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What is a Free-Body Diagram and How to Draw it (with Examples)

In this article, you will learn what a free-body diagram (or FBD) is, and how to draw it in 3 simple steps.

What is a free-body diagram?

A free-body diagram is a representation of an object with all the forces that act on it. The external environment (other objects, the floor on which the object sits, etc.), as well as the forces that the object exerts on other objects, are omitted in a free-body diagram.

Below you can see an example of a free-body diagram:

Free-body diagram of an object that is pushed horizontallyFNmg

Free-body diagrams are important because they allow us to analyze an object in isolation without distractions.

How to draw a free-body diagram?

You can draw a free-body diagram of an object following these 3 steps:

  1. Sketch what is happening
  2. Determine the forces that act on the object
  3. Draw the object in isolation with the forces that act on it

Let's go through these steps in more detail.

Step 1: Sketch what is happening

This simply means that after you've read the problem once or twice, you sketch the object in its environment, and represent the main forces acting on the object (e.g. the push or the pull exerted by somebody, the friction force, etc.) so that you can clearly see what is going on.

For example, if a block is pushed over the floor with friction, a sketch of what is happening could look like this:

A sketch of the block pushed over the floorPushFriction

This sketch will help you determine what forces act on the object.

Step 2: Determine the forces that act on the object

Carefully observe your sketch, and think about all the forces that are acting on the object.

Returning to our example: the block is pushed, so a pushing force acts on the block; there is friction between the block and the floor, so a friction force acts on the block (opposing its motion); the block is subject to the force of gravity; the floor exerts the normal force on the block in order to prevent the penetration of the block.

Therefore, we come to the conclusion that 4 forces are acting on our block:

  • the push, F
  • the friction force, Ff
  • the normal force, N
  • and the gravitational force mg

Step 3: Draw the object in isolation with the forces that act on it

Finally, draw the object on its own (omitting external elements like other objects, the floor, the ceiling, etc.) and the forces that are acting on it.

In our example, we draw the block and the 4 forces that act on it:

Free-body diagram of the pushed blockFFfNmg

And that's how you draw a free-body diagram.

Note: if you have multiple objects in a problem, you will need to draw a separate free-body diagram for each object, which you can do by following the 3 steps (step 1 being common to all objects, and step 2 and 3 specific to each object).

Examples of drawing free-body diagrams

To better understand how to draw free-body diagrams using the 3 steps, let's go through several examples.

Example 1

A box is pushed up an incline with friction which makes an angle of 20° with the horizontal. Let's draw the free-body diagram of the box.

The first step is to sketch what is happening:

Sketch of the box pushed up the incline20°PushFriction

The next step is to look at the sketch, and enumerate all the forces to which the box is subject:

  • the upward push, F
  • the force of friction, Ff
  • the normal force, N
  • and the force of gravity, mg

The final step is to draw the box with the 4 forces that act on it:

Free-body diagram of the box pushed up the inclineFFfNmg

Example 2

A mass hangs from a rope attached to the ceiling. Let's draw the FBD of the hanging mass.

We begin with the sketch:

Sketch of the mass hanging from the rope

Looking at the sketch, we infer that there are only 2 forces acting on our mass:

  • the force of gravity, mg, which is pulling the mass downward
  • the upward tension exerted by the rope, T, which prevents the mass from falling

Finally, we draw the mass and the two opposite vertical forces that act on it:

Free-body diagram of the mass hanging from the ropemgT

Example 3

A sphere is hanging from two ropes attached to the ceiling. The first rope makes an angle of 30° with the ceiling, while the second rope makes an angle of 45° with the ceiling. Let's draw the free-body diagram of the sphere.

1) We sketch what is happening:

Sketch of the sphere hanging from the two ropes attached to the ceiling30°45°

2) We look at our sketch and think of all the forces that act on the sphere:

  • the tension exerted by the first rope, T1
  • the tension exerted by the second rope, T2
  • and the force of gravity, mg

3) We draw the sphere with the 3 forces acting on it:

Free-body diagram of the sphere hanging from the two ropes attached to the ceilingT1T2mg

To practice drawing free-body diagrams yourself, do the exercises below.

Exercises

#1

Suppose that you are pushing a crate of mass m over a horizontal frictionless plane. Draw an FBD of the crate.

Solution

We have a crate pushed over a horizontal plane with no friction:

Sketch of the pushed cratePush

The FBD of the crate looks like this:

FBD of the pushed crateFNmg

#2

Jack is pulling a box up an incline which makes an angle of 30° with the horizontal. Assuming there is no friction, draw a free-body diagram of the box.

Solution

Sketch:

Sketch of the box pulled up the incline30°Pull

Free-body diagram of the box:

Free-body diagram of the box pulled up the inclineFNmg

#3

A block is pulled over a horizontal plane with a force F that makes an angle of 15° with the horizontal. Assuming there is friction between the block and the plane, draw a free-body diagram of the block.

Solution

Free-body diagram of the block pushed with the force that makes a 15-degree angle with the horizontal15°FFfNmg

#4

Fred is pushing his bag down a ramp with friction. The ramp makes an angle of 15° with the horizontal.

Draw an FBD of the bag.

Solution

FBD of the bag pushed down the inclineFFfNmg

#5

A sphere is hanging from a string attached to the ceiling.

Draw a free-body diagram of the hanging sphere.

Solution

Sketch:

Sketch of the hanging sphere

Free-body diagram of the sphere:

FBD of the hanging spheremgT

Problems with solutions

To further test your understanding of free-body diagrams, see our force problems, which include problems where you need to draw free-body diagrams of objects that move up an incline, hang from ropes attached to the ceiling, and hang from ropes that run over pulleys. For each problem, we provide a step-by-step guide on how to solve it.

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