Question

A ball with a mass of `144 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `64 (kg)/s^2` and was compressed by `8/3 m` when the ball was released. How high will the ball go?

Answer 1

The height is `=161.2m`

Explanation:

The spring constant is `k=64kgs^-2`

The compression is `x=8/3m`

The potential energy in the spring is

`PE=1/2*64*(8/3)^2=227.6J`

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 sacceleration 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=0.144kg`

`PE_(ball)=227.6=0.144*9.8*h`

`h=227.6*1/(0.144*9.8)`

`=161.2m`

The height is `=161.2m`