Free-body (Force) Diagram
The Core Components of a Free-body Diagram
Every free-body diagram is built from a few essential components. Understanding what each part represents is the first step to creating an accurate and useful diagram.
| Component | Description | Example |
|---|---|---|
| The Object | The system or object you are analyzing. It is isolated from its environment and drawn as a simple shape, like a dot or a box. | A book, a car, a person. |
| Force Vectors (Arrows) | Arrows that represent forces. The direction of the arrow shows the direction the force is acting. The length of the arrow represents the magnitude (size) of the force. | An arrow pointing down for gravity. |
| Coordinate System | A set of perpendicular axes (x and y) used to define directions. This makes it easier to break down forces into components for calculation. | The x-axis is horizontal, the y-axis is vertical. |
| Labels | Each force arrow is labeled with a symbol and often a subscript to identify its type and source. | $F_g$ for gravitational force, $F_N$ for normal force. |
Identifying Common Forces
Forces are interactions between objects. In physics, we give names to the most common types of forces you will encounter. Recognizing them is key to drawing a complete FBD.
| Force Type | Symbol | Direction | Description |
|---|---|---|---|
| Gravity (Weight) | $F_g$ or $W$ | Straight down, towards the center of the Earth. | The pull of gravity on an object's mass. Calculated as $F_g = m \times g$, where $g = 9.8 m/s²$ on Earth. |
| Normal Force | $F_N$ | Perpendicular (at a 90-degree angle) and away from the surface of contact. | The support force exerted by a surface on an object in contact with it. It prevents the object from "falling through" the surface. |
| Friction | $F_f$ | Parallel to the surface, opposing the motion (or attempted motion) of the object. | A force that resists the relative motion of two surfaces in contact. |
| Tension | $F_T$ or $T$ | Away from the object, along the rope, string, or cable. | The pulling force exerted by a stretched string, rope, or cable on an object. |
| Applied Force | $F_A$ or $F_{app}$ | The direction in which the force is applied (e.g., a push or a pull). | A general term for a force that is directly applied to an object by a person or another object. |
| Air Resistance (Drag) | $F_{air}$ | Opposite to the direction of motion relative to the air. | A type of frictional force that opposes the motion of an object through air. |
A Step-by-Step Guide to Drawing FBDs
Let's break down the process of creating a free-body diagram into simple, repeatable steps. We'll use the example of a book resting on a table.
Step 2: Identify All Forces. Think about every single thing that is touching the object or exerting a force on it from a distance. For the book on the table:
- Gravity: The Earth is pulling the book down.
- Normal Force: The table is pushing the book up.
Is the book moving? No. So there is no friction or applied force in this simple case.
Applying Free-body Diagrams to Real-World Scenarios
Free-body diagrams become incredibly useful when situations get more complex. Let's analyze a few common scenarios to see FBDs in action.
Scenario 1: A Pushed Box on a Rough Floor
Imagine you are pushing a heavy box to the right across a rough concrete floor. The box is moving at a constant velocity. What does the FBD look like?
- Forces:
- $F_g$: Downward (gravity).
- $F_N$: Upward (from the floor).
- $F_{app}$: To the right (your push).
- $F_f$: To the left (friction opposing the motion).
Since the box is moving at a constant velocity, its acceleration is zero. This means the net force is zero. Therefore, the force of your push ($F_{app}$) to the right must be exactly equal in magnitude to the friction force ($F_f$) to the left. Similarly, the normal force ($F_N$) upwards equals the gravitational force ($F_g$) downwards.
Scenario 2: A Skydiver Falling Through the Air
This scenario has two distinct phases, and the FBD changes between them.
Phase A: Immediately After Jumping
The skydiver has just jumped and is accelerating downwards. The primary forces are:
- $F_g$: Downward (large arrow).
- $F_{air}$: Upward (small arrow, as speed is still low).
The downward force of gravity is greater than the upward force of air resistance. The net force is downward, so the skydiver accelerates downward. The arrow for $F_g$ is longer than the arrow for $F_{air}$.
Phase B: After Falling for a While (Terminal Velocity)
As the skydiver falls faster, the air resistance increases. Eventually, it becomes large enough to balance the force of gravity.
- $F_g$: Downward.
- $F_{air}$: Upward (now an arrow of equal length to $F_g$).
The net force is now zero. The skydiver stops accelerating and continues to fall at a constant speed, known as terminal velocity. The FBD now looks like the book on the table, but with different forces!
Common Mistakes and Important Questions
Q: Should I include forces that the object exerts on other things?
A: No, this is the most common mistake. A free-body diagram only shows forces acting on the object you have isolated. For example, if you are analyzing a book on a table, you include the normal force from the table on the book ($F_N$), but you do not include the force of the book pushing down on the table. That force acts on the table, not the book.
Q: What if the object is accelerating? How does that affect the FBD?
A: The FBD itself doesn't change based on acceleration; it still shows all the forces. However, the result of those forces is acceleration. According to Newton's Second Law ($\Sigma F = m \times a$), if an object is accelerating, the net force ($\Sigma F$) is not zero. This means the arrows in your FBD will not cancel each other out. There will be a net force vector pointing in the direction of the acceleration. For example, a car accelerating to the right has a forward driving force that is larger than the backward friction and air resistance forces.
Q: How do I handle forces at an angle?
A: When a force is applied at an angle, you must "resolve" it into its x and y components. For instance, if you are pulling a sled with a rope at an angle $\theta$ above the horizontal, the tension force ($F_T$) has two parts: a horizontal component ($F_{T_x} = F_T \cos \theta$) that moves the sled forward, and a vertical component ($F_{T_y} = F_T \sin \theta$) that lifts the sled slightly, reducing the normal force. You would draw these component vectors on your FBD, often using a dashed-line arrow for the components and a solid-line arrow for the original force.
The free-body diagram is a fundamental and indispensable tool in physics. It transforms a complex physical situation into a clear, visual representation of the forces at play. By mastering the steps of isolating an object, identifying all forces, and drawing them accurately, you build a strong foundation for applying Newton's Laws and solving problems related to motion and equilibrium. Whether you are just starting in science or preparing for advanced high school physics, proficiency with FBDs will deepen your understanding of how and why things move.
Footnote
1 FBD: Free-body Diagram. A diagram used to visualize the forces acting on a single object.
2 Newton's Laws of Motion: Three fundamental laws formulated by Sir Isaac Newton that describe the relationship between a body and the forces acting upon it, and its motion in response to those forces.
3 Net Force ($\Sigma F$): The vector sum of all the individual forces acting on an object. It determines the object's acceleration.
4 Terminal Velocity: The constant maximum velocity reached by a falling object when the upward force of air resistance equals the downward force of gravity.