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
Mathematical Representation
\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
