A ball with a mass of $400 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $32 (kg)/s^2$ and was compressed by $5/7 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2017-05-07T08:18:45

The height is $=2.08m$

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The spring constant is $k=12kgs^-2$

The compression is $x=1/2m$

The potential energy is

$PE=1/2*32*(5/7)^2=8.16J$

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

$KE=1/2m u^2$

The initial velocity is $=u$

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

$u^2=2/0.4*8.16=40.8$

$u=sqrt40.8=6.39ms^-1$

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,

$0=40.8-2*9.8*h$

$h=40.8/(2*9.8)=2.08m$

A ball with a mass of 400 g400 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 32 (kg)/s^232 (kg)/s^2 and was compressed by 5/7 m5/7 m when the ball was released. How high will the ball go?