In the absence of external forces, what can be said about the total mechanical energy of a system?

In the absence of external forces, the total mechanical energy of a system remains constant due to the principle of conservation of mechanical energy. This principle states that if only conservative forces, such as gravitational or elastic forces, are acting on the system, the total energy (sum of potential and kinetic energy) does not change.

For example, consider a pendulum swinging back and forth. At its highest points, the pendulum has maximum potential energy and zero kinetic energy. As it swings down, potential energy converts to kinetic energy, reaching maximum kinetic energy and minimum potential energy at the lowest point. Throughout this motion, the total mechanical energy of the pendulum system—assuming no air resistance or friction—is conserved.

This concept underscores the idea that in a closed system where no external work is done and non-conservative forces are absent, the total mechanical energy remains unchanged.