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Chapter 8: Force Diagrams (Free-Body Diagrams)

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8.1 Introduction to Force Diagrams

Force diagrams, also known as free-body diagrams, are visual representations that show the forces acting on an object. These diagrams are an essential tool in understanding and analyzing the behavior of objects under the influence of various forces. Drawing a force diagram is often step one in solving for the motion of an object. By examining all of the forces—their directions and magnitudes—one can predict how an object will move or behave.

In a force diagram, an object is represented by a simple, labeled shape such as a box or sphere. In most cases, even just a dot is sufficient. The forces acting on the object are represented by arrows that point in the direction of the force and which are labeled with the name of the force. The length of the arrow should be proportional to the magnitude of the force. However, sometimes the magnitude is not known, so a rough estimate is sufficient. Often, these estimates turn out to be far from accurate, but that’s not the point. The process of solving the problem itself will work these errors out.

Figure 1. A simple force diagrams for a box on an inclined plane.
Figure 1. A simple force diagram for a box on an inclined plane.

8.2 Drawing Force Diagrams

Here are some key principles to keep in mind when creating and interpreting force diagrams:

  1. Start with the force due to gravity. It always points down!
  2. Next, label the normal force if the object is in contact with any surface. The normal force will point perpendicular to the surface.
  3. Add in any remaining forces. If any force is acting at an angle, break it into components (see vector components).
  4. Forces can cancel each other out: If two forces are equal in magnitude and opposite in direction, they can cancel each other out, resulting in a net force of zero. Often times, one force can be canceled by just a component of another force. However, even when you recognize that two forces will cancel, still draw them on the force diagram! This will go a long way in preventing mistakes.
  5. Forces are vectors: Forces have both magnitude and direction, and should be represented as such on the diagram. The direction of the force is shown by the direction of the arrow, while the magnitude is shown by the length of the arrow.

8.2.1 Example

Let’s now consider an example. A 10 kilogram box is placed on a table. Robert applies a 10-Newton force on the book to the right. Aaron applies a force to the left. The book is at rest. What force does Aaron apply? What is the value of the normal force?

Figure 2. Force diagrams example.
Figure 2. Force diagram example.

Start with analyzing F_g. We know that F_g = mg =98.1 N. Thus, we can conclude that F_N = 98.1 N as well, because we know that the object is at rest. Therefore, the net force on the object must equal zero. Note that I am leaving off the vector arrows right now because we already know the direction (as shown in the figure above).

Now consider F_R which is the applied force from Robert. It is equal to 10 newtons (to the right). Therefore, F_A (the applied force from Aaron) must equal 10 newtons as well, but in the opositie direction—to the left.

8.3 Newton’s Laws of Motion

Sir Isaac Newton will have a bit more to say about forces in a little bit. At this point, you may be wondering why an object at rest has a net force of zero. You may also wonder if it is possible for a moving object to have a net force of zero (the answer is yes). However, these topics will be addressed in the following chapter. For now, get comfortable with the idea of drawing these diagrams for different physical situations.

Chapter Summary

Force diagrams are an essential tool in physics for analyzing the behavior of objects under the influence of various forces. They allow us to visualize the forces acting on an object and predict its motion. By following the principles outlined above, one can create and interpret force diagrams with confidence and accuracy.

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Knowledge Check

Answer the quiz questions below.

What is the main purpose of a force diagram (also known as a free-body diagram)?
To calculate the mass of the object.
No, the purpose of a force diagram is not to calculate the mass of the object. It is used to visualize the forces acting on an object and help predict its motion.
To illustrate the velocity of an object.
No, force diagrams are not primarily used to illustrate the velocity of an object. They are used to represent the forces acting on the object.
To visualize the forces acting on an object and help predict its motion.
Correct! Force diagrams are used to represent all of the forces acting on an object, making it easier to analyze its behavior and predict its motion.
What does the direction of an arrow in a force diagram represent?
The direction the object is moving.
No, the direction of the arrow in a force diagram represents the direction of the force acting on the object, not necessarily the direction the object is moving.
The size or magnitude of the force.
No, the direction of the arrow in a force diagram represents the direction of the force, not its magnitude. The size or magnitude of the force is represented by the length of the arrow.
The direction of the force.
Correct! In a force diagram, the direction of an arrow represents the direction of the force acting on the object.
What can we say about the net force on an object at rest?
The net force is always nonzero.
No, the net force on an object at rest is zero. This is because there is no change in motion, so the forces acting on the object must balance each other out.
The net force is always equal to the gravitational force.
No, the net force on an object at rest is zero, not equal to the gravitational force. The gravitational force is balanced by the normal force (force from the surface supporting the object), resulting in a net force of zero.
The net force is zero.
Correct! An object at rest has a net force of zero because there is no change in motion, indicating that the forces acting on the object balance each other out.
In a force diagram, what does the length of an arrow represent?
The direction of the force.
No, the length of the arrow in a force diagram represents the magnitude of the force, not its direction. The direction of the force is represented by the direction of the arrow.
The speed of the object.
No, the length of the arrow in a force diagram represents the magnitude of the force, not the speed of the object.
The magnitude of the force.
Correct! In a force diagram, the length of an arrow represents the magnitude (size) of the force acting on the object.
If two forces are equal in magnitude and opposite in direction, what is the net force acting on the object?
The net force is equal to the magnitude of each force.
No, if two forces are equal in magnitude but opposite in direction, they cancel each other out, resulting in a net force of zero.
The net force depends on the mass of the object.
No, the net force is determined by the forces acting on the object, not its mass. If two forces are equal in magnitude and opposite in direction, they cancel each other out, resulting in a net force of zero.
The net force is zero.
Correct! If two forces are equal in magnitude but opposite in direction, they cancel each other out, resulting in a net force of zero.
Continue to Chapter 9: Newton’s Laws of Motion
Back to Chapter 7: Forces

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2 responses to “Chapter 8: Force Diagrams (Free-Body Diagrams)”

  1. Newton’s Laws of Motion – Tru Physics

    […] laws are extremely useful when drawing free-body diagrams. If an object is at rest, the forces must be balanced. If an object is moving with constant […]

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  2. Forces – Tru Physics

    […] Continue to Chapter 5: Force Diagrams (Free-Body Diagrams) […]

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