Free Body Diagram Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Free Body Diagram.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A simplified diagram that isolates a single object and represents all external forces acting on it as labelled arrows originating from the object's centre of mass.

A simplified picture that shows every push and pull acting on one isolated object.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Free Body Diagram asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to free body diagram but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

easy

10 \text{ kg}

box rests on a flat surface. Draw and label all forces in the free-body diagram. What are their magnitudes? Use

g = 9.8 \text{ m/s}^2

Answer

W = 98 \text{ N downward}, \quad N = 98 \text{ N upward}

First step

Identify all forces acting on the box: weight (gravity) pulling downward and normal force pushing upward.

Full solution

2
Weight: $W = mg = 10 \times 9.8 = 98 \text{ N}$ downward.
3
Since the box is in equilibrium, the normal force equals the weight: $N = 98 \text{ N}$ upward.

A free-body diagram shows all forces acting on a single object as arrows from the object's center. For a stationary object on a flat surface, the only forces are weight and normal force, which must balance.

Example 2

medium

5 \text{ kg}

block is pulled across a rough surface (

\mu_k = 0.2

) by a

30 \text{ N}

horizontal force. List all forces in the free-body diagram and find the acceleration. Use

g = 9.8 \text{ m/s}^2

Example 3

medium

2\text{ kg}

block sits on a table while a person presses down on it with

10\text{ N}

. Draw the FBD and find the normal force from the table. Use

g = 9.8\text{ m/s}^2

Example 4

medium

3\text{ kg}

block on a rough horizontal surface (

\mu_k = 0.3

) is pushed by a

20\text{ N}

horizontal force. Find the acceleration. Use

g = 9.8\text{ m/s}^2

Example 5

hard

4\text{ kg}

sign hangs from two ropes meeting at its top: rope A makes

30°

with the ceiling on the left, rope B makes

60°

with the ceiling on the right. Find the tension in each rope. Use

g = 9.8\text{ m/s}^2

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

4 \text{ kg}

block slides down a frictionless ramp inclined at

45°

. Identify all forces in the free-body diagram and find the acceleration. Use

g = 9.8 \text{ m/s}^2

Example 2

hard

6 \text{ kg}

block hangs from two ropes: one horizontal (attached to a wall) and one at

60°

above the horizontal (attached to the ceiling). Find the tension in each rope. Use

g = 9.8 \text{ m/s}^2

Example 3

easy

A book rests on a flat table. Which two forces appear on its free-body diagram?

Example 4

easy

A box is pushed right across a rough floor. Name the four forces on its free-body diagram.

Example 5

easy

A ball is in free fall (no air resistance). How many forces are on its free-body diagram?

Example 6

easy

On a free-body diagram, should you draw the force the object exerts on the ground?

Example 7

easy

A lamp hangs from a ceiling rope. What two forces are on its free-body diagram?

Example 8

easy

A block sits on a frictionless incline. Which forces appear on its free-body diagram?

Example 9

easy

A car drives at constant velocity. On its free-body diagram, how do the horizontal forces compare?

Example 10

easy

A ball is thrown upward and is momentarily at the top of its path (no air resistance). What is on its free-body diagram?

Example 11

medium

2

kg block on a

30^\circ

frictionless incline (

g=10

m/s

^2

). Find the normal force from its free-body diagram.

Example 12

medium

5

kg box is pulled by a

30

N rope at

37^\circ

above horizontal on a rough floor (

g=10

m/s

^2

\sin37^\circ=0.6

). Find the normal force.

Example 13

medium

3

kg block hangs from two ropes: one vertical and one horizontal pulling it sideways. List the forces and state the vertical-equilibrium condition.

Example 14

medium

4

kg block accelerates down a frictionless

30^\circ

incline (

g=10

m/s

^2

). From the free-body diagram, find the acceleration.

Example 15

medium

Two blocks (

1

kg and

2

kg) touch and are pushed by

9

N on the

1

kg block on a frictionless floor. From free-body diagrams, find the contact force between them.

Example 16

medium

10

N picture hangs from two symmetric wires at

53^\circ

from horizontal (

\sin53^\circ=0.8

). From the free-body diagram, find each wire's tension.

Example 17

medium

2

kg block in an elevator accelerating up at

2

m/s

^2

rests on the floor (

g=10

m/s

^2

). From the free-body diagram, find the normal force.

Example 18

medium

5

kg block on a rough horizontal floor is pushed at

20

N but stays still. From the free-body diagram, what is the friction force?

Example 19

medium

3

kg block hangs at rest from a rope in an elevator moving up at constant velocity (

g=10

m/s

^2

). From the free-body diagram, find the tension.

Example 20

challenge

4

kg block on a

3

kg block; the bottom block is pushed so both accelerate at

2

m/s

^2

on a frictionless floor. From free-body diagrams, find the friction the bottom block exerts on the top one (

g=10

m/s

^2

Example 21

challenge

2

kg ball on a string swings in a vertical circle (

r=0.5

g=10

m/s

^2

). At the top its speed is

3

m/s. From the free-body diagram, find the string tension at the top.

Example 22

challenge

1

kg block on a

37^\circ

rough incline is on the verge of sliding (

g=10

m/s

^2

\sin37^\circ=0.6

\cos37^\circ=0.8

). From the free-body diagram, find the friction force.

Example 23

easy

2\text{ kg}

apple hangs from a string. Identify the forces on its free-body diagram and give their magnitudes. Use

g = 9.8\text{ m/s}^2

Example 24

easy

3\text{ kg}

block slides at constant velocity on a horizontal floor while pushed with a

9\text{ N}

horizontal force. What is the friction force on the FBD?

Example 25

easy

1\text{ kg}

ball sits on a table. The table exerts a normal force on the ball. What is its magnitude? Use

g = 9.8\text{ m/s}^2

Example 26

medium

4\text{ kg}

block is on a frictionless ramp at

30°

. Resolve gravity into components parallel and perpendicular to the incline. Use

g = 9.8\text{ m/s}^2

Example 27

medium

5\text{ kg}

box is pulled along a horizontal floor by a

40\text{ N}

rope at

37°

above horizontal. Find the normal force from the floor. Use

g = 9.8\text{ m/s}^2

\sin 37° = 0.6

\cos 37° = 0.8

Example 28

medium

2\text{ kg}

ball hangs by a string from the ceiling of an elevator that accelerates upward at

2\text{ m/s}^2

. Find the tension in the string. Use

g = 9.8\text{ m/s}^2

Example 29

medium

Two blocks of masses

2\text{ kg}

and

3\text{ kg}

are connected by a string and pulled together along a frictionless floor with

20\text{ N}

on the

3\text{ kg}

block. What is the tension in the string? (Draw an FBD for the

2\text{ kg}

block.)

Example 30

medium

10\text{ kg}

crate sits in the bed of a pickup truck. The truck accelerates forward at

2\text{ m/s}^2

without the crate slipping. What is the friction force on the crate? In which direction?

Example 31

medium

0.5\text{ kg}

ball on a string is swung in a horizontal circle of radius

1\text{ m}

4\text{ m/s}

. What is the tension in the string (ignore gravity for this horizontal circle)?

Example 32

hard

Two blocks (

m_1 = 2\text{ kg}

on a frictionless table,

m_2 = 3\text{ kg}

hanging) are connected by a string over a frictionless pulley (Atwood-on-table). Find the acceleration and string tension. Use

g = 9.8\text{ m/s}^2

Example 33

hard

2\text{ kg}

block sits on a

5\text{ kg}

block on a frictionless floor. A

20\text{ N}

horizontal force is applied to the lower block. The blocks move together. Find the friction force from the lower block on the upper block.

Example 34

hard

5\text{ kg}

block on a

25°

rough incline (

\mu_k = 0.2

) is released from rest. Find its acceleration down the slope. Use

g = 9.8\text{ m/s}^2

Example 35

hard

70\text{ kg}

person stands in an elevator accelerating downward at

2\text{ m/s}^2

. What does a bathroom scale (which reads the normal force) show, in newtons? Use

g = 9.8\text{ m/s}^2

Example 36

hard

1200\text{ kg}

car rounds a flat curve of radius

50\text{ m}

15\text{ m/s}

. Find the minimum coefficient of static friction needed. Use

g = 9.8\text{ m/s}^2

Example 37

medium

2\text{ kg}

object accelerates at

3\text{ m/s}^2

to the right. Two horizontal forces act on it:

F_1 = 10\text{ N}

to the right and

F_2

unknown. Find

F_2

Example 38

challenge

5\text{ kg}

block lies on a

10\text{ kg}

board on a frictionless floor. The coefficient of static friction between block and board is

0.4

. What is the maximum horizontal force that can be applied to the board so the block does not slide on it? Use

g = 9.8\text{ m/s}^2

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Related Concepts

Force Vectors Newton's Second Law Equilibrium

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcevectors