I solved this Conservation of Energy problem but I don't fully understand how

[coldjeanz]

Homework Statement

Homework Equations

K.E = 1/2(m)(v final)^2
P.E = mgh
1/2k(x)^2 <--I don't understand how you would know to use this one

The Attempt at a Solution

Ok so I said that energy would be conserved so E initial would equal E final.

This is what I did to solve the problem but it was more luck than anything:

1/2k(x)^2 = 1/2(m)(v final)^2 + mgh

I solved for (v final) to get an answer of 1.9 m/s which is correct I think. But what I don't understand is why you are adding the potential and kinetic formulas together and then setting them equal to the 1/2k(x)^2 formula (what is this called, is it elastic?). What is the physics behind setting up the problem this way?

Thanks

 

[technician]

The only way the mass can gain energy in this problem is from the stored elastic potential energy of the compressed spring.
This energy is converted into KE and PE of the mass.
Your answer is good, I got the same by your method

 

[coldjeanz]

Alright that makes sense, thanks.