Conservation of Energy

Universal principle of mechanical energy conservation in closed and isolated systems.

General idea of the topic

When only conservative forces do work, the sum of kinetic and potential energy stays constant. Energy is transformed from one form to another, for example from potential to kinetic in a fall, but the mechanical total does not change.

The topic states the conservation principle in its general form, including all forms of energy, and specializes it to conservative systems, where it is enough to compare two instants to obtain speeds or heights without solving the equations of motion.

What you will truly understand

By the end you will be able to apply E_k + U = constant between two points, recognize which forces allow it and obtain speeds at the lowest point of a pendulum or at the end of a frictionless track.

You will also know why the total energy, including heat, is always conserved even though the mechanical energy is not.

Recommended learning route

1. Principle of Energy Conservation: the total energy of an isolated system is conserved, even if it changes form.
2. Conservative Systems: systems with conservative forces, constant mechanical energy and energy diagrams.

Physical criterion you must acquire

The essential criterion is to verify that no non-conservative forces do work before using mechanical conservation. The normal force on a frictionless track and the tension of a pendulum do no work, so the mechanical energy is conserved in those cases.

Connection with real problems

• pendulums and roller coasters.
• free fall and projectiles.
• spring oscillations.
• orbits and satellites.

Final goal of the topic

The final goal is to apply conservation of mechanical energy to conservative systems and justify when it can be used.