Question

A ball with a mass of `350 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `35 (kg)/s^2` and was compressed by `5/4 m` when the ball was released. How high will the ball go?

Answer 1

The height is `=7.97m`

Explanation:

The spring constant is `k=35kgs^-2`

The compression is `x=5/4m`

The potential energy in the spring is

`PE=1/2*35*(5/4)^2=27.34J`

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of the ball

`KE_(ball)=1/2m u^2`

Let the height of the ball be `=h`

The acceleration due to gravity is `g=9.8ms^-2`

Then ,

The potential energy of the ball is `PE_(ball)=mgh`

Mass of the ball is `m=0.350kg`

`PE_(ball)=27.34=0.35.*9.8*h`

`h=27.34*1/(0.35*9.8)`

`=7.97m`

The height is `=7.97m`