A roller coaster and its occupant’s have a combined mass of 800 kg. At a height of 70 m, the roller coaster has approximately zero speed. At the bottom, at maximum speed, a piston/cylinder apparatus is compressed adiabatically in order to bring the roller coaster to a stop. If the compression process is given by pV^(1.4) = constant, and the initial condition in the cylinder is that of Nitrogen at T=280K and p = 100kPa, answer the following.
1) Assuming a frictionless, ideal roller coaster, what is the speed at the bottom?
2) If the cross-sectional area of the piston is 0.5 m^2, and the total mass of Nitrogen in the cylinder is 10 kg, how far must it travel to bring the roller coaster to a stop?