# A ball with a mass of 144 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 3/5 m when the ball was released. How high will the ball go?

Jan 1, 2018

$h = 2.04 m \text{ }$(2dps)

#### Explanation:

when the ball is released from the spring all the Elastic Potential energy will be given to Gravitational Potential energy at maximum height.

$E P E = \frac{1}{2} k {x}^{2} = \frac{1}{2} \times 16 \times {\left(\frac{3}{5}\right)}^{2}$

$E P E = \frac{72}{25} J$

$\text{now } G P E = E P E$

$m g h = \frac{72}{25}$

$0.144 \times 9.8 \times h = \frac{72}{25}$

$1.4112 \times h = \frac{72}{25}$

$\therefore h = \frac{72}{25 \times 1.4112}$

$h = 2.04 m \text{ }$(2dps)