What physical laws determine how many hills, curves, and loops a roller coaster track can have?

I have a homework in Physics and this is one of its questions. I contemplated on it and did so much research but still, I was not able to get an answer.Please help me PEOPLE!!!!

What physical laws determine how many hills, curves, and loops a roller coaster track can have?
Really, there is only one physical law that limits the course of a roller coaster and that is the law of conservation of energy.





There is almost always only one %26#039;input%26#039; of energy into the roller coaster cars, and that is when they are initially lifted, usually by some sort of chain drive.





From the starting point, given the weight of the cars and the passengers, there is a certain potential energy available to the designers. They will have to consider losses to friction in the wheels and connecting linkages of the cars, and resistance from the air, along with losses of energy in angular momentum from twists and turns - that also ends up as heat from friction - when considering each %26#039;next%26#039; leg of a journey, when the cars reach another - albeit ever lower crest.





Higher efficiency in the wheels and better streamlining have made a large difference in just how long the system can retain some energy, but ultimately, the energy is dissipated. which is not always such a bad thing! imagine if it one could design a 100% efficient roller-coaster. It would never stop. Lucky for us that nature never works that way. Well! Maybe you%26#039;d prefer an infinite ride?
Reply:There are no physical limits. All that is necessary is that the coaster have enough energy to overcome friction losses throughout the course, and a high enough starting ramp can supply as much as one wants.



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