Question

A spring of spring constant $5\times {10}^3$ N/m is stretched initially by $5$ cm from the unstretched position. The work required to further stretch the spring by another $5$ cm is:

• A. 6.25 N-m
• B. 12.50 N-m
• C. 18.75 N-m
• D. 25.00 N-m

Answer 1

Answer: (C)

18.75 N-m

Energy stored in a spring when stretched by $x$ is $\frac{1}{2}k{x}^2$

The amount of work required is the change in energy of the spring.
$W=U_f-U_i=\frac{1}{2}k({x_2}^2-{x_1}^2)$

$\Rightarrow W=0.5\left(5000\right)({0.1}^2-{0.05}^2)=18.75N-m$
Option C.