Question

A ball with a mass of `360 g` is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of `9 (kg)/s^2` and was compressed by `4/3 m` when the ball was released. How high will the ball go?

Answer 1

The height is `=2.27m`

Explanation:

The spring constant is `k=9kgs^-2`

The compression is `x=4/3m`

The potential energy is

`PE=1/2*9*(4/3)^2=8J`

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=2/0.36*8=44.44`

`u=sqrt44.44=6.67ms^-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=44.44-2*9.8*h`

`h=44.4/(2*9.8)=2.27m`