conservation of energy
Summary
Conservation of energy says the total energy of an isolated system stays constant; energy changes form or moves between objects. Mechanical energy (KE + PE) is constant when only conservative forces do work; friction and other nonconservative forces change it, and the difference appears as thermal energy.
Detail
Meaning: The total energy of an isolated system stays constant. Energy changes form (kinetic, potential, thermal, chemical) or is transferred by work or heat, but the total does not change. Mechanical energy, KE + PE, is constant when only conservative forces such as gravity, springs and the electrostatic force do work. Friction and drag are nonconservative: they remove mechanical energy, which appears as thermal energy.
Equation: ½mvi² + mghi + Wnc = ½mvf² + mghf, where m is mass (kg), v is speed (m/s), g is 9.8 m/s² near Earth's surface, h is height (m), and Wnc is work done by nonconservative forces (J), negative for friction.
On the MCAT: Typical setups are a roller coaster, pendulum, block on an incline or falling object. Setting mgh = ½mv² gives v = √(2gh), and mass cancels. With friction, the thermal energy produced equals the mechanical energy lost. On a graph of KE and PE versus position, the two add to a flat line when no nonconservative force acts.
Common confusion: Energy lost to friction is not destroyed; mechanical energy drops, but total energy is conserved. Likewise, in an inelastic collision kinetic energy is not conserved, yet total energy is (and momentum is, if the system is isolated).
Sources
- Physics (Cutnell and Johnson)
- Physics (Giancoli)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.