My Teacher gave me an interesting problem in AP Physics which seemed simple at first but has me going insane. The problem was what would happen to the potential energy contained in a spring if 0.2 kg was added to the original 0.2 kg on the spring, which stretched the spring 5 cm. The mathematical answer is that the potential energy would quadruple. The problem I have with the answer is this: when you first add the 0.2 kg mass, the spring stretches 5 cm from its original state, but according to the answer, if you add the next 0.2 kg mass, the length must once again be increased by 5 cm. This is found using the equation Fs = (1/2)k(x^2). But as the spring lengthens, it takes more work to increase the length by the same amount again, so shouldn't another 0.2 kg increase the length of the spring by less than 5 cm? If this is so then the actual answer should only be that the potential energy is doubled. One example I tried to use against my teacher was this: Say that I stand on a spring scale. The scale should read my weight because of the work that gravity does on the scale by pulling me down onto the scale. Now if a person who weighs the exact same as I do stands on the scale with me, it should obviously read double my weight because gravity is now doing double the work. Now if the potential energy in the spring quadrupled then it would have the ability to do twice the work that gravity was doing, therefore launching my friend and I through the ceiling. Basically I'm extremely confused and maybe my logic is completely incorrect. Thank you if you read all of this...