Question

A ball with a mass of `70 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `5 (kg)/s^2` and was compressed by `7/6 m` when the ball was released. How high will the ball go?

Answer 1

The height is `=4.96m`

Explanation:

The spring constant is `k=5kgs^-2`

The compression is `x=7/6m`

The potential energy in the spring is

`PE=1/2*5*(7/6)^2=3.40J`

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=0.070kg`

`PE_(ball)=3.40=0.070*9.8*h`

`h=3.40*1/(0.07*9.8)`

`=4.96m`

The height is `=4.96m`