# A ball with a mass of 450 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 12 (kg)/s^2 and was compressed by 4/5 m when the ball was released. How high will the ball go?

Jul 5, 2016

$h = \frac{128}{15 g}$[m]

#### Explanation:

Calling

$h$ height attained
$m = 0.450$ ball mass
$K = 12$ spring constant
$\Delta x = \frac{4}{5}$ compressed length

Equating potential energies

$m g h = \frac{1}{2} K {\left(\Delta x\right)}^{2}$

then

$h = \frac{1}{2} \frac{K}{m g} {\left(\Delta x\right)}^{2} = \frac{128}{15 g}$