Momentum and External Force
Description and Assumptions
This model is [generally applicable] (assuming knowledge of the external forces and system constituents).
Problem Cues
This model is especially useful when describing the momentum of systems where external forces are absent (system momentum will be constant) or estimating the force in a process that occurs in a very short time interval such as collisions (impulse will be easier to determine than force).
Learning Objectives
Students will be assumed to understand this model who can:
- Define the momentum of a point particle.
- Define impulse in terms of momentum or in terms of force.
- Give an expression for the time-average force on a system in terms of its momentum.
- Calculate the net external force on a system containing several objects.
- Describe the conditions required for the momentum of a system to be conserved.
- Describe the system that must be considered and the assumptions that lead to approximate conservation of momentum in a collision.
Model
Compatible Systems
The system must be effectively composed of point particles, though rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid body when this model is used.
Relevant Interactions
Only external forces need be considered, since internal forces do not change the system's momentum.
Relevant Definitions
\begin
[ \vec
= m\vec
]\end
Laws of Change
Differential Form
\begin
[ \sum_
\frac{d\vec{p}}
= \sum_
\vec
]\end
Integral Form
\begin
[ \sum_
\vec
_
= \sum_
\vec
_
+ \sum_
\vec
= \sum_
\vec
_
+ \int \sum_
\vec
\:dt ]
\end
Diagrammatic Representations
Relevant Examples
ExamplesInvolvingConstantMomentum"> Examples Involving Constant Momentum
ExamplesInvolvingImpulse"> Examples Involving Impulse
ExamplesInvolving1-DCollisions"> Examples Involving 1-D Collisions
ExamplesInvolving2-DCollisions"> Examples Involving 2-D Collisions
ExamplesInvolvingElasticCollisions"> Examples Involving Elastic Collisions
ExamplesInvolvingTotallyInelasticCollisions"> Examples Involving Totally Inelastic Collisions
ExamplesInvolvingContinuousMomentumFlux"> Examples Involving Continuous Momentum Flux
AllExamplesUsingthisModel"> All Examples Using this Model
Photos courtesy:
Wikimedia Commons
by user No-w-ay in collaboration with H. Caps
Wikimedia Commons by user Uwe Langer
NASA Johnson Space Center (NASA-JSC)