# A ball with a mass of 140 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 42  kgs^-2 and was compressed by 5/3 m when the ball was released. How high will the ball go?

The spring potential energy is ${E}_{p} = \frac{1}{2} k {x}^{2} = \frac{1}{2} \times 42 \times {\left(\frac{5}{3}\right)}^{2} = 58.3$ $J$
This energy will be converted to gravitational potential energy, ${E}_{p} = m g h$. Rearranging: $h = {E}_{p} / \left(m g\right) = \frac{58.3}{0.14 \times 9.8} = 42.5$ $m$ (remembering to convert the mass to kg, the SI unit)