Question

A ball with a mass of `40 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `16 (kg)/s^2` and was compressed by `2/5 m` when the ball was released. How high will the ball go?

Answer 1

The height reached by the ball is `=3.27m`

Explanation:

The spring constant is `k=16kgs^-2`

The compression of the spring is `x=2/5m`

The potential energy stored in the spring is

`PE=1/2kx^2=1/2*16*(2/5)^2=1.28J`

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=0.040kg`

`PE_(ball)=1.28=0.040*9.8*h`

`h=1.28*1/(0.040*9.8)`

`=3.27m`

The height reached by the ball is `=3.27m`