Answer
The total length of the spring would be 21.52 cm.
Work Step by Step
We can find the force constant $k$ of the spring.
$kx = mg$
$k = \frac{mg}{x} = \frac{(3.15~kg)(9.80~m/s^2)}{0.0140~m}$
$k = 2205~N/m$
We can find the distance the spring stretches when it stores 10.0 J of potential energy.
$\frac{1}{2}kx^2 = 10.0 ~J$
$x^2 = \frac{20.0~J}{2205~N/m}$
$x = \sqrt{\frac{20.0~J}{2205~N/m}}$
$x = 0.0952~m$
The total length of the spring would be 12.00 cm + 9.52 cm, which is 21.52 cm.
