# When should gravitational potential energy be included in the law of conservation of energy

I have a problem that says:

A block of mass 0.249 kg is placed on top of a light, vertical spring of force constant 4 975 N/m and pushed downward so that the spring is compressed by 0.090 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?

My first intuition was to use the law of conservation of energy which goes like this $$mgh_1+\frac{Kh^2}{2} = mgh_2$$ $$0.249*9.8*(-0.09)+\frac{4975 * (-0.09)^2}{2} = 0.249*9.8*h_2$$ Here, I defined the point in which the spring is at equilibrium as my reference point (as per convention) which means that when the string is compressed we have two forms of energy, gravitational and elastic, and at point two which is when the object has reached it's maximum height, there is but only one form of energy which is gravitational potential energy.However, this does not seem to give the correct answer. The correct answer seems to come when i don't include the negative gravitational potential energy at the left side of the equation, but i don't know why is that. can someone please explain? thanks

• You have all the right ideas, you just misinterpreted where the reference point should be. The question asks for the height above the point of release (what you call $-0.09 m$). There are two ways you can proceed. 1. Redo the calculation but set your zero point at the release point (which amounts to setting $h_1$ to zero in what you've done. 2. Take what you've computed--the height above the springs equilibrium position--and add to it the amount the spring was compressed, 0.09 m. I think it could be very educational to try both methods and see you get the same answer. – Andrew Apr 13 '16 at 4:54
• Wow, I'm so stupid how did i miss read that? Anyway's thanks for your help sir. I'm not sure what if it would be appropriate for me to delete this question now since the entire issue was a misinterpretation. Should I delete it? – GamefanA Apr 13 '16 at 4:58
• I think this is an example of a good mistake you can learn from, it stems from a subtle point about how the "natural reference point for a spring" is not always the most interesting or natural origin to choose even in problems involving springs. I do think trying both methods and seeing they give the same answer could genuinely be useful. Also you can write up your own answer and accept it if you think you can resolve it. – Andrew Apr 13 '16 at 5:01