Name __________________________________
Physics
Date ___________
Period ________________
Graphical Vector Addition
OBJ: To sum vectors. To determine the components of a vector.
Go to the following website at the University of Colorado:
http://phet.colorado.edu/simulations/sims.php?sim=Vector_Addition
Once at the site, click on the green start button and let the applet load. This applet will
help you understand how to add vectors together.
Instructions for Operation:
The vectors are red and in the bucket at the top right of the screen.
Click on one and drag it out, you have your first vector. The length and direction of the
vector can be changed by left clicking on the tip of the vector and dragging it. This will
allow you to change the length and orientation of the vector.
At the top of the screen are values. The first two boxes describe the magnitude and
direction of the vector. When adjusting the vector, you are to use these boxes to ensure
you have set it correctly. If you click on any vector on the screen, the info boxes will
give the information for that vector.
Continue to grab and drag vectors until you have all you need for any problem.
The vector sum is obtained by clicking on the ‘Show Sum’ box on the right side of the
screen. However, it is only shown as the correct size and direction not position. You
must arrange your vectors properly to complete the addition of your vectors.
***Can the vectors be arranged in any pattern to reach a Sum? How must the vectors be
arranged to equal the Sum?
Describe the location of the starting and ending points of the Vector Sum. Are
these points important to the final value of the Vector Sum?
Make sure to show your teacher that you have gotten the proper Vector Sum.
Name __________________________________
Physics
Date ___________
Period ________________
Vector Study:
Create each of the following sets of vectors. Use the website to draw the vectors. Add
the vectors graphically and determine the resultant (sum). Write the magnitude and
direction of the resultant in the space next to each set.
Trial
A
B
C
D
1
10 N at 0o
5N at 90o
5.7 N at 45o
None
2
5.7 m at 45o
2.8 m at -45o
5.7 m at 135o
None
3
7.1 m at -135o
5.7 m at 45o
3 m at 90o
6 m at -90o
4
5.7 m at 45o
8.2 m at 76o
11.4 m at -74.7o
8 m at -180o
Resultant
Vector (sum)
Questions for Analysis:
How must the vectors be aligned to obtain the proper Vector Sum?
Does the Vector Sum have a specific direction to it? Where does the vector start and
where does it end?
Go back and do trial #3 and #4 again, however, add the vectors in a different order. Does
changing the order of the addition change the answer?
Name __________________________________
Physics
Date ___________
Period ________________
Adding vectors by components:
Instructions for Operation:
Every vector is the sum of two other vectors. These vectors are referred to as vector
components.
At the top of the screen are values. The first two boxes describe the magnitude and
direction of the vector. When adjusting the vector, you are to use these boxes to ensure
they have set it correctly. If you click on any vector on the screen, the info boxes will
give the information for that vector. The components for each vector are also given.
Continue to grab and drag vectors until you have all you need for any problem. Once
done grabbing vectors, click on Style 3 under the component display menu on the right.
You will now see the components for each of the vectors you have placed on the screen.
They are shown as arrows at the end of the extended lines.
*Each vector on the screen has a line that extends from the tip of the vector to
each axis and a line that extends from the tail of the vector to each axis. What is
the reason for these lines? What do the lines mark out on the screen?
Move the vector to the origin on the screen.
*If you were to add the components together and use the vector as the sum of the
components, what geometric shape is created? Click ‘Style 2” under the component
display menu on the right to help answer the question.
*What determines the length of each vector component?
*Describe how the components compare to the actual vector.
*Click Style 3 under the component display menu on the right. What happens to
the components? Fully describe and explain.
Now, place 3 more random vectors on the screen. Add the vectors together using the
method you learned above, then click on the ‘Vector Sum’. Observe how the
components for each vector combine as you sum the vectors.
*Explain how the components of each vector combine to produce the Vector
Sum. Did the components sum in a manor different than the individual vectors? Explain.
Now, using the vectors in the table below, add each pair and find the sum of the vectors.
Then answer the questions using complete sentences.
Name __________________________________
Physics
Date ___________
Period ________________
Vector Math
Here is the table of vectors to use. Add the vectors listed in each trial and complete the
table. Make sure to include the component values for each vector and the resultant.
Trial
1
2
3
4
Vector
X
component
Y
component
Resultant
Resultant X
component
Resultant Y
component
5 at 0o
5 at 90o
10 at 0o
10 at 90o
11 at 0o
7.1 at 45o
2 at -90o
5.7 at -45o
Analysis:
1. Apply the Pythagorean Theorem and calculate the magnitude of the resultant vector
using the components you have found. Compare it to the value given by the computer.
Describe what you have found.