Question

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?

Answer 1

9.448m

Explanation:

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

We will use the conservation of energy.

The energy put by the spring:
`U_("spring")=1/2kx^2`
The energy for the gravitation:
`U_g=mgy`

If we apply the conservation of energy to this situation:
`U_("spring")=U_g`

We put the three equations together:
`1/2kx^2=mgy`

We isolate the height (y):
`=>(kx^2)/(2mg)=y`

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