Conservation of Linear Momentum in Collisions

Conservation of Linear Momentum in Collisions

Definition of a Collision

• A collision is an isolated event in which two or more objects exert forces on each other in a short period of time.
• During a collision, the objects involved come into physical contact with each other.

Conservation of Linear Momentum in Collisions

• The total linear momentum before a collision is equal to the total linear momentum after the collision.
• Mathematically, this is represented as: ∑p₁ = ∑p₂, where p₁ and p₂ are the initial and final momenta, respectively.
• This is a direct result of Newton's third law, which states that every action has an equal and opposite reaction.

Types of Collisions

• Elastic Collision: A collision in which the total kinetic energy is conserved.
  • Example: Billiard balls bouncing off each other.
• Inelastic Collision: A collision in which the total kinetic energy is not conserved.
  • Example: A car crashing into a wall.
• Completely Inelastic Collision: A collision in which the objects stick together after the collision.
  • Example: A meteorite colliding with the Earth's surface.

Key Concepts

• Momentum Transfer: The transfer of momentum from one object to another during a collision.
• Impulse: The product of the force and time over which it is applied.
• Center of Mass: The point at which the entire mass of an object can be considered to be concentrated.

Important Equations

• Conservation of Linear Momentum: ∑p₁ = ∑p₂
• Momentum Transfer: Δp = F × Δt
• Elastic Collision: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Note: v₁ and v₂ are the initial velocities, v₁' and v₂' are the final velocities, m₁ and m₂ are the masses of the objects, and F is the force exerted during the collision.

Conservation of Linear Momentum in Collisions

Definition of a Collision

• A collision occurs when two or more objects exert forces on each other in a short period of time, resulting in physical contact.
• Collisions are isolated events.

Conservation of Linear Momentum

• The total linear momentum before a collision is equal to the total linear momentum after the collision.
• This is represented mathematically as: ∑p₁ = ∑p₂, where p₁ and p₂ are the initial and final momenta, respectively.
• This conservation is a direct result of Newton's third law, which states that every action has an equal and opposite reaction.

Types of Collisions

Elastic Collisions

• Total kinetic energy is conserved in an elastic collision.
• Example: Billiard balls bouncing off each other.

Inelastic Collisions

• Total kinetic energy is not conserved in an inelastic collision.
• Example: A car crashing into a wall.

Completely Inelastic Collisions

• Objects stick together after the collision.
• Example: A meteorite colliding with the Earth's surface.

Key Concepts

Momentum Transfer

• The transfer of momentum from one object to another during a collision.
• Occurs due to the force exerted between the objects.

Impulse

• The product of the force and time over which it is applied.
• Represents the total effect of a force on an object over a period of time.

Center of Mass

• The point at which the entire mass of an object can be considered to be concentrated.
• Important in understanding the motion of complex systems.

Important Equations

• Conservation of Linear Momentum: ∑p₁ = ∑p₂
• Momentum Transfer: Δp = F × Δt
• Elastic Collision: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'