1. The problem statement, all variables and given/known data Hello everyone, I am having immense trouble with this problem. I'm not too sure if this is classified as Advanced Physics, but currently I'm a high school senior in AP Physics. You are given a spring with spring constant k=40,000 N/M. A 2 KG block is put onto the spring, compressing it 4 cm (.04 m). Find the velocity at half of the total height traveled. Find the total height. Let it be known that whenever I have an "i" next to a variable, it references initial in regards to said variable. Variables without an "i" are to be considered as the final versions of said variable. 2. Relevant equations (kx^2)/2 - (kxi^2)/2 (mv^2)/2 - (mvi^2)/2 mgh-mghi Basically the Potential and Kinetic Energy equations. 3. The attempt at a solution What I ended up doing was something to this degree. Given: K=40000 m=2 ΔX=.04 Total height = (h+.04) ΔKE + ΔU + W' (No symbol for prime...) = 0 W' = 0 because of no outside forces ΔKE = -ΔU (mv^2)/2 - (mvi^2)/2 = -[(kx^2)/2 - (kxi^2)/2 ] (mvi^2)/2 = 0 since vi = 0 (kx^2)/2 = 0 since x = 0 mv^2/2 = kxi^2/2 mv^2 = kxi^2 v= √(kxi^2/m) Well, it all went pretty downhill from here, but let's keep going... Given mv^2/2 - mvi^2/2 = -mgh + mghi mgh = 0 because h = 0 -mvi^2/2 = 0 because vi = 0 Since kxi^2/2 = mv^2/2 I can substitute kxi^2/2 = mg((h+.04)/2) Plugging values in, I got 40000(.04).04)/2 = 32 2(10)(h+.4)/2 = 10h+.4 32 = 10h+.4 31.6=10h h=3.16 m Solving for v using newly found h, I did mv^2/2 = mgh/2 v^2/2 = gh/2 V^2 = gh V = √(31.6) V = ~5.2ish m/s My teacher doesn't mind discrepancies due to rounding, hence g = 10 So, after speaking to my fellow classmates, I came to the conclusion I did something wrong. What though? Any help would be much appreciated. Tomorrow I'm talking to him about the problem to figure out my mistake. Or, maybe I'm just smarter than everyone else in my class and they got the wrong answer. We'll see.