# A ball with a mass of 350 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 16  kgs^-2 and was compressed by 7/6 m when the ball was released. How high will the ball go?

The spring potential energy is given by $F = \frac{1}{2} k {x}^{2} = \frac{1}{2} \times 16 \times {\left(\frac{7}{6}\right)}^{2} = 10.9$ $J$. This will be converted to gravitational potential energy (but remember to express mass in the SI unit, $k g$, as $0.350$ $k g$). ${E}_{p} = m g h$. Rearranging, $h = {E}_{p} / \left(m g\right) = \frac{10.9}{0.35 \times 9.8} \approx 3.18$ $m$.