Momentum and Impulse

Learning Objectives

Define momentum and calculate it using p = mv.

Define impulse and relate it to the change in momentum (Impulse-Momentum Theorem).

State and apply the Law of Conservation of Momentum.

Distinguish between elastic and inelastic collisions.

The 'Quantity of Motion'

Momentum (p) is a vector quantity that can be thought of as 'mass in motion'. It is a measure of how hard it is to stop a moving object.

Formula: p = mv

m is the mass of the object.

v is the velocity of the object.

The SI unit for momentum is kg·m/s.

Impulse and the Impulse-Momentum Theorem

Impulse (J) is a change in momentum. It is caused by a net force acting on an object over a period of time.

Formula: J = FΔt

F is the average net force.

Δt is the time interval over which the force acts.

Impulse-Momentum Theorem: The impulse applied to an object is equal to the change in the object's momentum.

FΔt = Δp = mv_final - mv_initial

This theorem is very useful. It explains why we bend our knees when we land from a jump or why cars have crumple zones. In both cases, we are increasing the time (Δt) over which the momentum changes, which reduces the average force (F) experienced.

Conservation of Momentum

The Law of Conservation of Momentum is one of the most fundamental principles in physics.

The Law: In an isolated system (one with no external net forces), the total momentum of the system remains constant.

Application: This law is crucial for analyzing collisions and explosions. The total momentum of all objects before the interaction is equal to the total momentum of all objects after the interaction.

Σp_initial = Σp_final

Types of Collisions

Elastic Collision: A collision in which the total kinetic energy of the system is conserved. The objects bounce off each other perfectly.

Inelastic Collision: A collision in which the total kinetic energy is not conserved (some is converted into heat, sound, or deformation).

A perfectly inelastic collision is one in which the objects stick together after colliding.

Important Note: Momentum is conserved in all collisions, whether elastic or inelastic. Kinetic energy is only conserved in elastic collisions.

Key Terms

Momentum (p): A vector quantity defined as the product of an object's mass and velocity (p = mv).
Impulse (J): A change in momentum, equal to the product of the average force exerted on an object and the time interval over which the force is exerted (J = FΔt).
Impulse-Momentum Theorem: The principle that the impulse applied to an object is equal to the object's change in momentum (FΔt = Δp).
Law of Conservation of Momentum: The principle that the total momentum of an isolated system remains constant over time.
Elastic Collision: A collision in which both momentum and kinetic energy are conserved.
Inelastic Collision: A collision in which momentum is conserved, but kinetic energy is not.