Question

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

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

Answer 1

The correct option is B 18.75 N-m

work done in stretching a spring by a distance x is
$W=\frac{1}{2}k{x}^2$
where k is the spring constant.
work required to stretch the string by 10cm is
$W_1=\frac{1}{2}k{x}^2=\frac{1}{2}5\times {10}^3(0.1{)}^2=25J$
work required to stretch the string by 5cm is
$W_2=\frac{1}{2}k{x}^2=\frac{1}{2}5\times {10}^3(0.05{)}^2=6.25J$
Hence the work done in stretching it from 5cm to 10cm is
$W_1-W_2=25-6.25=18.75J$