Gravitation Potential Energy Problem pls help!!! I would greatly appreciate help on a couple questions I have. I have been sic for the past few days and unable to go in to school to ask my TA's questions. My first question is when should use the equation Ki + Ui = Kf + Uf or Kf -Ki = Uf - Ui ? I know you would use both equations when there is conservation of energy but when would I use either one, aren't they pretty much the same? And my second question is in reference to homework problem 1. The problem statement, all variables and given/known data A rolelr coaster car (mass=988 kg including passengers) is about to roll down a track. The diameter of the circular loop is 20.0 m and the car starts from rest 40.0 m above the lowest point of the track. Ignore friction and air resistance. At what speed does the car reach the top of the loop? 2. Relevant equations The solution the professor gave was change in K = change in -U --> Kf - Ki = -mg(hf-hi) --> 1/2mv^2 - 0 = mg(hi-hf) --> v = sqrt 2*g*(hi-hf) --> v = sqrt 2*9.8*(40-20) = 19.8 m/s So my question in reference to this problem is why did he switch hf-hi to hi-hf, was that to get rid of the negative sign in front of mg? And if so how does that make sense? And also why did he set up the equation to be Kf -Ki = Uf - Ui instead of Ki + Ui = Kf + Uf? Thank you very much i really appreciate it!