Question

A system consists of two springs connected in series and having the stiffness coefficients k1 and k2. Find the minimum work to be performed in order to stretch this system by dL.

Answer 1

Solution

When two springs are connected in series then equivalent stiffness coefficient is

$k_{eq}=\frac{k_1 k_2}{k_1+k_2}$

For increment of mechanical energy

$\Delta K+\Delta U=W$

so

$0+\frac {k_1 k_2dL^2}{2(k_1+k_2)}=W$

$W=\frac {k_1 k_2dL^2}{2(k_1+k_2)}$

so work done to increase the length by dL is $\frac {k_1 k_2dL^2}{2(k_1+k_2)}$ .