A ball with a mass of $500 g$ $500 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $36 \frac{k g}{s^{2}}$ $36 (kg)/s^2$ and was compressed by $\frac{8}{3} m$ $8/3 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2017-05-23T10:00:17

The height is $= 26.12 m$ $=26.12m$

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The spring constant is $k = 36 k g s^{- 2}$ $k=36kgs^-2$

The compression is $x = \frac{8}{3} m$ $x=8/3m$

The potential energy in the spring is

$P E = \frac{1}{2} \cdot 36 \cdot {(\frac{8}{3})}^{2} = 128 J$ $PE=1/2*36*(8/3)^2=128J$

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 $P E_{b a l l} = m g h$ $PE_(ball)=mgh$

$P E_{b a l l} = 128 = 0.5 \cdot 9.8 \cdot h$ $PE_(ball)=128=0.5*9.8*h$

$h = 128 \cdot \frac{1}{0.5 \cdot 9.8}$ $h=128*1/(0.5*9.8)$

$= 26.12 m$ $=26.12m$

A ball with a mass of 500 g500g500 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 36 (kg)/s^236kgs236 (kg)/s^2 and was compressed by 8/3 m83m8/3 m when the ball was released. How high will the ball go?