Force Diagrams

Free-body diagrams and isolation techniques for systematic dynamic force analysis.

General idea of the topic

A force diagram is the graphical translation of a dynamics problem: on an isolated body only the real forces acting on it are drawn, each with its direction, sense and the agent that produces it.

This topic teaches three chained steps: identifying which forces are present, drawing the free body without duplicating effects or including forces acting on other bodies, and resolving each vector into components to write the second-law equations.

What the student is expected to understand

By the end, the student should be able to decide which forces appear in a situation from contacts and long-range interactions, draw a correct free body and choose axes that simplify the resolution.

The student should also be able to check the diagram against the expected direction of the acceleration before calculating anything.

Recommended learning route

1. Identifying Forces: goes through contacts and long-range interactions to list the real forces of each situation and discard those that are not.
2. Free-Body Diagrams: builds the free-body diagram: isolated system, forces on it and axes chosen with care.
3. Vector Resolution Into Components: resolves oblique forces into components and prepares the equations along each axis.

Essential physical criterion

The essential criterion is that the diagram contains only forces that other bodies exert on the body under study. A force with no identifiable agent, or one that the body exerts on another, does not belong on its diagram; neither does the acceleration, which is not a force.

Connection with real problems

• inclined planes and pulleys.
• bodies resting, hanging or being pushed.
• structures and supports.
• any problem that ends in a Newton equation.

Final goal of the topic

The final goal is to build the free-body diagram of any situation without errors and resolve it into the equations that solve the motion.