Library Exercise for Physics (Vectors)
We are going to begin our study of vectors by using two websites dedicated to physics and the use of
computer simulations. These are www.physicsclassroom.com and phet.colorado.edu.
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Go to www.physicsclassroom.com
Select Physics Tutorials
Select Vectors – Motion and Forces in Two Directions
Read and do lessons 1a through 1f. Once you are done here, go to phet.colorado.edu.
Look at the left side of the page and select Math. This will display two subareas. Choose Tools. This
will bring up icons for all the simulations that exist under the Math > Tools folder. Select Vector
Addition and then select Run Now. It may take a few moments to load the simulation. At this time,
spend a few minutes playing around with the simulation to get a feel for what it can do.
We are now ready to begin the next part of the lesson. Follow the directions below and write your
answers to the questions on a separate sheet of paper. Graph paper is available if you wish to use
some.
Questions:
Before you begin these questions… under Component Display click the circle next to “Style 2” and Check the
box next to “Show Grid”. These settings will not change for the rest of the activity. Answer all questions in
complete sentences.
1. Drag a vector into the grid.
a. What does Rx represent?
b. What does Ry represent?
c. What does Θ represent?
d. What does |R| represent?
2. Why does the vector have an arrowhead? What does that arrowhead indicate?
3. Reshape your first vector so that it is completely horizontal. Move that vector to (0,0). What is the value
of Rx? Ry? Θ? |R|? Do these values make sense?
4. Drag another vector into the grid. Reshape it so it is completely vertical. Move that vector so that the tail
of the arrow is touching the tip of the other vector on your screen. For this new vector, what is the value
of Rx? Ry? Θ? |R|? Do these values make sense?
5. What have you begun to create? Draw what you see on the screen TO SCALE on your own paper.
6. Click on the “Show Sum” button. A new vector (green) appears on your screen. Drag it so that the tail of
the vector is at (0,0). What is the value of Rx? Ry? Θ? |R|? Do these values make sense?
7. Draw the new vector TO SCALE on the picture you drew for #5. How do you believe the value for |R| was
determined? Calculate it on your own to verify the computer’s result. SHOW ALL YOUR WORK!
8. Does the method you used work for all triangles? If not, what special types of triangles does this method
work for?
9. Drag all of your vectors to the trash. Create a new vector that starts at (0,0) and is not completely
horizontal or completely vertical. What are the values of Rx? Ry? Θ? |R|? Do these values make sense?
10. What type of triangle is made? Draw what you see on the computer screen on your own page TO SCALE.
Using the value of |R| and Ry, how would you calculate Rx? Verify the value of Rx by calculating it on your
own. SHOW ALL YOUR WORK!
11. Create another vector that is not completely horizontal or completely vertical. Drag it so that its tail is
touching the tip of the vector from #9. What are the values of R x? Ry? Θ? |R|? Do these values make
sense?
12. Add the vector from #11 to your picture. Be sure to draw it TO SCALE on your paper. Click the “Sum”
button. Move the new vector so that its tail is at (0,0). Draw this vector to scale on the drawing you made
in #9 and 11.
13. For your newest vector, what are the values of Rx? Ry? Θ? |R|? Do these values make sense?
14. For your newest vector, how was Rx determined? How was Ry determined? How was |R| determined?
Try to verify the results the computer gave you by calculating the |R| yourself. SHOW ALL YOUR WORK!
15. In general, if you know the measurements of the horizontal parts (components) of vectors and you know
the measurements of the vertical components of vectors, how can you find their sum (resultant)?
16. Suppose you are driving 13.6 miles/hour with a compass reading of 36°north of east. Represent the
vector using the simulation. How fast is your car traveling in the north direction? How fast in the east
direction? Figure out how the components could be calculated using geometry if you couldn’t use the
simulation.
17. To get to the sandwich shop, you left home and drove 6 miles south and then 10 miles west. If a bird flew
from your house to the sandwich shop in a straight line, how far do you think the bird would fly? Use the
simulation to check your reasoning. What direction should it fly from your house to get to the shop?
Describe the direction as some number of degrees South of West. Explain how you could use geometry
equations to answer these questions.
18. Suppose you and a friend are test driving a new car. You drive out of the car dealership and go 10 miles
east, and then 8 miles south. Then, your friend drives 8 miles west, and 6 miles north. If you had the
dealer’s homing pigeon in the car, how far do you think it would have to fly to get back to the dealership?
Use the simulation to test ideas. The distance that the bird has to fly represents the sum of the 4
displacement vectors. Use the simulation to test ideas you have about vector addition.