Free-Body Diagrams: Key Concepts and Examples

Free-Body Diagrams: Key Concepts and Examples

  • Free-body diagram (FBD) purpose

    • Before analyzing any situation, identify all forces present and the directions they point using a diagram called a free‑body diagram (FBD).
    • An FBD shows all the forces acting on an object, each represented as an arrow.
    • Each arrow conveys the magnitude and direction of that force; both pieces of information are important.
    • Arrows are usually drawn from the center of the object and point away from the object to indicate the direction of the force.
    • If enough information is available, arrows can be drawn with lengths proportional to their magnitudes.

  • How to draw a free‑body diagram (example: pushing a car up a hill)

    • Simplify the object to a box, circle, or dot.
    • Identify all forces exerted on the object.
    • Consider anything in contact with the object may exert one or more forces; include field forces (most likely gravity) for now.
    • Do not include forces exerted by the object on other objects.
    • Draw arrows for all forces originating from the object's center, pointing in the correct directions.
    • If information available, draw arrows with lengths proportional to magnitude.
    • Typical forces to consider:
    • Gravity: $F_g$ points down.
    • Normal force: $F_N$ is perpendicular to the contact surface, away from the surface.
    • Tension: $F_T$ goes in the direction of the rope/cable toward the rope.
    • Friction: $F_f$ resists motion relative to the surface (or impending motion); friction can exist even when the object is at rest.
    • Applied force: $F_A$ from an external agent (someone pushing, pulling, etc.).
    • Decision guide for forces to include
    • Is there mass and is the object on Earth? If yes, gravity $F_g$.
    • Is the object against a surface? If yes, normal force $F_N$.
    • Is there a rope/cable? If yes, tension $F_T$.
    • Is there resistance to motion? If yes, friction $F_f$.
    • Is someone applying a push or pull? If yes, applied force $F_A$.
    • Thought process in drawing: determine the direction of each force and draw arrows accordingly.
    • Key orientation rules
    • Gravitational force points downward.
    • Normal force is perpendicular to the surface and points away from the surface.
    • Tension acts along the rope toward the rope.
    • Friction opposes motion or potential motion relative to the surface.
    • Applied force points in the direction of the push/pull.

  • Practical considerations when constructing an FBD

    • Forces on the object, not the forces the object exerts on others (action‑reaction pairs belong on the other objects’ diagrams).
    • Field forces are included when present (gravity on Earth is a field force).
    • Arrows should originate from the object’s center and point outward for forces acting on the object.
    • Use the FBD as a tool to set up Newton’s laws:
    • Newton’s second law in vector form: ∑F⃗=ma⃗\sum \vec{F} = m \vec{a}

  • Free‑body diagram examples (Page 2 illustrations described in the transcript)

    • Falling object (no air resistance)
    • Forces: gravitational force $F_g$ downward. In the idealized case with no contact, this may be the sole force.
    • Book on a table
    • Forces: gravity $Fg$ downward; normal force $FN$ upward from the table.
    • Meter stick leaning against a wall
    • Forces: gravity $F_g$ downward; normal forces from wall and possibly from the floor (depending on the setup); horizontal normal from the wall perpendicular to the wall; (friction may appear if discussed in a more detailed treatment).
    • Puck sliding without friction
    • Forces: gravity $Fg$ downward; normal force $FN$ upward from surface; no friction force (frictionless surface).
    • Block on a frictionless incline
    • Forces: gravity $Fg$ downward; normal force $FN$ perpendicular to the incline; no friction.
    • Block at rest on incline
    • Forces: gravity $Fg$ downward; normal force $FN$ perpendicular to the incline; static friction $F_f$ up or down the incline as needed to prevent motion (direction opposes possible motion).
    • Pushing a block across a floor with friction
    • Forces: gravity $Fg$ downward; normal force $FN$ upward; applied force $FA$ in the push direction; friction $Ff$ opposing motion.
    • Ball hanging on a string
    • Forces: gravity $Fg$ downward; tension $FT$ along the string toward the pivot.

  • Thought process recap (how to approach any FBD task)

    • Step 1: Identify mass and Earth to decide if gravity is present: include $F_g$ if applicable.
    • Step 2: Check for contact with surfaces to identify normal forces: include $F_N$.
    • Step 3: Check for ropes/cables to identify tension: include $F_T$.
    • Step 4: Check for resisting forces to identify friction: include $F_f$.
    • Step 5: Check for any external agent applying force: include $F_A$.
    • Step 6: Draw arrows from the object's center, in the correct directions.
    • Step 7: Use the diagram to set up the equation of motion via ∑F⃗=ma⃗\sum \vec{F} = m \vec{a} or, for equilibrium, ∑F⃗=0\sum \vec{F} = 0.
    • Important reminder: The FBD is about forces on the object of interest; do not include the forces the object exerts on others.

  • Quick reference: force names and directions (summary)

    • $F_g$: gravitational force, downward (on Earth).
    • $F_N$: normal force, perpendicular to the contact surface, away from the surface.
    • $F_T$: tension, along the rope toward the rope.
    • $F_f$: friction, resists motion relative to the surface.
    • $F_A$: applied force, from an external agent.

  • Practical tips for study and exam prep

    • Use FBDs to translate a physical situation into a set of vectors that can be plugged into Newton’s laws.
    • Start by listing potential forces, then draw arrows in the correct directions.
    • Always verify that all present forces are included and that the directions are consistent with the physical setup.
    • Practice with the provided examples (falling object, book on table, leaning meter stick, frictionless puck, incline scenarios, pushing blocks, and a hanging ball) to reinforce recognition of which forces appear in each case.

  • Notation and formatting reminders for the exam

    • Represent forces with clear labels: $Fg$, $FN$, $FT$, $Ff$, $F_A$.
    • Use arrows to indicate direction and, if possible, proportional lengths to magnitudes.
    • Include equations in LaTeX format when presenting relationships (e.g., Fg=mgF_g = m g for gravity magnitude on Earth).