A ball with a mass of $350 g$ $350 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $9 \frac{k g}{s^{2}}$ $9 (kg)/s^2$ and was compressed by $\frac{7}{4} m$ $7/4 m$ when the ball was released. How high will the ball go?

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Answer 1 · 2017-11-22T13:56:57

The height is $= 4.02 m$ $=4.02m$

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The spring constant is $k = 9 k g s^{- 2}$ $k=9kgs^-2$

The compression is $x = \frac{7}{4} m$ $x=7/4m$

The potential energy is

$P E = \frac{1}{2} \cdot 9 \cdot {(\frac{7}{4})}^{2} = 13.78 J$ $PE=1/2*9*(7/4)^2=13.78J$

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 $= h$ $=h$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

Then ,

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

Mass of the ball is $m = 0.35 k g$ $m=0.35kg$

$P E_{b a l l} = 13.78 = 0.35 \cdot 9.8 \cdot h$ $PE_(ball)=13.78=0.35*9.8*h$

$h = 13.78 \cdot \frac{1}{0.35 \cdot 9.8}$ $h=13.78*1/(0.35*9.8)$

$= 4.02 m$ $=4.02m$

The height is $= 4.02 m$ $=4.02m$

A ball with a mass of 350g350 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 9kgs29 (kg)/s^2 and was compressed by 74m7/4 m when the ball was released. How high will the ball go?