# A ball with a mass of 360 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 5/3 m when the ball was released. How high will the ball go?

May 19, 2017

9.448m

#### Explanation:

The mass has to be put in kg:
$360 g = 0.36 k g$

We will use the conservation of energy.

The energy put by the spring:
${U}_{\text{spring}} = \frac{1}{2} k {x}^{2}$
The energy for the gravitation:
${U}_{g} = m g y$

If we apply the conservation of energy to this situation:
${U}_{\text{spring}} = {U}_{g}$

We put the three equations together:
$\frac{1}{2} k {x}^{2} = m g y$

We isolate the height (y):
$\implies \frac{k {x}^{2}}{2 m g} = y$

We take all the values of our situation and put them in there:
=>y=((24)(5/3)^2)/((2)(0.36)(9.8)
$= 9.448 m$