# Free-Body Diagrams

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• 0:03 Forces and Vectors
• 0:56 Examples
• 3:13 Lesson Summary

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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Forces that act on an object can be drawn through special vector diagrams called free-body diagrams. In this video lesson you'll identify how to correctly represent forces in a free-body diagram through vector arrows and force labels.

## Forces and Vectors

In another lesson, we learned how force is a vector quantity. This means that it has both magnitude and direction. So saying that a force is 5 Newton isn't enough; we also need to know the direction of the force - for example, 5 Newton to the left. A vector diagram shows us the relative magnitude and direction of a vector quantity using vector arrows. In this type of diagram, the size of the arrow tells us the relative magnitude of the force, and the direction the arrow is pointing tells us the direction of the force.

A free-body diagram is a unique type of vector diagram. In this type of diagram, we label each vector with the type of force that it is representing, and we use a box to represent the object the force (or forces) is acting on. There is no limit to the number of forces that can be represented in a free-body diagram; you should draw as many forces as there are for that object!

## Examples

Let's take a look at some free-body diagrams to see how they work. For example, let's say we have a book sitting on a table. This book is at rest, but that doesn't mean there aren't forces acting on it! There is the force of gravity pulling the book down, but there is also the normal force pushing up from below. Because the book is at rest, we know that these are balanced forces, meaning that they are equal in magnitude and opposite in direction.

Now let's say that someone comes along and pushes that book from the left and gets it moving across the table ever so slightly. We still have the force of gravity pulling down and the normal force pushing up. Because the book is not moving vertically, this means that those forces are still balanced.

But since the book is now moving horizontally, we can see that there are unbalanced forces at work. Unbalanced forces are those that are not equal in magnitude, and this causes a change in the book's state of motion. From the person pushing the book, we have an applied force, which is greater in magnitude than the force of friction acting in the opposite direction. This starts the book moving, but when the person stops pushing the book there's no longer an applied force and the book returns to its state of rest.

Now let's say that the person pushes the book so that it travels at a constant velocity, which means it travels at a constant speed and direction. The horizontal forces are now balanced, and the book is in equilibrium, meaning that there is no change in the object's state of motion. Objects that are moving can be in equilibrium as long as they are traveling at a constant velocity, and our free-body diagram now reflects this with equal size arrows in all directions (gravity and the normal force are still balanced here).

But what happens when that person pushes the book off the end of the table? The book falls because the vertical forces are now unbalanced. There is some air resistance pushing up on the book as it falls, but gravity is the greater magnitude force so the book hits the floor.

Once on the floor it goes back to a state of rest because the normal force balances with gravity again. Once at rest, the book is back in equilibrium (just like when it was moving at constant velocity), and the vector arrows are drawn the same size to reflect this.

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