Honors Physics - Chapter 4: Lesson 2

Chapter 4: Lesson 2

Free Body Diagrams

Chapter 4: Lesson 2 - Free Body Diagrams

Vectors:

Remember vectors show magnitude and direction. We can represent vectors with arrows. Position, velocity, acceleration, and FORCES are all vector quantitites.

We represent the magnitude of the of vector by the size of the arrow. The longer the arrow, the bigger the magnitude. The direction that the arrow is pointing is also important.

Free Body Diagrams:

Free body diagrams are used to show all the relative magnitude and direction of all the forces acting upon an object in a give situation. Just like I said above, the size of the arrow is important, it shows the relative magnitude of the force. Where the arrow is pointing shows the direction in which the force is acting.

When considering how a force affects motion, it is important to identify the object of interest. When looking at the object, we only care about what is directly touching or affecting the object.

Look at this example of a book sitting on a table. If we wanted to look at the book as my object of interest, I only want to talk about what is touching or directly affecting the book.

Anything that is not touching or affecting the book is considered outside or external forces.

The book is sitting on the table and a hand is pushing on the book. If we are ignoring friction, this means that there is the gravitational force pushing down on the book, the normal force pushing perpendicular to the surface of the table, and an applied force pushing to the right.

We don't need to worry about the table legs experting a force on the floor or the arm of the person pushing the book because those are outside forces and do not directly affect our book.

We need an easy way to represent the forces that are acting on an object. This is where we can draw a free body diagram to represent all the forces that are acting on an object. I have said before that physicists are lazy and are always looking for an easier way to represent objects. In this case, when we are drawing free body diagrams, we represent the object with a box. This makes it easy to have the four sides that the forces could be pushing or pulling from. Drawing a box is also a lot easier than drawing the real object.

Rules for Drawing Free Body Diagrams:

Understand all the forces that are acting on the object.
Draw a box to represent the object.
Determine the direction and magnitude for each force and add arrows for each existing force in the appropriate direction. When drawing the force vectors, the vector starts from the center of the box and goes in the direction that the force is acting.
Label each force! This is very important as you could have more than one force pointing in the same direction.

Look at this example. There are four forces acting on this object, normal force (Fnorm), gravitational force or weight (Fgrav), applied force (Fapp), and friction (Ffrict).

All free body diagrams will not have four fources. You only need to remember to depict all of the forces present when drawing free body diagrams.

Watch this video to see some examples of how we draw free body diagrams:

Click here to access the paper that I used in the video.

Determining the Net Force:

The net force is the vector sum of all the forces that are acting on an object. The picture to the right shows balanced forces. There is 20 N pointing up and 20 N pointing down. They are equal and opposite to each other. When the forces cancel each other out, we can say that the net force is zero.

If the net force is zero, then the object is in equilibrium.

Unbalanced forces exist when vertical (up/down) or horizontal (left/right) do not cancel each other out.

Look at the picture to the left. Although the vertical forces cancel each other out, there is still a force of 5 N pointing to the left. The net force of this book is -5 N or 5 N to the left.

If you have a 4 N force to the right and a 2 N force to the left, your resultant force would be 2 N to the right.

Check Your Understanding:

For the eleven questions below, think about the question, then click on the down arrow when you have your answer to check to see if you are correct.

Use the picture below for questions 1-4. Free body diagrams for four situations are shown below. For each situation, determine the net force acting upon the obejct.

Look at situation A. What is the net force on the object?

The net force is 0 N. The vertical forces of 3 N cancel each other out and the horizontal forces of 5 N cancel each other out.

2. Look at situation B. What is the net force on the object?

The net force is -5 N or you could say the net force is 5 N to the left. The vertical forces of 3 N cancel each other out and you are left with 5 N to the left.

3. Look at situation C. What is the net force on the object?

The net force is 0 N. The vertical forces of 20 N cancel each other out.

4. Look at situation D. What is the net force on the object?

The net force is -15 N or 15 N up. You subtract the two forces because they are pointing in opposite directions and add the direction (in this case the negative sign) in front of the answer.

Use the picture to the right for questions 5-11. Free body diagrams for four situations are shown to the right. The net force is know for each situation. However, the magnitudes of a few individual forces are not known. Analyze each situation individually and determine the magnitude of the unknown forces.

5. What is the magnitude of the force for vector A?

50 N since the net force is 0 N. When the net force is zero, both the horizontal and the vertical forces must cancel each other out.

6. What is the magnitude of the force for vector B?

200 N since the net force vertically is 0 N. When the net force is zero, both the horizontal and the vertical forces must cancel each other out.

7. What is the magnitude of the force for vector C?

C-200 = 900, so C=1100 N

Since the net force of 900 N is UP, then there is 900 N more pointing up than there is pointing down. The vector that is pointing up must be 900 N greater than the vector that is pointing down, which is 200 N.

8. What is the magnitude of the force for vector D?

80-D = 60, so D=20 N

Since the net force of 60 N is to the left, then there is 60 N more pointing left than there is pointing to the right. The vector that is pointing to the left, 80 N, must be 60 N greater than the vector that is pointing to the right.

9. What is the magnitude of the force for vector E?

300 N since the net force vertically is 0 N. The net force is 60 N to the left, so both vertical forces must cancel each other out.

10. What magnitude could force vectors F and H be?

They can be any number as long as they are the same number. The number also has to be greater than 0 since we know that there is a force there because we see an arrow.

11. What is the magnitude of the force for vector G?

G-20 = 30 so G=50 N

Since the net force of 30 N is to the right, then there is 20 N more pointing to the right than there is pointing to the left. The vector that is pointing to the right must be 30 N greater than the vector that is pointing to the left, which is 20 N.

You have finished Lesson 2!

Be sure to head over to google classroom and fill out the exit pass.

Report abuse