Question

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

• A. $6.25Nm$
• B. $12.50Nm$
• C. $18.75Nm$
• D. $25.00Nm$

Answer 1

Answer: (C)

$18.75Nm$

$W=U_f-U_i=\frac{1}{2}K(X_f^2-X_i^2{)}^2$
$=\frac{1}{2}\times 5\times {10}^3\left[\right(0.1{)}^2-\left(0.05{)}^2\right]$
$=18.75J$