In the gure, a frictionless roller coaster car of mass m = 829 kg tops the rst hill with speed v0 = 16.0 m/s at height h = 41.0 m. What is the speed of the car at (a) point A, (b) point B, and ((2) point C? (d) How high will the car go on the last hill, which is too high for it to cross? Use g=9.81 m/s2. (a) Number (b) Number (c) Number (d) Number m Assistance Used Any decrease in elevation decreases the gravitational potential energy. The total amount of energy (kinetic energy plus potential energy) does not change. How is kinetic energy related to speed? Key Ideas . The mechanical energy Emec of a system is the sum of its kinetic energy K and potential energy U: Emec = K + U. . An isolated system is one in which no external force causes energy changes. If only conservative forces do work within an isolated system, then the mechanical energy Emec of the system cannot change. This principle of conservation of mechanical energy is written as K2 + U2 = K1+ U1, in which the subscripts refer to different instants during an energy transfer process. This conservation principle can also be written as AE mec = AK + AU = 0