physics unit four notes

physics 1 unit four linear momentum

Linear Momentum

A vector quantity defined as the product of an object's mass and velocity.

Impulse

The change in momentum of an object, equal to the product of the net force and the time interval.

Impulse-Momentum Theorem

The theorem stating that the change in momentum of an object is equal to the impulse applied to it.

Conservation of Momentum

In a closed system, the total linear momentum remains constant before and after any interactions or collisions.

Elastic Collision

A collision in which both momentum and kinetic energy are conserved.

Inelastic Collision

A collision in which only momentum is conserved, but kinetic energy is not.

Perfectly Inelastic Collision

A type of collision where the colliding objects stick together and move with a common velocity after the collision.

Coefficient of Restitution (e)

A measure of the elasticity of a collision; e = 1 for perfectly elastic and e = 0 for perfectly inelastic.

Center of Mass

The point where the entire mass of a system can be considered concentrated.

Linear Momentum Formula

Linear momentum (p) is calculated as p=mv, where m is mass and v is velocity.

Impulse Formula

Impulse (J) is defined as J=FΔt, where F is the net force and Δt is the time interval.

Impulse-Momentum Theorem (Formula)

Δp=J, or mΔv=FΔt, indicating the relationship between change in momentum and impulse.

Conservation of Momentum Equation

In a closed system, p_initial=p_final or m1v1+m2v2=m1v1'+m2v2', representing conservation of momentum.

Perfectly Elastic Collision Definition

A collision where e = 1, in which no kinetic energy is lost.

Perfectly Inelastic Collision Definition

A collision where e = 0, where objects stick together after colliding.

Center of Mass Position Formula

x_COM=∑(m_i x_i)/∑m_i, where m_i is the mass and x_i is the position of individual objects.

Conservation of Momentum Principle

The total momentum in a closed system remains constant in the absence of external forces.

Collision Analysis

An examination of the interactions between two or more objects, involving changes in momentum and velocity.

Elastic Collision Characteristics

Both momentum and kinetic energy are conserved, resulting in no loss of energy.

Inelastic Collision Characteristics

Only momentum is conserved, with kinetic energy converted into other forms of energy.

Problem-Solving Strategy for Collisions

Identify the closed system, determine the type of collision, and apply conservation principles.

Rocket Propulsion Example

The forward momentum of a rocket equals the backward momentum of exhaust gases, illustrating conservation of momentum.

Misconception about Momentum vs Kinetic Energy

Momentum is a vector quantity while kinetic energy is a scalar; they are distinct concepts despite both involving mass and velocity.

Common Momentum Misconception

Heavier objects do not always have more momentum; momentum also depends on velocity.

Application of Impulse-Momentum Theorem in Sports

Sports equipment design utilizes this theorem to optimize momentum transfer from equipment to the ball.