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What a 'free-body' diagram is and How to draw it

A free-body diagram (or FBD) displays an object taken in isolation with all the forces that act on that object.

Therefore the forces exerted by the object itself are not included.


Here's an example of a free-body diagram for a box pushed over the floor with a force F:

Free-body diagram of a box

All we can see is the box, and the forces exerted on that box.


Also notice that the external elements (the floor etc.) are omitted in the FBD. Indeed we take the object in isolation.


- Why is it useful to draw a free-body diagram?


Because it helps us eliminate all the distractions (external elements) and focus ourselves on the object alone. FBDs make the study of objects and all the forces that act on those objects easier.


3 easy steps to draw a free-body diagram

An FBD can be drawn following these steps:


  1. Sketch what you think is happening in the problem.
  2. List all the forces acting on the object you have to examine.
  3. Draw the free-body diagram for that object with the help of the sketch and the list.

Let's examine these 3 steps in more detail:


Step 1: Sketch what you think 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 (like the push or pull exerted by someone, or the friction force) so that you can clearly see what is going on. You can also specify whether the object is accelerating, moving at constant velocity, or being at rest.


For example, if you are solving a problem where a block is being pushed over the floor with friction, a sketch of what is happening could look like this:

A sketch of the block pushed over the floor

As simple as that.


Such a sketch helps you determine what forces act on the object, which is what we do in step 2.


Step 2: List all the forces acting on the object

Carefully observe the sketch you've made in step 1, and write down a list of all the forces that you think are acting on your object.


Returning to our previous example: our block is pushed, and there is friction between the block and the floor. The block is also subject to the force of gravity, and the normal force which the floor exerts in order to prevent the penetration of the block.

We can conclude that 4 forces are acting on our block:


Step 3: Draw the free-body diagram

After you have enumerated all the forces acting on the object (in step 2), you can finally draw the free-body diagram.

This is as simple as drawing the object and the forces that act on it.


In our example of the pushed block, we would draw the block alone (without the floor etc.), and the 4 forces that act on it.

Here's what the FBD could look like:

FBD of the pushed block

Note that if you have multiple objects in a problem, you will often need to draw a separate free-body diagram for each of them.


By doing the exercises below, you will find many concrete examples of free-body diagrams. After doing those, don't forget to check out our step-by-step guide for solving problems. There you will find many more examples of free-body diagrams, and see how they are used to solve actual problems.


Exercises

#1

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


#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 for the box.


#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 for the block.


#4

Fred is pushing his bag down a ramp with friction. The ramp makes an angle of 10° with the horizontal.

Draw an FBD for the bag.


#5

A sphere of mass m is hanging from a massless string attached to the ceiling.

Draw a free-body diagram for the hanging sphere.


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