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.
8.2 Drawing Force Diagrams
Here are some key principles to keep in mind when creating and interpreting force diagrams:
- Start with the force due to gravity. It always points down!
- Next, label the normal force if the object is in contact with any surface. The normal force will point perpendicular to the surface.
- Add in any remaining forces. If any force is acting at an angle, break it into components (see vector components).
- 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.
- 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?
Start with analyzing . We know that . Thus, we can conclude that 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 which is the applied force from Robert. It is equal to 10 newtons (to the right). Therefore, (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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