1. The problem statement, all variables and given/known data This is the conservation of energy in the absence of external forces ΔKE + ΔPE + ΔTE + ΔU= 0 TE is friction, U is other internal energy, like the spring So expand and disregard U and TE for a moment ½m(v² - v₀²) + mg(h - h₀) = 0 Now comes the question, why is + mg(h - h₀) and not -mg(h - h₀)? Is gravitational potential energy not the same thing as the work done by gravity? Because gravity pulls down and if you go up, that's negative work. I've used the equation (with the positive mgh) many times and have not failed me.