A ball with a mass of $160 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $21 (kg)/s^2$ and was compressed by $3/8 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2017-10-21T08:14:37

The height is $=0.94m$

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The spring constant is $k=21kgs^-2$

The compression is $x=3/8m$

The potential energy in the spring is

$PE=1/2kx^2=1/2*21*(3/8)^2=1.48J$

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 $=h$

Then ,

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

The mass of the ball is $=0.160kg$

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

$PE_(ball)=1.48=0.160*9.8*h$

The height is $h=1.48*1/(0.160*9.8)$

$=0.94m$

A ball with a mass of 160 g160 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 21 (kg)/s^221 (kg)/s^2 and was compressed by 3/8 m3/8 m when the ball was released. How high will the ball go?