Name __________________________________
Physics CP
Date ___________
Period ________________
Graphical Vector Addition
OBJ: How 2D vectors are Summed.
Go to the following website at the University of Colorado:
http://phet.colorado.edu/simulations/sims.php?sim=Vector_Additi
on
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. Make sure to show your teacher that you have
gotten the proper Vector Sum.
Name __________________________________
Physics CP
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
Resultant
Vector (sum)
11.4 m at -74.7o 8 m at -180o
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?
Describe the starting and ending points of the Vector Sum.
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?
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
Name __________________________________
Physics CP
Date ___________
Period ________________
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. Move the vector to the origin on the screen.
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.
Time to find the vector sum, it 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 move it to complete the addition
of your vectors.
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.
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.
Read and answer question 4 after each trial.
Trial
1
2
3
4
Vector
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
X
Y
component component
Resultant
Resultant
Resultant
X
Y
component component
Name __________________________________
Physics CP
Date ___________
Period ________________
Questions:
Answer all questions in complete sentences.
1. Each vector on the screen has a line that extends from the tip of the
vector to each axis. What did this line mark for each vector on each
axis?
2. What did each of the fainter arrow lines represent for each of the
vectors drawn?
3. When you graphically added each pair of vectors together, what
happened to the vector components on the screen?
How were the vector components placed on the screen in relation to each
other as the vectors were added in the order you picked? Describe what
you saw as the order.
4. 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.
Name __________________________________
Physics CP
Date ___________
Period ________________
Now go to :
http://illuminations.nctm.org/ActivityDetail.aspx?ID=42
At this site, follow the directions and use vector addition to get
the boat to hit the Island a total of 5 times. For each of the
trials record the water velocity vector, the boat velocity vector
and the result vector for each successful result.