Mechanical Energy Conservation and Work

This section examines the principles of mechanical energy conservation and work-energy relationships in both gravitational and electric fields.

Definition: Total mechanical energy (Em) is the sum of potential energy (Epp) and kinetic energy (Ec): Em = Epp + Ec

Highlight: Conservation of mechanical energy states that EMB - EMA = 0 between points A and B in a system.

Example: For gravitational potential energy: Epp = mgh For kinetic energy: Ec = ½mv²

Vocabulary: Work-Energy Theorem (Théorème de l'énergie cinétique) relates the change in kinetic energy to the work done by forces.

Quote: "EMB - EMA = 0" expresses the fundamental principle of mechanical energy conservation.

Gravitational Field and Trajectory Equations

This section details the fundamental equations and principles governing motion in gravitational fields. The content focuses on kinematic equations and trajectory calculations in uniform fields.

Definition: The gravitational field is characterized by acceleration components (ax=0, ay=-g, az=0), where g represents gravitational acceleration.

Example: For projectile motion, the horizontal velocity remains constant (vox = vo × cos α) while vertical motion is affected by gravity.

Highlight: The trajectory equations are derived through integration:

• x = v₁cos(α)t + x₀
• y = -½gt² + v₁sin(α)t + y₀

Vocabulary: Portée (xp) refers to the horizontal distance between the launch point and the impact point with the ground.

Quote: "2nd loi de Newton: ΣF = ma" establishes the fundamental relationship between force and acceleration.