Question

A structural steel rod has a radius r=10 mm and a length =1m.When a force F=100kN is applied it stretches it along its length. Young modulus of elasticity =2×10^11, stress=3.18×10^8 and strain=1.59mm
Find
(a)elastic energy density
(b)elastic potential energy

Answer 1

The elastic potential energy of the rod is 2.52 × 10`5.

Radius of the steel rod = 10mm (Given)

Length of the rod = 1m (Given)

Force applied = F = 100kN (Given)

Young's modulus of elasticity = =2×10^11 (Given)

Stress = 3.18×10^8

Strain on the rod = 1.59mm

Elastic energy density, u = 1/2 stress x strain

= 1/2 × 3.18×10^8 × 1.59 × 10³/ 1

= 2.52 × 10`5

Thus, the elastic energy density is  2.52 × 10`5.