An external force causes a change in the system's total momentum (impulse).

The objects stick together and move with a common final velocity, with a loss of kinetic energy.

Internal forces within a system act in equal and opposite pairs, resulting in no net change in the system's total momentum.

1. Identify the system. 2. Check for external forces. 3. Apply: $\sum \vec{p}_{initial} = \sum \vec{p}_{final}$. 4. Solve for unknowns.

1. Calculate the total kinetic energy before the collision. 2. Calculate the total kinetic energy after the collision. 3. If kinetic energy is conserved (KE_initial = KE_final), the collision is elastic.

1. Determine the change in momentum ($\Delta\vec{p}$). 2. Alternatively, find the force applied ($\vec{F}$) and the time interval ($\Delta t$). 3. Calculate: $\vec{J} = \Delta\vec{p} = \vec{F}\Delta t$.

A measure of an object's motion; a vector quantity equal to mass times velocity: $\vec{p} = m\vec{v}$

The change in momentum of an object, equal to the force applied times the time interval: $\vec{J} = \Delta\vec{p} = \vec{F}\Delta t$

A system where no external forces act upon it, meaning the total momentum remains constant.

A collision where both momentum and kinetic energy are conserved.

A collision where momentum is conserved, but kinetic energy is not. Some kinetic energy is converted to other forms of energy.

A collision where objects stick together after impact, resulting in the maximum loss of kinetic energy.