# 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?

Oct 21, 2017

The height is $= 0.94 m$

#### Explanation:

The spring constant is $k = 21 k g {s}^{-} 2$

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

The potential energy in the spring is

$P E = \frac{1}{2} k {x}^{2} = \frac{1}{2} \cdot 21 \cdot {\left(\frac{3}{8}\right)}^{2} = 1.48 J$

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

$K {E}_{b a l l} = \frac{1}{2} m {u}^{2}$

Let the height of the ball be $= h$

Then ,

The potential energy of the ball is $P {E}_{b a l l} = m g h$

The mass of the ball is $= 0.160 k g$

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

$P {E}_{b a l l} = 1.48 = 0.160 \cdot 9.8 \cdot h$

The height is $h = 1.48 \cdot \frac{1}{0.160 \cdot 9.8}$

$= 0.94 m$