Physics: How Height Becomes Speed on a Rollercoaster

The Law of Conservation of Mechanical Energy states that, in the absence of friction and air resistance, the total mechanical energy of a system remains constant. Energy may transform between gravitational potential energy and kinetic energy, but none is created or destroyed. This principle explains why a rollercoaster car sitting at the top of a hill, where it possesses gravitational potential energy, can later race through a valley at maximum speed. Understanding this relationship matters because it links height, mass, and motion through a single elegant idea. Gravitational potential energy depends on the car's position above the ground, while kinetic energy depends on its speed, given by the formula Ek = ½mv². As the car descends, gravitational potential energy steadily converts into kinetic energy. Equating the energy at the top with the energy at the bottom, Ep = ½mv², allows the speed at any point to be deduced from the height lost.