# A ball with a mass of 480 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 24 (kg)/s^2 and was compressed by 8/9 m when the ball was released. How high will the ball go?

Sep 29, 2017

6.28 m/s

#### Explanation:

If Spring compressed by $x$ then Potential Energy stored in it
$U = \frac{1}{2} k {x}^{2}$
$k = \text{spring constant} = 24 \frac{k g}{s} ^ 2$
$x = \text{Displacement } = \frac{8}{9} m$

$U = \frac{1}{2} \left(24\right) {\left(\frac{8}{9}\right)}^{2} = \frac{24 \times 64}{2 \times 81} = 9.48 J$

After Release spring loaded contraption Potential Energy Changes into Kinetic Energy. (Conservation of Energy)
Hence Mass of 480g has Kinetic Energy $\frac{1}{2} m {v}^{2}$

Now Using Conservation of Energy
$\text{Kinetic Energy"="Potential Energy}$
$U = \frac{1}{2} m {v}^{2}$
$9.48 = \frac{1}{2} \left(0.48\right) {\left(v\right)}^{2}$
${v}^{2} = 39.50$
$v = \sqrt{39.50}$
$v = 6.28 \frac{m}{s}$