Question

A ball with a mass of `200 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 `7/4 m` when the ball was released. How high will the ball go?

Answer 1

The height is `=0.5m`

Explanation:

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

The compression is `x=7/4m`

The potential energy is

`PE=1/2*64*(7/4)^2=98J`

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=2/0.2*98=9.8`

`u=sqrt9.8=3.13ms^-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=9.8-2*9.8*h`

`h=9.8/(2*9.8)=0.5m`