Free-body diagrams begin with a boundary

Imagine two carts joined by a light connector and pulled along a smooth horizontal track. A boundary around the rear cart excludes the connector and front cart. The connector's pull must therefore appear as an external force on that cart. A boundary around both carts makes the connector interaction internal. Its two opposing forces cancel in the sum for the combined system, although each cart still feels a force individually. An internal force has not ceased to exist; it has ceased to affect the total momentum of this chosen collection.

Represent a compact object by a point when its translational motion is the target. Draw weight from Earth, the track's normal reaction, and every other identified contact or field interaction. An arrow labeled motion or acceleration is not an additional force. Newton's law relates acceleration to the vector sum of interaction forces. If rotation matters, a point diagram loses essential information about application points and lever arms; retain the body's geometry and add a torque balance. Choose the model to answer a stated question rather than always drawing the simplest possible picture.

Choose axes that make the constraints clear. On a straight incline, one axis along the surface and one perpendicular to it usually reduce the algebra. Weight remains one downward force even when you replace it by two components in the equations. Do not draw both the original weight and its components as three independent interactions. A normal force acts perpendicular to the local contact surface, so its magnitude is not automatically equal to weight. Resolve the complete equation perpendicular to the surface before deciding what the normal reaction must be.

Third-law partners act on different bodies. Earth's gravitational pull on a cart and the cart's gravitational pull on Earth therefore cannot cancel in the cart's own equation. Weight and a supporting normal force can balance on the same body, but they are not a third-law pair: they arise from different interactions. This distinction becomes practical when a lift accelerates. The passenger's acceleration requires unequal upward and downward forces even though every interaction still has an equal and opposite partner acting somewhere else. Balanced forces describe zero acceleration, not an absence of interactions.

After solving, check whether the assumed contacts remain physically possible. An ordinary floor can push upward but cannot pull a detached object downward. If the algebra demands a negative normal reaction, the maintained-contact assumption has failed and a free-flight model is needed. A slack string similarly cannot transmit compression. These conditions are part of the model, not optional corrections after the answer. An acceleration measured with video can distinguish a missing interaction from an incorrect mass estimate, especially when you repeat the experiment after changing the applied force.

A useful audit has three parts: inspect units, compare a limiting case, and identify an independent measurement. Doubling a horizontal pull on the same frictionless cart should double its horizontal acceleration. Joining another equal cart should halve the acceleration for the same total pull. If neither prediction holds, inspect track friction, connector mass, and the definition of the measured system. Real experiments can challenge several assumptions simultaneously, so change one control at a time. The diagram earns its value by explaining how a particular observation could show that its boundary or interaction list is inadequate.