Question

A spring is initially compressed by $2\text{m}$. Find out the work done required to compress another $6\text{m}$ if spring constant $k=2\text{N/m}$.

• A. $60\text{J}$
• B. $32\text{J}$
• C. $68\text{J}$
• D. $36\text{J}$

Answer 1

The correct option is A $60\text{J}$

Work done required to compress the spring = change in potential energy of spring
Initial compression in spring $x_0=2\text{m}$
Compression in spring when spring is compressed another $6\text{m}$ is $x_1=6+2$
$x_1=8\text{m}$
Change in potential energy of spring $=\frac{1}{2}k{x}_1^2-\frac{1}{2}k{x}_2^2$
$=\frac{1}{2}k[x_{1}2-x_0^2]$
$=\frac{1}{2}k[8^2-2^2]=60\text{J}$
Therefore work done required $=60\text{J}$