A ball with a mass of $150 g$ $150 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $90 \frac{k g}{s^{2}}$ $90 (kg)/s^2$ and was compressed by $\frac{4}{3} m$ $4/3 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2017-05-12T15:32:25

The height is $= 54.42 m$ $=54.42m$

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The spring constant is $k = 90 k g s^{- 2}$ $k=90kgs^-2$

The compression is $x = \frac{4}{3} m$ $x=4/3m$

The potential energy in the spring is

$P E = \frac{1}{2} \cdot 90 \cdot {(\frac{4}{3})}^{2} = 80 J$ $PE=1/2*90*(4/3)^2=80J$

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

$K E_{b a l l} = \frac{1}{2} m u^{2}$ $KE_(ball)=1/2m u^2$

Let the height of the ball be $= h$ $=h$

Then ,

The potential energy of the ball is $P E_{b a l l} = m g h$ $PE_(ball)=mgh$

$P E_{b a l l} = 80 = 0.15 \cdot 9.8 \cdot h$ $PE_(ball)=80=0.15*9.8*h$

$h = 80 \cdot \frac{1}{0.15 \cdot 9.8}$ $h=80*1/(0.15*9.8)$

$= 54.42 m$ $=54.42m$

A ball with a mass of 150g150 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 90kgs290 (kg)/s^2 and was compressed by 43m4/3 m when the ball was released. How high will the ball go?