Energy and Conservation Principles

This page delves into various forms of energy and the principle of conservation of mechanical energy. It covers:

1. Kinetic Energy (Ec): The formula for kinetic energy is presented as Ec = ½ × m × v².

Vocabulary: Kinetic energy is the energy an object possesses due to its motion.

2. Theorem of Kinetic Energy: ΔEc(AB) = Ec(B) - Ec(A) = Σ W_AB(F)

This theorem relates the change in kinetic energy to the work done by all forces acting on the object.

3. Gravitational Potential Energy (Epp): The formula for gravitational potential energy is given as Epp = m × g × z.

Definition: Gravitational potential energy is the energy an object possesses due to its position in a gravitational field.

4. Mechanical Energy (Em) and Conservation: Mechanical energy is defined as the sum of kinetic and potential energies: Em = Ec + Epp

The principe de conservation de l'énergie mécanique (principle of conservation of mechanical energy) is introduced:

• If the sum of work done by non-conservative forces is zero, mechanical energy is conserved $Em = constant$.
• If non-conservative forces do work, mechanical energy is not conserved.

Highlight: The conservation of mechanical energy is a fundamental principle in physics, applicable when only conservative forces are present.

This page provides a comprehensive overview of energy concepts, laying the groundwork for understanding more complex mechanical systems and energy transformations.

Work Done by Forces

This page introduces the concept of work done by forces in physics. The fundamental formula for calculating work is presented:

W_AB(F) = AB × F × cos(AB, F)

Where:

• W_AB is the work done
• AB is the displacement
• F is the force
• cos(AB, F) is the cosine of the angle between the force and displacement vectors

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

The page then explores different scenarios of work:

1. Motoring work: When the force is in the same direction as displacement (0°), resulting in positive work.
2. Resistive work: When the force opposes the displacement (180°), resulting in negative work.
3. Null work: When the force is perpendicular to the displacement (90°), resulting in zero work.

Example: For a weight force P, the work is calculated as W_AB(P) = m × g × (Z_A - Z_B), where Z_A and Z_B are the initial and final heights.

The page also introduces the concepts of conservative and non-conservative forces:

Highlight: Conservative forces, like gravity, do not depend on the path taken, while non-conservative forces, like friction, do depend on the path.