Study Notes on Free-Body Diagrams

Free-Body Diagram Overview

• Title: Free-body Diagram Prepared by Engr. Jhoneil M. Viernes, LPT.

Introduction to Free-Body Diagrams

• To find the net force acting on a system, begin by constructing an idealized model.

• This model is depicted through a free-body diagram (FBD) that illustrates all the external forces acting on a body or system.

Definition of Free-Body Diagram

• A free-body diagram, also known as a force diagram, is a sketch that includes:

  • All force vectors acting on the object.

  • The initial points of these vectors start at the location of the object itself.

Construction of Free-Body Diagrams

• When constructing a free-body diagram, include only the forces that act on the body, not the forces exerted by the body on others.

Examples of Free-Body Diagrams

Example 1: Falling Brick

• Situation: A brick with a weight of 50 N falls toward the ground.

• Action: Draw a free-body diagram and find the net force.

• Assumption: Neglect air resistance.

  • The only force acting on the brick is its weight.

• Net Force Calculation:

  • $F_{net} = -w$,

  • where $w = 50 N$,

  • Thus, $F_{net} = -50 N$.

Example 2: Moving Chair

• Situation: A student applies a leftward force to a chair to move it across the floor at constant velocity.

• Considerations: Take into account frictional forces while neglecting air resistance.

• Free-Body Diagram Components:

  • F_{applied} (leftward force)

  • F_{friction} (rightward opposing force)

  • F_{normal} (upward force)

  • F_{gravity} (downward force)

Example 3: Sitting Gorilla

• Task: Create a free-body diagram for a gorilla sitting.

• Components Shown:

  • W (Weight of the gorilla) acting downward,

  • N (Normal force) acting upward.

Example 4: Wooden Swing with Parrot

• Task: Draw a free-body diagram of a wooden swing with a parrot.

• Components Shown:

  • W (Weight of the swing and the parrot),

  • T{1}, T{2} (Tension forces from the ropes supporting it).

Example 5: Pin at Point A

• Task: Draw a free-body diagram of a pin at point A on a bridge.

• Forces: Additional force acting into the paper due to the beam connection,

  • T{AE}, T{AC}, T{AB}, T{AD} (tension forces acting on the pin).

Example 6: Bungee Jumper

• Situation: Draw a free-body diagram of the bucket from which the bungee jumper leaps.

• Components:

  • W (Weight of the diver and the bucket),

  • T (Tensile force from the cable).

Example 7: Traffic Light Supported by Cables

• Task: Draw a free-body diagram of the ring at point C of a traffic light.

• Forces Shown: T{CA}, T{CD}, T_{CB} (Tension forces acting on the ring).

Example 8: Free-Body Diagram of Traffic Light

• Components:

  • W (Weight acting downward),

  • T_{CD} (Tension in the cables supporting the light).

Complex Free-Body Diagrams

• Big Idea: Interactions of objects produce forces, significantly impacting system behavior.

• Free-body diagrams are crucial in determining unknown forces, moments, and equations of motion for both statics and dynamics analysis.

Applications in Structural Analysis

• Free-body diagrams of structural components help to determine shear forces and bending moments, integral in engineering and physics.

Conceptual Framework: Free-Body Diagram Story

• Introduction of characters (Vinnie the Vector, Billy the Box, and Terry the Table) to explain and clarify concepts of weight and forces.

  • Concept of Weight: Weight is defined as the force due to gravity acting on mass.

  • Example Calculation:

  • Mass of Billy = 10 kg,

  • Accordingly, weight (W) = mass (m) × gravitational acceleration (g),

  • $W = mg = 10 ext{ kg} × 9.8 ext{ N/kg} = 98 ext{ N}$ .

Characteristics of Vectors in Forces

• Vectors: Forces possess both magnitude and direction and are represented graphically in diagrams.

  • Example:

  • Weight vector = 98 N downward,

  • Normal force vector = 98 N upward (balancing weight).

• Balance of Forces:

  • When the forces are equal and opposite, the net force equals zero, indicating equilibrium.

Examples of Derived Forces and Equilibrium

• If an external force is applied, such as a 12 N force, the situation must remain balanced with opposing forces (e.g., friction) to maintain constant speed.

• Consider multiple scenarios involving various forces that lead to accelerating or decelerating objects, including the use of friction as a counterbalance to applied forces.

• For instance:

  • If the effective net force indicates acceleration, then the friction must be appropriately accounted for as a discrepancy between applied and net forces.

Free-Body Diagram Overview

Introduction and Definition

A free-body diagram (FBD), or force diagram, is an idealized sketch used to determine the net force acting on a system. It graphically illustrates all external force vectors acting on a body or system, with their initial points located at the object itself.

Construction Principles

When constructing an FBD, only include forces that act on the body, not forces exerted by the body on other objects.

Illustrative Examples

Examples such as a falling brick, a moving chair, a sitting gorilla, or a traffic light demonstrate how to apply FBD principles to various scenarios. These diagrams help visualize forces like weight ($w$), normal force ($N$), applied force ($w<em>{applied}$), friction ($F</em>{friction}$), and tension ($T$), allowing for calculation of net forces (e.g., $F_{net} = -w$ for a falling object neglecting air resistance).

Advanced Applications

FBDs are fundamental for determining unknown forces, moments, and equations of motion in both statics and dynamics. They are vital in structural analysis for identifying shear forces and bending moments within engineering and physics contexts.

Fundamental Concepts

Forces are vector quantities, possessing both magnitude and direction, and are represented graphically in FBDs. Weight ($W$) is the force due to gravity acting on mass ($W = mg$), where $g$ is gravitational acceleration (e.g., $9.8 N/kg$). Equilibrium is achieved when the net force on an object is zero, meaning all acting forces are balanced (equal and opposite). When forces are unbalanced, the object accelerates or decelerates, with friction often playing a counteracting role.

Conclusion

Free-body diagrams are indispensable tools in physics and engineering, simplifying complex force interactions into clear visual representations. By isolating a body and illustrating all external forces acting upon it, FBDs enable systematic analysis for calculating net forces, understanding equilibrium, and predicting motion. Their utility spans from basic mechanics to advanced structural analysis, making them a foundational concept for comprehending how objects interact with their environment.