How do you find the stopping distance of the roller coaster?

Imagine that you are an engineer designing a roller coaster. The track is a fairly simple one, without any loops or curves. The start is about 50m high and it goes directly diagnolly downwards, until it reaches the ground. Then, it will continue to extend in a horizontal manner on the ground. So, can anyone work out and tell me what the stopping distance would be? Where would the roller coaster stop?





I think that it may have something to do with the equation





KE(initial) + PE(initial) + W(external) = KE(final) + PE(final).


Also,it may have something to do with the equation of kinetic energy, which is [Kinetic energy = 1/2mv^2] and the equation of the gravitational potential energy,which is [GPE = Mass x gravitational acceleration x height]

How do you find the stopping distance of the roller coaster?
It has to do with how much friction there is between the roller coaster and the track. When you know the frictional force you can figure out how much energy it will lose.


You start with all gravitational potential energy and that gets converted to kinetic, but all the while it loses energy through friction.


The amount of friction will depend on the kind of materials used for the wheels and the track as well as the mass of the coaster. It'd be easiest to find out how fast it goes at the bottom, and how fast it should go at the bottom. You can use that difference to find out how much energy the roller coaster lost to friction.
Reply:To stop the roller coaster a force is necessary. When no other force is applied, friction alone can stop it.





One msut know the coefficient of friction between the roler coaster and the path along which it moves to find the stopping distance.





With out friction, the roller coaster will attain a speed of 31.03 m/s and will continue to move along the horizontal floor.





Friction stops this motion.



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