Kinetic Energy Theorem and Conservation of Mechanical Energy

This page delves into the théorème de l'énergie cinétique and the concept of conservation of mechanical energy.

Definition: The théorème de l'énergie cinétique states that the change in kinetic energy of a system moving along a displacement AB is equal to the sum of the work done by external forces applied during the motion.

The theorem is expressed mathematically as:

ΔE = Ec₁ - Ec₂ = W(Fext)

Where:

• ΔE is the change in kinetic energy
• Ec₁ and Ec₂ are initial and final kinetic energies
• W(Fext) is the work done by external forces

The page then introduces the concept of mechanical energy conservation:

Highlight: Mechanical energy (Em) is the sum of kinetic energy (Ec) and potential energy (Epp).

Em = Ec + Epp

For gravitational potential energy: Epp = mgz, where m is mass, g is gravitational acceleration, and z is altitude in meters.

Definition: A conservative force is one whose work during a displacement from A to B does not depend on the path chosen.

The page concludes with two important principles:

1. For systems with only conservative forces: ΔEm(A→B) = 0
2. For systems with non-conservative forces: ΔEm(A→B) = W(Fnc)

Vocabulary:

• Conservative force: A force whose work is path-independent (e.g., gravity)
• Non-conservative force: A force whose work depends on the path taken (e.g., friction)

These concepts are crucial for understanding energy transformations in mechanical systems and form the basis for solving complex problems in physics.