Introduction to the ModelDescription and AssumptionsThis model is generally applicable (assuming knowledge of the external forces and system constituents). The 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 ObjectivesStudents will be assumed to understand this model who can:
Relevant DefinitionsUnknown macro: {latex}
\begin Unknown macro: {large} [ \vec Unknown macro: {p}
= m\vec Unknown macro: {v}
]\end S.I.M. Structure of the ModelCompatible SystemsThe 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 InteractionsOnly external forces need be considered, since internal forces do not change the system's momentum. Laws of ChangeMathematical RepresentationDifferential FormUnknown macro: {latex} \begin Unknown macro: {large} [ \frac{d\vec{p}} Unknown macro: {dt}
= \sum \vec Unknown macro: {F}
^ Unknown macro: {rm ext}
]\end Integral FormUnknown macro: {latex} \begin Unknown macro: {large} [ \vec Unknown macro: {p}
_ Unknown macro: {f}
= \vec _ Unknown macro: {i}
+ \sum \vec Unknown macro: {J}
^ Unknown macro: {rm ext}
_ Unknown macro: {fi}
= \vec Unknown macro: {p}
_ + \int_{t_{i}}^{t_{f}} \sum \vec Unknown macro: {F}
^ Unknown macro: {rm ext}
\:dt ] Diagrammatic RepresentationsRelevant ExamplesExamplesInvolvingConstantMomentum"> Examples Involving Constant MomentumExamplesInvolvingImpulse"> Examples Involving ImpulseExamplesInvolving1-DCollisions"> Examples Involving 1-D CollisionsExamplesInvolving2-DCollisions"> Examples Involving 2-D CollisionsExamplesInvolvingElasticCollisions"> Examples Involving Elastic CollisionsExamplesInvolvingTotallyInelasticCollisions"> Examples Involving Totally Inelastic CollisionsExamplesInvolvingContinuousMomentumFlux"> Examples Involving Continuous Momentum FluxAllExamplesUsingthisModel"> All Examples Using this ModelUnknown macro: {search-box}
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