Energy Is Conserved as It Changes Form

Here at the top of this roller coaster, let me show you one of the most powerful ideas in all of physics: energy is never created or destroyed — it only changes form. Right now, this cart has gravitational potential energy (PE) because it is high above the ground. PE = mgh, where m is mass in kilograms, g is 9.8 m/s², and h is height in meters. The moment it rolls over the peak, that PE starts converting into kinetic energy (KE) — the energy of motion — given by KE = ½mv². In a perfectly isolated, frictionless system — one that exchanges neither mass nor energy with its surroundings — the total mechanical energy stays exactly constant: KE + PE = constant. So at any point on the track, whatever PE the cart loses, it gains as KE, and vice versa. At the bottom of a valley, PE is at its minimum and KE (speed) is at its maximum. But real roller coasters have friction and air resistance. Friction converts some mechanical energy into thermal energy — the increased random kinetic energy of molecules inside the track and cart. That thermal energy then transfers to the surroundings as heat, the name we give to energy flowing because of a temperature difference. The cart ends up moving a little slower than our frictionless model predicts. The total energy of the universe is still conserved; it has just spread into a form we cannot easily recover. Key check: if you ever calculate that a system gained total energy from nothing, recheck your work — the law of conservation of energy says that cannot happen.