A ball with a mass of $140 g$ 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 $7/3 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2018-05-11T06:22:04

The height reached by the ball is $=31.75m$

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The spring constant is $k=16kgs^-2$

The compression of the spring is $x=7/3m$

The potential energy stored in the spring is

$PE=1/2kx^2=1/2*16*(7/3)^2=43.56J$

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 $m=0.140kg$

$PE_(ball)=43.56=0.140*9.8*h$

$h=43.56*1/(0.140*9.8)$

$=31.75m$

The height reached by the ball is $=31.75m$

A ball with a mass of 140 g140 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 7/3 m7/3 m when the ball was released. How high will the ball go?