1. The problem statement, all variables and given/known data So theres an assignment that I must complete which is to build a rollercoaster. The main problem is during the blueprint stage, I'm extremely confused with the calculations. This roller coaster must have one loop, a collision and 2 hills, the goal is the conserve the most energy as a object (marble) going through the circuit. In addition the rollercoaster must be activated by a spring. What I had in mind was to have one hill, a collision followed by another hill and finally the loop. Further more, the height of the first hill may be at most 30.cm above the finishing height. The starting height may be up to 15 cm above the bottom. 2. Relevant equations Ek=1/2mv^2 Eg=mgh Fc=m(v^2/r) Es=1/2kx^2 3. The attempt at a solution To be honest I just need to find a radius of the loop and k value for the spring but I have no idea where to start calculation, it seems like always one variable is missing. Can anyone give me a start?