2.1 Force Types, Direction, and Free-Body Diagrams

Force is a vector, so each force must include both magnitude and direction. In chapter problems you repeatedly meet weight, tension, normal reaction, drag, buoyant force, and friction. The practical skill is not naming them in isolation, but determining which of them actually apply in a given physical setup.

Weight points toward the local gravitational center and has magnitude W = mg. Its direction is fixed by gravity, not by the slope of a surface. Normal force is perpendicular to the contact surface, so on an incline it tilts with the plane. Tension acts along a taut string or rope and pulls away from the object at the attachment point.

Friction opposes relative motion or impending motion at a contact. Static friction self-adjusts up to a maximum value, while dynamic friction is often modeled as a near-constant value once sliding begins. Drag opposes motion through a fluid and usually grows with speed. Buoyant force arises from fluid pressure differences and points upward, with size linked to displaced fluid volume.

Because several of these forces are response forces, they should not be assigned blindly from memory. For example, static friction is not always μsR; that expression gives a maximum possible value. In equilibrium with a small pull, static friction can be much smaller and exactly balances what is needed to keep acceleration at zero.

Two additional force models from this chapter are worth keeping active in your toolkit. For slow flow around small spherical objects, Stokes drag is modeled as F_D = 6πηrv, so drag scales linearly with speed. Buoyant force follows F_B = ρgV_imm, so the upward force is set by displaced fluid, not the object's own mass. These models become powerful when combined with equilibrium: terminal speed occurs when weight is balanced by drag plus buoyancy.

A free-body diagram isolates one object and replaces contacts with force arrows. Do not draw motion arrows in place of forces. Start by sketching the object as a point or box, then add each force from identified interactions: gravity interaction, contact interactions, and any long-range field interactions.

For high-quality diagrams, arrow lengths should roughly reflect relative magnitudes whenever values are known. That visual proportionality helps catch algebra mistakes later. If your final equations predict a direction opposite your original arrow, keep the same arrow and let the solved sign communicate the correction.