AcademyForces and Newton's Laws
Academy
Drawing Free-Body Diagrams
Level 1 - Physics topic page in Forces and Newton's Laws.
Principle
A free-body diagram records only external forces acting directly on the isolated body.
Notation
\(\vec{W}\)
weight
\(\mathrm{N}\)
\(\vec{N}\)
normal reaction
\(\mathrm{N}\)
\(\vec{T}\)
tension
\(\mathrm{N}\)
\(\vec{f}\)
friction
\(\mathrm{N}\)
\(\vec{F}_{\mathrm{app}}\)
applied force
\(\mathrm{N}\)
\(\theta\)
incline angle
rad or deg
Method
A free-body diagram is a force inventory before it is an equation.
Isolate body
\[\text{draw one boundary around the chosen object}\]
Add field force
\[\vec{W}=m\vec{g}\]
Add contacts
\[\vec{N}\perp\text{surface},\quad \vec{f}\parallel\text{surface},\quad \vec{T}\parallel\text{string}\]
Resolve incline weight
\[W_{\parallel}=mg\sin\theta,\qquad W_{\perp}=mg\cos\theta\]
The free-body diagram below shows only forces acting on the block, not forces the block exerts.
After the inventory is complete, choose axes and write component equations from the listed forces.
Rules
These are the compact direction and component rules used while drawing.
Weight
\[\vec{W}=m\vec{g}\]
Normal direction
\[\vec{N}\perp\text{surface}\]
Tension direction
\[\vec{T}\parallel\text{string}\]
Incline components
\[W_{\parallel}=mg\sin\theta,\qquad W_{\perp}=mg\cos\theta\]
Examples
Question
A block rests on a horizontal table and is pulled by a horizontal string. Name the forces on the block.
Answer
The block has \(W\) downward, \(N\) upward, and \(T\) along the string. The table's normal force is not the block's weight.
Checks
- Do not draw forces exerted by the chosen body.
- Do not draw acceleration as a force.
- Normal force is perpendicular to the contact surface.
- For inclines, parallel and perpendicular axes usually make the equations shortest.