Question

(a) Derive the formula for elastic potential energy, PEE, in terms of applied force F, stiffness

constant k, and extension ΔL of a wire. State any assumptions made.

(b) Figure 4.6a shows a F versus ΔL graph for a wire of length 2.0 m and diameter 1.2 mm.

(i) Determine the stiffness constant of the wire from the graph.

(ii) Determine the Young’s modulus for the material of the wire.

(iii)What is a practical advantage of knowing the Young’s modulus as compared with the

stiffness constant of the wire?

Answer 1

The spring is assumed to be massless.

F=k∆L

Elastic potential energy,U= $\frac{1}{2}*force*displacement$

$U=\frac{1}{2}(k∆L)∆L$

$U=\frac{1}{2}k(∆L)^2$

Where ,U=elastic potential energy

k=stiffness constant

∆L=displacement