Work, Energy, and Conservation Laws

This page delves into the concepts of work, energy, and conservation laws, providing key formulas and relationships.

Definition: Work is defined as the product of force and displacement in the direction of the force: W = F · s · cos θ

The page presents formulas for various forms of energy:

• Kinetic energy: E_c = 1/2 mv²
• Potential energy $gravitational$: U = mgh
• Elastic potential energy: U = 1/2 kx²

Highlight: The principio di conservazione dell'energia meccanica formula states that the total mechanical energy $kinetic + potential$ remains constant in a closed system: E_initial = E_final

The work-energy theorem is presented, relating work done to change in kinetic energy: W = ΔE_c

Vocabulary: Impulso $impulse$ is defined as the product of force and time interval: I = F · Δt

The page also covers concepts in Galilean relativity and gravity, including Newton's law of universal gravitation.

Example: The gravitational force between two masses m₁ and m₂ is given by F = G$m₁m₂$/r², where G is the gravitational constant.

Motion and Momentum

This final page focuses on various types of motion and the concept of momentum, providing formulas and relationships for different scenarios.

Definition: Quantità di moto $momentum$ is defined as the product of mass and velocity: p = mv

The page presents formulas for different types of motion:

• Uniformly accelerated motion: s = v₀t + 1/2 at²
• Free fall: v² = 2gh
• Projectile motion: Range = $v₀² sin 2θ$/g

Highlight: The teorema dell'impulso states that the change in momentum equals the impulse: Δp = F · Δt

The conservation of momentum is illustrated for collisions:

Example: In a collision between two objects, m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂', where primed velocities are after collision.

The page also includes formulas for accelerated and decelerated motion, as well as two-dimensional motion.

Vocabulary: Moto circolare uniformemente accelerato refers to circular motion with constant angular acceleration.

Lastly, the page provides trigonometric relationships for solving problems involving triangles in physics contexts.