A ball with a mass of $70 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $19 (kg)/s^2$ and was compressed by $7/6 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2018-04-10T13:45:38

The height reached by the ball is $=2.57m$

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The spring constant is $k=19kgs^-2$

The compression of the spring is $x=7/6m$

The potential energy stored in the spring is

$PE=1/2*19*(7/6)^2=12.93J$

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

$KE_(ball)=1/2m u^2$

Let the height of the ball be $=h$

The acceleration due to gravity is $g=9.8ms^-2$

Then ,

The potential energy of the ball is $PE_(ball)=mgh$

Mass of the ball is $m=0.070kg$

$PE_(ball)=12.93=0.070*9.8*h$

$h=12.93*1/(0.07*9.8)$

$=1.22m$

The height reached by the ball is $=2.57m$

A ball with a mass of 70 g70 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 19 (kg)/s^219 (kg)/s^2 and was compressed by 7/6 m7/6 m when the ball was released. How high will the ball go?