# A ball with a mass of 400 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 64 (kg)/s^2 and was compressed by 3/4 m when the ball was released. How high will the ball go?

May 19, 2016

Taking $g = 10$[m/s²] we obtain $h = 4.5$[m]
The spring mechanical energy ${E}_{m} = \frac{1}{2} K {x}^{2}$ is transformed in potential energy for the ball ${E}_{p} = m g h$. Equating both energy forms we get
$\frac{1}{2} K {x}^{2} = m g h$
Solving for $h = \frac{1}{2} K {x}^{2} / \left(m g\right)$ with $g = 10$ we get
$h = 4.5$[m]