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.

Work of a Force

This page introduces the concept of work done by a force in mechanical systems. It explains how forces can affect various aspects of an object's motion and energy.

Definition: Work is the product of force and displacement, considering the angle between them.

The page presents the formule travail d'une force for constant forces:

W₁(F) = F · AB · cos(F, AB)

Where:

• W₁(F) is the work done
• F is the force in Newtons
• AB is the displacement in meters
• cos(F, AB) is the cosine of the angle between force and displacement

Highlight: The work can be classified as motor (positive), resistant (negative), or null based on the angle between force and displacement.

The page also discusses specific cases:

1. Work done by weight: W₁ = P(zA - zB)
2. Work done by support force: WAB(R) = 0
3. Work done by friction: W₁(F) = -F · AB

Example: For the work done by weight, if zA > zB, the work is motor (positive), and if zA < zB, the work is resistant (negative).

Vocabulary:

• Motor work: When the force assists the motion (0° < α < 90°)
• Resistant work: When the force opposes the motion (90° < α < 180°)
• Null work: When the force is perpendicular to the displacement $α = 90°$