1. Calculate the initial momentum of each object. 2. Calculate the total initial momentum of the system. 3. Apply the conservation of momentum: The total initial momentum equals the total final momentum. 4. Solve for the unknown.

For the same impulse, increasing the time interval will decrease the force required, and vice versa ($\vec{J} = \vec{F}\Delta t$).

The net force (vector sum of all forces) determines the change in momentum of the system.

Objects stick together after the collision, and kinetic energy is not conserved.

In a closed system, the total momentum remains constant.

Measure of how much "oomph" an object has in motion; product of mass ($m$) and velocity ($\vec{v}$): $\vec{p} = m\vec{v}$

Change in momentum ($\Delta \vec{p}$), result of a force acting over a period of time: $\vec{J} = \Delta \vec{p} = \vec{F}\Delta t$

In a closed system, the total momentum remains constant: $\vec{p}_{initial} = \vec{p}_{final}$

A collision where kinetic energy is conserved; objects bounce off each other without losing energy.

A collision where kinetic energy is not conserved; some energy is lost as heat, sound, or deformation.