Force and free-body diagrams
A practical starting point for turning a physical component into a solvable force model.
ENGINEERING PRINCIPLE
A free-body diagram isolates the body, identifies external interactions and creates a consistent sign convention before equations are written.
ΣF = maVariables and units
- ΣF = resultant external force (N)
- m = mass (kg)
- a = acceleration (m/s²)
Worked example
A 1,500 kg trolley accelerating at 2.5 m/s² requires a 3,750 N net force before rolling resistance or gradients are added.
Calculation method
- Isolate one body at a time.
- Draw each applied force, support reaction and weight once.
- Choose axes, resolve components and apply the force balance.
Practical applications
- Fixtures and mechanisms
- Machine-frame reactions
- Vehicle and material-handling motion
Review boundary and reference
- A correct equation cannot rescue an incomplete free-body diagram.
- Include inertia only when the selected reference frame requires it.
Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.
Source: Classical Newtonian mechanics; SI unit relationships follow NIST Special Publication 811.