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?

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Answer 1 · 2017-04-28T16:16:40

The height is $=2.27m$

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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,

$0=44.44-2*9.8*h$

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

A ball with a mass of 360 g360 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 9 (kg)/s^29 (kg)/s^2 and was compressed by 4/3 m4/3 m when the ball was released. How high will the ball go?