A ball with a mass of $600 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $16 (kg)/s^2$ and was compressed by $3/5 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2017-04-02T08:42:19

The height is $=0.49m$

The energy stored in the spring will be converted to kinetic energy and this will give the initial speed of the ball.

Mass is $m=0.6kg$

Spring constant is $k=16kgs^-2$

Compression is $x=3/5m$

Energy in the spring $E_s=1/2kx^2$

Kinetic energy is $KE=1/2mv^2$

$1/2kx^2=1/2mv^2$

$v^2=k/mx^2$

$=16/0.6*(3/5)^2$

$=9.6m^2s^-2$

$v=sqrt9.6=3.1ms^-1$

We apply the equation of motion

$v^2=u^2+2as$

To find the greatest height

$v=0$

$u=3.1$

$a=-g=-9.8$

$s=h$

So,

$0=3.1^2-2*9.8*h$

$h=9.6/(2*9.8)$

$h=0.49m$

A ball with a mass of 600 g600 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 16 (kg)/s^216 (kg)/s^2 and was compressed by 3/5 m3/5 m when the ball was released. How high will the ball go?