Hello, I am trying to get an understanding of work and energy conservation and am getting confused. My thought experiment revolves around a mass hanging from a spring and moving the resting mass. Assume a 10kg mass hanging from a spring with k = 30 N/m. The mass will stretch the spring to x1 ~= -100/30 = -3.33m (-ve x is downwards). Given an equilbrium position of x1 = -3.33m I then "lift" the mass 1m. By lifting the mass I have done work on the spring by adding PE to the mass. ΔPE to mass = mgΔh = 100*1 = 100J I have also removed PE from the spring as I have moved it back towards its unstrained position. ΔPE to spring = 0.5×30x((-2.33)^2 - (-3.33)^2) = -85J I assume this mean the work I have done by lifting the mass is 100 - 85 = 15J ? I then allow the mass to return to the -3.33m position for experiment 2. In this experiment I pull down on the mass until it is at the -4.33m position. By pulling the mass downwards I have removed PE from the mass. ΔPE removed from mass = mgΔh = 100*1 = -100J I have also added PE to the spring as I have stretched it. ΔPE added to spring = 0.5×30x((-4.33)^2 - (-3.33)^2) = 115J I assume this mean the work I have done by pulling down the mass is 100 - 85 = 15J which is the same a lifting the mass? So working with or against gravity doesn't change the amount of work I do? This doesn't seem intuitive to me?