AcademyForces and Newton's Laws
Academy
Action-Reaction Pairs
Level 1 - Physics topic page in Forces and Newton's Laws.
Principle
Each interaction creates equal and opposite forces on two different objects.
Notation
\(\vec{F}_{AB}\)
force on A by B
\(\mathrm{N}\)
\(\vec{F}_{BA}\)
force on B by A
\(\mathrm{N}\)
\(m_A\)
mass of object A
\(\mathrm{kg}\)
\(m_B\)
mass of object B
\(\mathrm{kg}\)
\(\vec{a}_A\)
acceleration of A
\(\mathrm{m\,s^{-2}}\)
\(\vec{a}_B\)
acceleration of B
\(\mathrm{m\,s^{-2}}\)
Method
The third law is about one interaction, but Newton's second law must still be applied to each object separately.
Name the pair
\[\text{force on A by B}\leftrightarrow\text{force on B by A}\]
Apply direction
\[\vec{F}_{AB}=-\vec{F}_{BA}\]
Draw separately
\[\vec{F}_{AB}\in\text{diagram for A},\qquad \vec{F}_{BA}\in\text{diagram for B}\]
Find accelerations
\[\vec{a}_A=\frac{\sum\vec{F}_A}{m_A},\qquad \vec{a}_B=\frac{\sum\vec{F}_B}{m_B}\]
The graph separates the paired forces by object so they are not mistaken for canceling forces on one diagram.
Because the arrows sit on different objects, each object gets its own resultant force and acceleration.
Rules
These are the compact interaction-pair and object-dynamics statements.
Third law
\[\vec{F}_{AB}=-\vec{F}_{BA}\]
Equal magnitudes
\[|\vec{F}_{AB}|=|\vec{F}_{BA}|\]
Object A
\[\sum\vec{F}_A=m_A\vec{a}_A\]
Object B
\[\sum\vec{F}_B=m_B\vec{a}_B\]
Examples
Question
A hand pushes a box right with
\[25\,\mathrm{N}\]
State the paired force.Answer
The box pushes the hand left with
\[25\,\mathrm{N}\]
The forces are equal in size and act on different objects.Checks
- The two forces act on different objects.
- The forces are the same interaction type.
- Equal force magnitudes do not imply equal accelerations.
- Third-law pairs never cancel in one object's force sum.