# A ball with a mass of 500 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 16 (kg)/s^2 and was compressed by 8/3 m when the ball was released. How high will the ball go?

Jun 3, 2016

$h = 11.6 \text{ } m e t e r s$

#### Explanation:

$\text{The potential energy that is stored at any spring can be calculated using formula:} :$
${E}_{p} = \frac{1}{2} \cdot K \cdot \Delta {x}^{2}$

${E}_{p} : \text{Potential Energy}$

$\text{K:Spring Constant}$

$\Delta x : \text{amount of compress or stretch}$

${E}_{p} = \frac{1}{2} \cdot 16 \cdot {\left(\frac{8}{3}\right)}^{2}$

${E}_{p} = 8 \cdot \frac{64}{9} = \frac{512}{9} \text{ } J$

$\text{while object is rising ,"E_p" turns to the gravitational potential energy }$

$\frac{512}{9} = m \cdot g \cdot h$

$m = 500 \text{ "gr=0.5" } k g$

$g = 9.81 \text{ } \frac{N}{k g}$

$\frac{512}{9} = 0.5 \cdot 9.81 \cdot h$

$h = \frac{512}{9 \cdot 0.5 \cdot 9.81}$

$h = 11.6 \text{ } m e t e r s$