free body diagram
Summary
A free body diagram is a sketch of one object, drawn as a point or box, showing only the forces acting on it as labeled arrows. Its most testable use is to sum the force components along each axis to get net force (ΣF = ma), which is zero in equilibrium.
Detail
Meaning: A free body diagram (FBD) isolates one object and shows every external force on it as an arrow from the object, with length proportional to magnitude and direction matching the force. Typical forces are weight (mg, downward), normal force (perpendicular to a surface), tension (along a rope, away from the object), friction (parallel to a surface, opposing motion or its tendency) and applied forces. Forces the object exerts on other things are not drawn.
Equation: ΣF = ma, where ΣF is the vector sum of forces on the object (N), m is mass (kg) and a is acceleration (m/s²). Apply it separately along each chosen axis. In static or constant-velocity equilibrium, ΣF = 0.
On the MCAT: Passages describe a block on an incline, a hanging mass, a pulley or a person in an elevator, and ask for a tension, normal force, friction or acceleration. Tilt the axes so one lies along the incline: weight splits into mg sinθ along the slope and mg cosθ perpendicular to it. Questions may also ask which arrows belong in the diagram.
Common confusion: Students add a "force of motion" or "centripetal force" arrow. Neither is a separate force. Motion needs no force arrow, and centripetal force is the net inward result of forces already drawn, such as tension or gravity. Also, Newton's third-law pairs act on different objects, so they never appear together in one FBD.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- College Physics (Serway, Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.