The principle of conservation of mechanical energy

Definition of mechanical energy

The mechanical energy Em of a system is the sum of its kinetic energy and its potential energy (gravitational and/or elastic):

Em = Ec + Ep

The principle of conservation

When only conservative forces act on a system (typically weight, or the restoring force of a spring, in the absence of friction and air resistance), mechanical energy is conserved: it remains constant throughout the motion.

Ke(initial) = Ke(final)

This means that kinetic energy and potential energy can be converted into one another, but their sum remains constant.

Example: free fall

An object dropped from a height h with no initial velocity, in the absence of friction, sees its potential energy decrease and its kinetic energy increase at the same rate. Just before impact, all the initial potential energy has been converted into kinetic energy: m * g * h = 1/2 * m * v^2

Example: the pendulum

A pendulum oscillating without friction constantly exchanges kinetic energy (Ec) and potential energy (Epp): maximum velocity (Ec max, Epp min) at the lowest point, zero velocity (Ec = 0, Epp max) at the extreme points.

Pitfalls to avoid

• Applying the conservation of Em when friction is present (covered in the next lesson).
• Forgetting to clearly identify the initial and final states before writing the energy equation.