Forces and Newton's Laws
4. Free-Body Diagrams
Learning outcomes
- I can draw free-body diagrams for simple situations.
- I can identify all forces acting on an object.
- I can distinguish between real and nonexistent forces.
- I can represent forces using correct vector notation.
- I can use free-body diagrams to analyze motion.
Introduction
Before solving any force problem in physics, it is important to identify all the forces acting on an object. A simple and powerful way to do this is by drawing a free-body diagram (FBD).
A free-body diagram isolates a single object and shows every external force acting on it using arrows called vectors. By carefully analysing these diagrams, scientists and engineers can determine whether the forces are balanced or unbalanced and predict how the object will move. Free-body diagrams are one of the most important tools in mechanics and are used extensively in physics, engineering, and robotics.
What Is a Free-Body Diagram?
A free-body diagram (FBD) is a simplified drawing that shows all the external forces acting on one object.
In a free-body diagram:
- The object is represented by a simple shape, usually a box or a dot.
- Every external force is shown as an arrow.
- The arrows show both the magnitude and direction of each force.
- Only forces acting on the chosen object are included.
The purpose of a free-body diagram is to make force analysis easier.
Figure 1. A free-body diagram shows all the external forces acting on a single object.
Why Use Free-Body Diagrams?
Free-body diagrams help us:
- Identify all the forces acting on an object.
- Determine the net force.
- Decide whether forces are balanced or unbalanced.
- Predict motion using Newton's Laws.
- Solve force and acceleration problems.
Almost every mechanics problem begins with a free-body diagram.
Identifying the Object
The first step is to choose one object to analyse.
Examples include:
- A book on a table.
- A car on a road.
- A skydiver.
- A hanging sign.
- A sled being pulled.
Only forces acting on that object are included.
Forces the object exerts on other objects are not shown.
Common Forces in Free-Body Diagrams
Some of the most common forces are:
| Force | Symbol | Direction |
|---|---|---|
| Weight (gravitational force) | Fg or W | Downward |
| Normal force | FN | Perpendicular to the surface |
| Friction | Ff | Opposes motion or attempted motion |
| Tension | FT | Along a rope or cable |
| Applied force | FA | Direction of the push or pull |
| Air resistance (drag) | FD | Opposite the direction of motion |
| Spring force | Fs | Toward the spring's equilibrium position |
Recognising these forces is the key to drawing accurate diagrams.
Figure 2. The most common forces shown in free-body diagrams.
Representing Forces as Vectors
A force is a vector quantity, meaning it has:
- Magnitude.
- Direction.
In a free-body diagram:
- Arrows represent forces.
- Longer arrows represent larger forces.
- The arrow points in the direction of the force.
For example:
- ↑ Normal force
- ↓ Weight
- → Applied force
- ← Friction
The arrows should begin at the object.
Balanced Forces
When the forces are balanced:
- Net force = 0 N.
- No acceleration occurs.
The object:
- Remains at rest, or
- Continues moving with constant velocity.
Example:
A book resting on a table.
The upward normal force equals the downward weight.
Unbalanced Forces
When the forces are unbalanced:
- Net force ≠ 0 N.
- The object accelerates.
Acceleration may involve:
- Speeding up.
- Slowing down.
- Changing direction.
The direction of the acceleration is the same as the direction of the net force.
Figure 3. Balanced forces produce no acceleration, while unbalanced forces cause acceleration.
Real and Nonexistent Forces
A correct free-body diagram includes only real external forces.
Real Forces
Examples:
- Gravity.
- Normal force.
- Friction.
- Tension.
- Air resistance.
- Applied force.
Common Mistakes
Do not include:
- "Force of motion."
- "Force of velocity."
- "Force of acceleration."
- "Force in the direction the object wants to go."
These are not real forces.
Motion itself is not a force.
Only interactions between objects produce forces.
Drawing a Free-Body Diagram
Follow these steps:
Step 1
Choose the object.
Step 2
Draw the object as a box or dot.
Step 3
Identify every external force acting on it.
Step 4
Draw each force as an arrow.
Step 5
Label every force clearly.
Step 6
Compare the sizes and directions of the forces to determine the net force.
Example 1 – Book on a Table
Forces acting:
- Weight downward.
- Normal force upward.
The forces are equal.
Result:
- Balanced forces.
- No acceleration.
Example 2 – Box Being Pushed
Forces acting:
- Applied force to the right.
- Friction to the left.
- Weight downward.
- Normal force upward.
If the applied force is larger than friction:
- Net force acts to the right.
- The box accelerates to the right.
Figure 4. A free-body diagram helps determine the direction of the net force and the resulting motion.
Using Free-Body Diagrams to Analyse Motion
Once the diagram is complete:
- Combine forces in the horizontal direction.
- Combine forces in the vertical direction.
- Calculate the net force.
- Apply Newton's Second Law: Fnet = ma
The free-body diagram provides the information needed to predict the object's motion.
Why Free-Body Diagrams Are Important
Free-body diagrams are used by:
- Physicists.
- Engineers.
- Architects.
- Vehicle designers.
- Aerospace engineers.
- Robotics engineers.
They help analyse everything from bridges and elevators to satellites and spacecraft.
Figure 5. Free-body diagrams are essential tools in science and engineering.
Worked Example
Question
A 10 kg box is pulled across a floor.
The forces acting are:
- Applied force = 50 N to the right.
- Friction = 20 N to the left.
- Weight downward.
- Normal force upward.
Draw the free-body diagram and identify the net force.
Solution
The diagram contains four forces:
- → Applied force (50 N)
- ← Friction (20 N)
- ↑ Normal force
- ↓ Weight
Horizontal net force:
Vertical forces balance.
Therefore:
- Net force = 30 N to the right.
- The box accelerates to the right.
Real-World Connection
Mechanical engineers use free-body diagrams whenever they design vehicles, cranes, bridges, or amusement park rides. Before a bridge is built, engineers draw free-body diagrams of every major component to calculate the forces acting on it. These calculations help ensure that the structure can safely support traffic, wind, and other loads.
Did You Know?
Although free-body diagrams are simple sketches, they are used by engineers working on some of the world's most advanced technologies, including Formula One racing cars, aircraft, rockets, and even Mars rovers. Breaking a complex system into individual objects with carefully drawn force diagrams makes it much easier to understand how each part behaves.
Key Terms
Applied force – A force exerted directly by a person or another object.
Free-body diagram (FBD) – A simplified diagram showing all the external forces acting on a single object.
Friction – A force that opposes motion between surfaces in contact.
Net force – The overall force acting on an object after all forces have been combined.
Normal force – The support force exerted by a surface, acting perpendicular to it.
Tension – The pulling force transmitted through a rope, string, or cable.
Vector – A quantity with both magnitude and direction, represented by an arrow.
Weight – The gravitational force acting on an object.
Key Takeaways
- A free-body diagram shows all the external forces acting on a single object.
- Common forces include weight, normal force, friction, tension, applied force, and air resistance.
- Forces are represented as vectors, with arrows showing both magnitude and direction.
- Only real external forces should appear in a free-body diagram—motion itself is not a force.
- Free-body diagrams help determine the net force and predict an object's motion using Newton's Laws.
- Drawing an accurate free-body diagram is the first step in solving most mechanics problems.