Forces and Free-Body Diagrams

Objective: Distinguish forces from motion and identify source and target.

A force is an interaction that can change an object’s velocity or shape. It is a vector measured in newtons (N); specifying a force requires magnitude, direction, and the object on which it acts. Contact forces include pushes, tension, and normal forces, while gravitational and electromagnetic forces can act without direct contact in familiar models. A moving object does not require a forward net force to continue at constant velocity; force predicts acceleration, not velocity itself. Describing “the cart’s force” without naming an agent is ambiguous. For each force, ask what object exerts it, what object receives it, and in what direction.

Objective: Draw and interpret forces acting on one chosen object.

A free-body diagram isolates one target object and shows external forces acting on it as labeled arrows. Arrow directions represent force directions; lengths can indicate relative magnitudes when a scale is specified. Do not draw forces that the object exerts on other objects on the same diagram. A book resting on a table generally has a downward gravitational force and an upward normal force; if stationary in an inertial frame, those vectors sum to zero. The normal force is a contact force perpendicular to the surface and is not automatically equal to weight in every situation. A velocity arrow is not a force arrow.

Objective: Find one-dimensional vector sums and connect zero net force to acceleration.

Net force is the vector sum of all external forces on a chosen object, ΣF. In one dimension, choose positive direction and add signed force components. A 12 N force right and a 7 N force left produce a net +5 N right. Equal and opposite forces on the same object yield zero net force and zero acceleration in an inertial frame, whether the object is at rest or moving steadily. Forces must have the same target to cancel in a free-body sum. In two dimensions, components are summed by direction. A large force is not necessarily the net force if other interactions oppose it.