Point Particle Dynamics
Description and Assumptions
This model is applicable to a point particle (or to a system of objects treated as a point particle located at the system's center of mass) when the external forces are known or needed. It is a subclass of the model Momentum and External Force defined by the constraint dm/dt = 0.
Problem Cues
This model is typically applied to find the acceleration in cases where the forces will remain constant, such as an object moving along a flat surface like a ramp or a wall. It is also useful in combination with other models, such as when finding the normal force exerted on a passenger in a roller coaster at the top of a loop-the-loop (in which case, it would be combined with [Mechanical Energy and Non-Conservative Work]).
Learning Objectives
Students will be assumed to understand this model who can:
- State and explain the significance of Newton's Laws of Motion.
- Define normal force and describe its relationship to weight.
- Discriminate between static and kinetic friction.
- Explain the role of the coefficient of friction in both the kinetic and static cases.
- Construct a free body diagram for an object subject to contact forces, gravity, elastic forces, and/or tension forces.
- Construct and solve a system of equations describing the dynamics of more than one object that interact with one another.
Model
Compatible Systems
A single point particle, or a system of constant mass that is treated as a point particle located at the system's center of mass.
Relevant Interactions
External forces must be understood sufficiently to draw a free body diagram for the system. Internal forces will always cancel from the equations of Newton's 2nd Law for the system and can be neglected.
Law of Change
\begin
[ \sum \vec
^
= m\vec
] \end
As with all vector equations, this Law of Interaction should really be understood as three simultaneous equations:
\begin
[ \sum F^
_
= ma_
]
[ \sum F^
_
= ma_
]
[\sum F^
_
= ma_
]\end
Diagrammatical Representations
Relevant Examples
ExamplesInvolvingVectorComponents"> Examples Involving Vector Components
ExamplesInvolvingNormalForce"> Examples Involving Normal Force
ExamplesInvolvingApparentWeight"> Examples Involving Apparent Weight
ExamplesInvolvingTension"> Examples Involving Tension
ExamplesInvolvingInclinedPlanes"> Examples Involving Inclined Planes
ExamplesInvolvingStaticFriction"> Examples Involving Static Friction
ExamplesInvolvingKineticFriction"> Examples Involving Kinetic Friction
ExamplesInvolvingCentripetalAcceleration"> Examples Involving Centripetal Acceleration
AllExamplesUsingthisModel"> All Examples Using this Model
