conservation of energy in a spring

Question

You have a spring of spring constant k, and a block of mass 0.200 kg. You set the spring up vertically and compress the spring 0.300 m. It launches the block up to a max height of 2.20 m. What is the spring constant? 

Answer 1

The potential energy stored in the compressed spring is 1/2 x k x X^2 where X is the distanced of compression (0.3 m). When released with the mass on top of the spring, this potential energy is converted into kinetic energy that projects the mass to a height 2.20 meters. The potential energy at this height must be equal to the initial potential energy of the spring system.

1/2 k X² = MgH where M is the mass (0.2 kg) and H the height (2.20 m}, g the acceleration of gravity (9.8 m/s²)

This equation can be solved for k since all other variables are given.

k = 2MgH/X² = 2 x 0.200 kg x 9.8 m/s² x 2.20 m / 0.300 m = 29 kg/s². (I used g to 2 sig figs.)