To solve this problem it is necessary to apply the concepts related to the Force from Hooke's law, the force since Newton's second law and the potential elastic energy.
Since the forces are balanced the Spring force is equal to the force of the weight that is
[tex]F_s = F_g[/tex]
[tex]kx = mg[/tex]
Where,
k = Spring constant
x = Displacement
m = Mass
g = Gravitational Acceleration
Re-arrange to find the spring constant
[tex]k = \frac{mg}{x}[/tex]
[tex]k = \frac{8*9.8}{0.1}[/tex]
[tex]k = 784N/m[/tex]
Just before launch the compression is 40cm, then from Potential Elastic Energy definition
[tex]PE = \frac{1}{2} kx^2[/tex]
[tex]PE =\frac{1}{2} 784*0.4^2[/tex]
[tex]PE = 63.72J[/tex]
Therefore the energy stored in the spring is 63.72J
