Free-body diagrams in code
A free-body diagram lists every external force on one selected object. In code, that list becomes named vector values before it becomes one net force.
Think like a programmer
Model checklist
- Inputs
- Mass, gravity, contact forces, friction, and applied forces.
- State
- A list of force vectors for one selected body.
- Rule
- Add vectors component by component.
- Output
- Net force and acceleration.
- Check
- Balanced vertical forces sum to zero.
Net force becomes acceleration
Change an applied force and mass. Friction stays at 2 N to the left, so only net force changes velocity.
Applied force 8 N; net force 6.0 N; acceleration 3.00 m/s².
const forces = [appliedForce, frictionForce, gravityForce, normalForce];
const totalForce = netForce(forces);
Try this experiment
Prediction: Equal left and right forces produce no horizontal acceleration.
Adjust applied force until the status reports zero net force. Name the individual force that cancels the applied force rather than calling the result “no force.”Where this model breaks
Summary
Model one body at a time, name each external force, then test the sum. The free-body list is a debugging tool as much as a physics diagram.
Glossary
- Free-body diagram: force inventory for one object.
- Normal force: contact force perpendicular to a surface.
- Friction: contact force opposing relative sliding or attempted sliding.
Self-check
- Why keep individual forces before summing?
- What does balanced force mean?
- Which force direction may depend on motion?
Sources
- OpenStax, University Physics Volume 1, force chapter.
Model contract
Treat the lesson as a small function before treating it as a fact to memorize. Give every value a unit, keep only the state needed for the next step, and make the output easy to inspect.
\[\text{observable output} = f(\text{inputs},\,\text{state})\]- Inputs
- Quantities you set or measure, with units and useful bounds.
- State
- Values the program must retain to reproduce the next result.
- Rule
- The relationship or update that turns inputs and state into a result.
- Check
- A known limit, unit check, invariant, or measured result that can expose a bad model.
Implement the idea as a model
For Free-Body Diagrams in Code, write down the quantities you can control, the values your program must retain, and the result a reader could inspect. In Forces and Laws of Motion, the useful program is not the drawing: it is the smallest explicit model that makes a prediction you can test.
Guided experiment
Prediction: changing one declared input while holding the others fixed should change only the outputs that the model connects to that input. Choose one input, predict the direction of change, then check a limiting case such as zero, a symmetric arrangement, or a familiar low-speed or small-change approximation.
Where this model breaks
This lesson is a teaching model, not a complete simulator. Before using it outside the stated question, check which interactions, scales, uncertainties, boundary conditions, and measurement limits it leaves out.
Summary
Treat Free-Body Diagrams in Code as a contract: named inputs and units enter a rule, the rule produces an observable result, and a known limit or invariant checks whether the implementation deserves trust.
Glossary
- Input: a measured value or chosen parameter supplied to a model.
- State: the smallest set of values needed to continue or reproduce a model.
- Validation: comparing an output with a known result, limit, invariant, or measurement.
Self-check
- Which values are inputs, and which values must remain state?
- What observable result would tell you the model is behaving as expected?
- Which assumption would you test first before applying the model to a real system?
Model review: turn Free-Body Diagrams in Code into a test
Represent gravity, friction, and applied forces as named vectors, then sum them before updating motion.
- Name the inputs and units that the forces and laws of motion model needs.
- Separate the state you must keep from values you can calculate when needed.
- Write one rule that maps the current state and inputs to an observable result.
- Choose a limiting case, unit check, invariant, or known result before trusting an output.
- State one assumption you would change before using this simplified model for a real decision.