# A ball with a mass of 420 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 6/5 m when the ball was released. How high will the ball go?

Oct 15, 2017

7.34 m

#### Explanation:

Potential energy in spring when it’s in compressed state is
$U = \frac{k {x}^{2}}{2}$

U = (21 kgs^-2 × (6/5 m)^2) / 2 = 15.12 J

According to law of Conservation of Energy
Total energy stored in spring = Total energy gained by ball

$15.12 J = \frac{m g h}{2}$

h = (2 × 15.12 J) / (mg)

h = (2 × 15.12 J) / (420 text(grams) × 10^-3 text(kg/grams) × 9.8 ms^-2)

$h = 7.34 m$