Free Body Diagrams
A Free Body Diagram (FBD) is a visual representation of all the external forces acting on a single object. It is the essential first step in any mechanics problem — before you can apply Newton's Laws, you need to know exactly which forces are at play.
This guide covers how to identify forces, draw FBDs step by step, handle inclined planes and tension problems, key formulas, worked examples, memory aids, common mistakes, and a 10-question practice quiz.
Free Body Diagram: Forces on an Object
1What Are Free Body Diagrams and Why Do They Matter?
A Free Body Diagram is a simplified drawing that isolates a single object and shows every external force acting on it. It strips away all unnecessary details — the environment, other objects, internal structure — and focuses solely on the pushes and pulls that determine the object's motion.
FBDs are fundamental for applying Newton's Laws of Motion. They help you organize your thoughts, identify all relevant forces, and set up the correct equations to solve for unknowns like acceleration, tension, or friction. Without an accurate FBD, it's easy to overlook forces or include irrelevant ones, leading to incorrect solutions.
You're designing a rope system to lift construction materials. Before calculating the required rope strength or motor power, you sketch a box and draw arrows showing the load pulling down, the rope tension pulling up, and the wind pushing from the side. That sketch is a free body diagram — the first step to solving any force problem.
- Bridge design — engineers use FBDs to ensure every beam can handle the forces on it
- Rock climbing — understanding tension in ropes and harnesses keeps climbers safe
- Car on a hill — the parking brake must provide enough friction to balance the gravitational component along the slope
- Elevators — tension in the cable must exceed the weight to accelerate upward
2Key Definitions
Free Body Diagram (FBD)
A diagram showing all external forces acting on a single isolated object. The object is drawn as a simple shape with force arrows.
Force (F)
A push or pull that can cause an object to accelerate or deform. A vector quantity with magnitude (N) and direction.
Net Force (Fnet)
The vector sum of all individual forces on an object. Determines the object's acceleration via Fnet = ma.
Weight (W or Fg)
Force of gravity on an object, always directed straight down. W = mg. Units: newtons (N).
Normal Force (FN)
Perpendicular contact force from a surface on an object. Points away from the surface. Prevents objects from passing through.
Friction (Ff)
Opposes relative motion between surfaces. Parallel to the surface. Static: Fs ≤ μsFN. Kinetic: Fk = μkFN.
Tension (T)
Pulling force transmitted by a string, rope, or cable. Acts along the rope, pulling away from the object. Ropes can only pull, not push.
Equilibrium
Fnet = 0. The object is either at rest or moving at constant velocity. No acceleration.
3What Is a Free Body Diagram?
A Free Body Diagram is a visual tool used to analyze the forces acting on a single object. It's "free" because the object is isolated from its surroundings — only the forces directly acting on it are shown.
Key Features of an FBD
What NOT to Include
4Types of Forces You'll See in FBDs
Weight (W = mg)
Direction: Always straight down (toward Earth's center)
Formula: W = mg, where g = 9.8 m/s²
Key fact: Present on every FBD unless the object is in deep space
Normal Force (FN)
Direction: Perpendicular to the contact surface, pointing away from it
Key fact: Prevents objects from passing through surfaces. Does NOT always equal mg
On an incline: FN = mg cos θ
Friction (Ff)
Direction: Parallel to surface, opposite to motion or attempted motion
Static friction: Fs ≤ μsFN (prevents motion from starting)
Kinetic friction: Fk = μkFN (acts on moving objects)
Tension (T)
Direction: Along the rope/string, pulling away from the object
Key fact: Ropes can only pull, never push. For ideal (massless) ropes, tension is the same throughout
Applied Force (Fapp)
Direction: Whatever direction you push or pull
Key fact: Can be at any angle. If at an angle, resolve into horizontal and vertical components
Spring Force (Fs = −kx)
Direction: Opposite to displacement from equilibrium (Hooke's Law)
Key fact: k = spring constant (N/m), x = displacement (m)
Air Resistance (Fair)
Direction: Opposite to the direction of motion through the fluid
Key fact: Often negligible in introductory problems unless stated otherwise
5How to Draw a Free Body Diagram (5 Steps)
Step 1: Identify the object of interest
Decide which single object you are analyzing. If there are multiple objects (e.g., two blocks connected by a rope), draw a separate FBD for each one.
Step 2: Draw the object as a simple shape
Represent it as a dot, box, or circle. The exact shape doesn't matter — keep it simple so the focus stays on the forces.
Step 3: Identify ALL forces acting ON the object
Systematically check: Is there gravity? Any surfaces (normal + friction)? Ropes (tension)? Pushes or pulls (applied)? Springs? Air resistance? This is the most critical step.
Step 4: Draw each force as an arrow from the center
Place the tail at the center of the object. Point the arrow in the correct direction. Make the length roughly proportional to the magnitude.
Step 5: Label every arrow
Write the force symbol (FN, W, T, Ff) and the magnitude if known. Add a coordinate system (x-y axes), especially for inclines or angled forces.
6FBDs in Different Situations
Book on a Table
Forces: Weight (W) down, Normal (FN) up
Result: FN = W (equilibrium)
Acceleration: Zero
Hanging Object (Single Rope)
Forces: Weight (W) down, Tension (T) up
Result: T = W = mg
Acceleration: Zero (static equilibrium)
Block on Inclined Plane
Forces: W straight down, FN perpendicular to ramp, Ff up the ramp
Weight components: mg sin θ (parallel), mg cos θ (perpendicular)
FN = mg cos θ
Object in Free Fall
Forces (no air): Only Weight (W) down
With air resistance: W down, Fair up
Acceleration: g = 9.8 m/s² downward (no air)
Box Pulled with Friction
Forces: W down, FN up, Fapp right, Ff left
Constant velocity: Fapp = Ff and FN = W
Accelerating: Fapp − Ff = ma
Object Suspended by Two Ropes
Forces: W down, T1 up-left, T2 up-right
Analysis: Resolve tensions into x and y components
ΣFx = 0, ΣFy = 0
At equilibrium (at rest or constant velocity), the net force is zero: ΣFx = 0 and ΣFy = 0. When the object accelerates, the net force is non-zero: Fnet = ma.
7Worked Examples
Example 1: Book on a Table
A 2 kg book rests on a horizontal table. Draw its FBD and find the normal force.
Step 1: Object = book. Forces ON the book: gravity (down) and table's normal force (up).
Step 2: Weight: W = mg = 2 × 9.8 = 19.6 N downward
Step 3: Since the book is at rest (equilibrium), ΣFy = 0: FN − W = 0
Step 4: FN = W = 19.6 N upward
Example 2: Hanging Sign
A 5 kg sign hangs motionless from a single rope. Find the tension in the rope.
Step 1: Object = sign. Forces ON the sign: gravity (down) and tension (up along rope).
Step 2: Weight: W = mg = 5 × 9.8 = 49 N downward
Step 3: Since the sign is at rest: T − W = 0
Step 4: T = W = 49 N
Example 3: Block on an Inclined Plane
A 10 kg block slides down a frictionless ramp inclined at 30°. Find the normal force and the acceleration.
Step 1: Forces: W = mg = 10 × 9.8 = 98 N straight down, FN perpendicular to ramp
Step 2: Decompose weight: parallel = mg sin 30° = 98 × 0.5 = 49 N; perpendicular = mg cos 30° = 98 × 0.866 = 84.9 N
Step 3: Perpendicular: FN = mg cos 30° = 84.9 N
Step 4: Parallel (down the ramp): ma = mg sin 30° ⇒ a = g sin 30° = 9.8 × 0.5 = 4.9 m/s² down the ramp
Example 4: Box Pulled at an Angle with Friction
A 5 kg box is pulled across a rough floor at constant velocity with a force of 20 N at 30° above the horizontal. Find μk.
Step 1: W = 5 × 9.8 = 49 N. Resolve Fapp: horizontal = 20 cos 30° = 17.3 N, vertical = 20 sin 30° = 10 N (upward)
Step 2: Vertical equilibrium: FN + 10 − 49 = 0 ⇒ FN = 39 N
Step 3: Horizontal (constant velocity, a = 0): Fapp,x − Ff = 0 ⇒ Ff = 17.3 N
Step 4: μk = Ff / FN = 17.3 / 39 = 0.44
Example 5: Atwood Machine (Two Blocks and a Pulley)
Block A (3 kg) sits on a frictionless table, connected by a rope over a pulley to Block B (2 kg) hanging freely. Find the acceleration and the tension.
FBD for Block A (on table): WA down, FN up, T to the right. Horizontal: T = mAa = 3a
FBD for Block B (hanging): WB = 2 × 9.8 = 19.6 N down, T up. Vertical: mBg − T = mBa ⇒ 19.6 − T = 2a
Solve simultaneously: Substitute T = 3a into second equation: 19.6 − 3a = 2a ⇒ 19.6 = 5a
Result: a = 19.6 / 5 = 3.92 m/s²; T = 3 × 3.92 = 11.76 N
8Key Formulas at a Glance
Weight
W = mg
Newton's 2nd Law
Fnet = ma
Kinetic Friction
Fk = μkFN
Static Friction (max)
Fs,max = μsFN
Incline (parallel)
mg sin θ
Hooke's Law
Fs = −kx
| Concept | Formula |
|---|---|
| Weight | W = mg |
| Newton's 2nd Law | Fnet = ma |
| Kinetic friction | Fk = μkFN |
| Static friction (max) | Fs,max = μsFN |
| Normal on incline | FN = mg cos θ |
| Parallel component on incline | mg sin θ |
| Hooke's Law | Fs = −kx |
| Equilibrium | ΣF = 0 |
9Memory Aids
Weight, Applied, Normal, Tension, Spring, Friction — check for each one every time you draw an FBD.
The normal force is the surface saying "you shall not pass." It always pushes perpendicular to the surface and away from it — even on an incline.
Friction always opposes the fun — it acts opposite to the direction of motion or attempted motion. If the object slides right, friction points left. Always.
mg sin θ is the component that slides you down the slope. mg cos θ is the component that crushes you into the surface (balanced by FN).
Before drawing any arrow, ask: "Is this force acting ON my object, or is my object exerting it on something else?" If it's BY the object, it goes on the other object's FBD.
10Common Mistakes Students Make
"Including forces the object exerts on other things."
FBDs only show forces ON the object. When you stand on a floor, your weight pushes down on the floor — but on YOUR FBD, you draw the floor's normal force pushing up on YOU. The force you exert on the floor appears on the floor's FBD.
"Forgetting the normal force."
If an object is resting on or pressed against any surface, there MUST be a normal force perpendicular to that surface. Students often forget it, especially on inclined planes where the normal force is not vertical.
"Drawing friction in the wrong direction."
Friction always opposes relative motion or attempted motion. If a box is being pushed to the right, friction acts to the left. On an incline, if the block tends to slide down, friction points up the slope. Always ask: "Which way would the object move without friction?" Then draw friction opposite.
"Drawing the net force as an arrow on the FBD."
The FBD should only contain individual forces. The net force is the result of adding them all up — it is not a force that acts on the object separately. Calculate it after drawing the FBD.
"Confusing mass (kg) with weight (N)."
Mass is measured in kilograms and is a scalar. Weight is a force measured in newtons: W = mg. A 5 kg object has a weight of 49 N on Earth. Always convert mass to weight before drawing force arrows on your FBD.
Frequently Asked Questions
- What is a free body diagram and why is it important?
- A free body diagram (FBD) is a simplified drawing that shows all the external forces acting on a single, isolated object. It is important because it helps you systematically identify every force, apply Newton's Laws correctly, and set up the right equations to solve for unknowns like acceleration, tension, or friction.
- What forces should I include in a free body diagram?
- Include only external forces acting ON the object: weight (gravity), normal force from surfaces, friction, tension from ropes or cables, applied forces (pushes/pulls), spring forces, and air resistance if relevant. Do NOT include forces the object exerts on other things, internal forces, or the net force.
- How do I draw forces on an inclined plane?
- On an inclined plane, draw weight (mg) straight down, normal force perpendicular to the surface (away from it), and friction parallel to the surface (opposing motion). It helps to decompose weight into components: mg sin θ parallel to the incline and mg cos θ perpendicular to it. The normal force equals mg cos θ when no other perpendicular forces act.
- Does the normal force always equal the weight?
- No! The normal force equals the weight only on a flat horizontal surface with no other vertical forces. On an incline, F_N = mg cos θ (less than mg). If someone pushes down on the object, F_N increases. If a rope pulls the object upward, F_N decreases. Always solve for F_N using Newton's Second Law in the perpendicular direction.
- What is the difference between mass and weight?
- Mass (m) is a scalar measured in kilograms — it describes how much matter an object contains and its resistance to acceleration. Weight (W) is a force measured in newtons — it is the gravitational pull on the object, calculated as W = mg. Mass stays the same everywhere; weight changes with gravitational strength (e.g., less on the Moon).
Practice Quiz
Test your understanding of free body diagrams — select the correct answer for each question.
1.A free body diagram should include which of the following?
2.The normal force on an object resting on a flat horizontal surface acts in which direction?
3.In which direction does kinetic friction act on a box sliding to the right across a floor?
4.According to Newton's Third Law, if you push a wall with 50 N of force, how should this appear on the wall's FBD?
5.What is the weight of a 5 kg object on Earth (g = 9.8 m/s²)?
6.For a block on a frictionless inclined plane at angle θ, which expression gives the normal force?
7.A 10 kg lamp hangs motionless from a single rope attached to the ceiling. What is the tension in the rope? (g = 9.8 m/s²)
8.An object is at rest on a table with no other forces applied. What must be true about the forces in its FBD?
9.A 3 kg box is pushed to the right with an applied force of 15 N on a frictionless surface. What is the net force and the resulting acceleration?
10.Which of the following is a common mistake when drawing a free body diagram?
Final Study Advice
- 1. Always draw the FBD before writing any equations. It forces you to think carefully about every force.
- 2. Use the "W-ANTS-F" checklist: Weight, Applied, Normal, Tension, Spring, Friction — check each one.
- 3. For inclined planes, tilt your coordinate axes to align with the surface — it makes the math much simpler.
- 4. Ask "forces ON, not BY" for every arrow you draw. If you can't identify what's exerting the force on your object, it shouldn't be on the FBD.
- 5. Practice with real objects around you — pick up your phone, a book, or a cup and mentally identify every force acting on it.