I am currently learning about elastic potential energy and this is a question that was given to us by my teacher:
When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring.
To solve this question he used total mechanical energy (ME= GPE+ EPE+ KE)and the conversion of the energy from GPE to EPE (as the object falls down it's energy changes from GPE to EPE and the KE is 0 because the final and initial velocities are zero.)
Because this is a conserved system then ME =0 deltaGPE=-deltaEPE then he substituted the given into the equations: (13.2)(10) (0-0.0593)=-1/2 (k) (0.0593^2-0^2) k= 4451.9 N/m
However by using Hooke's law (which I got from the internet- In class we still didn't take hooke's law and all what we know about springs...(elastic) is from EPE equation.): F=kx the force here is Fg=(13.2)(10)=132 132=k(0.0593) k=2225.96 N/m
So my question is why are the answers diffrent what is missing in either of these ways??