Question

A ball with a mass of `640 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `36 (kg)/s^2` and was compressed by `5/8 m` when the ball was released. How high will the ball go?

Answer 1

The height is `=1.12m`

Explanation:

The spring constant is `k=36kgs^-2`

The compression is `x=5/8m`

The potential energy is

`PE=1/2*36*(5/8)^2=7.03J`

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

`KE=1/2m u^2`

The initial velocity is `=u`

`u^2=2/m*KE=2/m*PE`

`u^2=2/0.64*7.03=21.97`

`u=sqrt21.97=4.69ms^-1`

Resolving in the vertical direction `uarr^+`

We apply the equation of motion

`v^2=u^2+2ah`

At the greatest height, `v=0`

and `a=-g`

So,

`0=21.97-2*9.8*h`

`h=21.97/(2*9.8)=1.12m`