In this article, you will learn what a free-body diagram (or FBD) is, and how to draw it in 3 simple steps.
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 diagrams are important because they allow us to analyze an object in isolation without distractions.
You can draw a free-body diagram of an object following these 3 steps:
Let's go through these steps in more detail.
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:
This sketch will help you determine what forces 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:
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:
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).
To better understand how to draw free-body diagrams using the 3 steps, let's go through several examples.
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:
The next step is to look at the sketch, and enumerate all the forces to which the box is subject:
The final step is to draw the box with the 4 forces that act on it:
A mass hangs from a rope attached to the ceiling. Let's draw the FBD of the hanging mass.
We begin with the sketch:
Looking at the sketch, we infer that there are only 2 forces acting on our mass:
Finally, we draw the mass and the two opposite vertical forces that act on it:
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:
2) We look at our sketch and think of all the forces that act on the sphere:
3) We draw the sphere with the 3 forces acting on it:
To practice drawing free-body diagrams yourself, do the exercises below.
Suppose that you are pushing a crate of mass m over a horizontal frictionless plane. Draw an FBD of the crate.
We have a crate pushed over a horizontal plane with no friction:
The FBD of the crate looks like this:
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.
Sketch:
Free-body diagram of the box:
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.
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.
A sphere is hanging from a string attached to the ceiling.
Draw a free-body diagram of the hanging sphere.
Sketch:
Free-body diagram of the sphere:
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.