AcademyForces and Newton's Laws
Academy
Forces as Interactions
Level 1 - Physics topic page in Forces and Newton's Laws.
Principle
A force is an external interaction represented by a vector on one chosen system.
Notation
\(\vec{F}\)
force vector
\(\mathrm{N}\)
\(\sum\vec{F}\)
resultant external force
\(\mathrm{N}\)
\(F_x\)
x-component of a force
\(\mathrm{N}\)
\(F_y\)
y-component of a force
\(\mathrm{N}\)
\(\hat{\imath},\hat{\jmath}\)
unit vectors along chosen axes
Method
Force models start by deciding what object or collection is inside the system boundary.
Choose system
\[\mathrm{system}=\text{body or collection being modeled}\]
Changing the boundary changes which forces are external.
Name outside agents
\[\vec{F}_{\text{on system by agent}}\]
Forces by the system belong on another object's diagram.
Resolve directions
\[\vec{F}=F_x\hat{\imath}+F_y\hat{\jmath}\]
Add components
\[\sum\vec{F}=(\sum F_x)\hat{\imath}+(\sum F_y)\hat{\jmath}\]
The graph shows tail-to-tail force vectors on the same object; the diagonal vector is their resultant.
In component form, the diagonal vector is built by adding horizontal parts together and vertical parts together.
Rules
These are the compact results from the component construction above.
External sum
\[\sum\vec{F}=\vec{F}_1+\vec{F}_2+\cdots\]
Component sum
\[\sum F_x=F_{1x}+F_{2x}+\cdots,\qquad \sum F_y=F_{1y}+F_{2y}+\cdots\]
Vector form
\[\sum\vec{F}=(\sum F_x)\hat{\imath}+(\sum F_y)\hat{\jmath}\]
Force unit
\[1\,\mathrm{N}=1\,\mathrm{kg\,m\,s^{-2}}\]
Examples
Question
Two horizontal forces act on a trolley:
\[18\,\mathrm{N}\]
right and \[7\,\mathrm{N}\]
left. Find the resultant.Answer
Take right as positive.
\[\sum F_x=18-7=11\,\mathrm{N}\]
The resultant force is \[11\,\mathrm{N}\]
right.Checks
- Every force needs an object and an outside agent.
- Perpendicular components combine by vector addition, not scalar cancellation.
- Opposite directions on the same axis require opposite signs.
- The resultant is a single vector, not a new interaction.