b) Define UU in terms of tensile strain Δl/l\Delta l / l of the rod.

Reveal Answer
1.310. (a) U=1/6πr2l3ρ2g2/EU=1 /{ }_{6} \pi r^{2} l^{3} \rho^{2} g^{2} / E (b) U=2/3πr2lE(Δl/l)2.U=2 / 3 \pi r^{2} l E(\Delta l / l)^{2} . Here ρ\rho is the density of steel.
Prev
Next