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.

1. Calculate initial momentum of each object. 2. Calculate total initial momentum. 3. Apply conservation of momentum. 4. Solve for the unknown.

Momentum ($\vec{p}$) is a measure of how much "oomph" an object has in motion. It's the product of an object's mass ($m$) and its velocity ($\vec{v}$).

Change in momentum ($\Delta \vec{p}$), also known as impulse ($\vec{J}$), is the result of a force acting over a period of time. It's the difference between the final and initial momentum.

Impulse is equal to the change in momentum. It's also equal to the force ($\vec{F}$) multiplied by the time interval ($\Delta t$) over which the force acts: $\vec{J} = \Delta \vec{p} = \vec{F}\Delta t$

In a closed system (no external forces), the total momentum remains constant. This means the total momentum before a collision equals the total momentum after the collision: $\vec{p}_{initial} = \vec{p}_{final}$

A collision in which kinetic energy is conserved. Objects bounce off each other without losing energy (idealized).

A collision in which kinetic energy is not conserved. Some energy is lost as heat, sound, or deformation. Objects may stick together (perfectly inelastic).