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KEY PhET Vectors Simulations Lab Introduction: A vector quantity is one that has both a magnitude and a direction. For instance, a velocity vector will have a magnitude (24 m/s) and a direction (northeast or 45 degrees). These simulations will demonstrate how the acceleration vector affects the velocity vector and how vectors can be added to produce a resulting vector.

Part I: Vector Simulation Procedure: 1. Go to http://phet.colorado.edu/ 2. Click the “Play with sims… >” button

3. From the list on the left, select “Math”, then “Applications” 4. From the array of applet pictures, select “Motion in 2D”

5. Click the “Run Now!” button

Questions: 1. Make sure the Show both and Stop radio buttons are both selected. Drag the object around with your mouse and notice the actions of the two vectors. Spend some time investigating the vectors. Which vector is velocity and which is acceleration and how did you make your decision? Type your answer in the text box below.

The velocity vector is green and the acceleration vector is blue. I made my decision because the green vector always points in the direction I am moving the object, but the blue vector changes direction when I change the speed of the object.

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY 2. Select the Linear Acc 1 radio button. Observe the motion. A larger blue vector causes what motion? Type your answer in the text box below. A larger blue vector causes the object to speed up or slow down, depending on the direction of the velocity vector. If they both point in the same direction, the object is speeding up. If they point in opposite directions, the object is slowing down.

3. Select the Simple Harmonic radio button. Observe the motion. A larger blue vector causes what motion? Type your answer in the text box below.

A larger blue vector causes the object to change direction.

4. Select the Circular radio button. Observe the motion. What orientation must the vectors (to each other) have to turn the object? Type your answer in the text box below.

The vectors must be perpendicular to one another.

5. Select the Stop radio button. Attempt to move the object like a car or runner on a racetrack (in an oval). What must the car/runner do in order to turn? Type your answer in the text box below.

In order to turn, the object must continue with the same velocity, but slow down, so it will have an acceleration vector pulling it inward.

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY 6. Move the object like a car moving forward then coming to a quick stop. Describe the acceleration vector. Type your answer in the text box below.

The acceleration vector clearly points in the same direction as the velocity vector as the car moves forward, but when it comes to a complete stop, the acceleration vector points in the opposite direction (and gets larger until it stops completely).

Part II: Vector Addition Simulation Procedure: 1. Go to http://phet.colorado.edu/ 2. Click the “Play with sims… >” button

3. From the list on the left, select “Math”, then “Tools” 4. From the array of applet pictures, select “Vector Addition”

5. Click the “Run Now!” button

How the applet works:

To get a vector, grab an arrow from the bucket. The length of the vector is found in the |R| box. The angle of the vector (measured in degrees) is in the θ box. Select the Style 2 radio button in the “Component Display” box to show the X and Y components.

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY Place two vectors in the work area. Change their direction and magnitude by dragging the heads of the arrows representing each vector – you may choose any size and direction you like. Place the vectors you wish to add head to tail (it will be beneficial to place the tail of your first vector at the origin). Each time you create a new vector, you will be given the following information about that vector:

Remember, |R| = Magnitude of the vector

θ = angle of the vector

Rx = X component

Ry = Y component

To get the resultant vector, check the “Show Sum” box and move the green sum vector so that the tail touches the tail of your first vector and the head touches the head of your second vector as shown below:

Questions: 1. Click on your first vector and record the vector information in Table 1 below. 2. Click on your second vector and record the vector information in Table 1 below. 3. Click on the resultant vector and record the vector information in Table 1 below. Table 1

R

q

Rx

Ry

Vector 1

16.6

65

7

15

Vector 2

17.8

128.2

-11

14

Resultant Vector

29.3

97.9

-4

29

4. Paste a screenshot of your vector sum from the sim here (I can enlarge it if I need to):

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY 5. Examine the values in the Table 1 columns labeled Rx and Ry along with your diagram from the sim. Make a conjecture as to how these values for the resultant vector can be calculated from their values for Vector 1 and Vector 2. Type your conjecture in the text box below. Add the Rx and Ry values for each Vector to arrive at the Rx and Ry values for the resultant vector.

6. Examine the value of R for the resultant vector of Table 1 along with your sim vector diagram. Make a conjecture as to how the value of R of the resultant vector can be calculated from the values of Rx and Ry . Type your conjecture in the text box below. Pythagorean Theorem:

7. Examine your sim vector diagram. Make a conjecture as to the relationship between q , Ry , and Rx for each vector. Type your conjecture in the text box below.

8. Click the “Clear All” button and repeat the process with two new vectors, recording the same data in Table 2 below. Table 2

R

q

Rx

Ry

Vector 3

Will vary

Will vary

Will vary

Will vary

Vector 4

Will vary

Will vary

Will vary

Will vary

Resultant Vector

Will vary

Will vary

Will vary

Will vary

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY 9. Paste a screenshot of your vector sum from the sim here: will vary

10. Do your conjectures for Table 1 hold true with Table 2? Confirm or refute below by typing your calculations using Math Type. Calculations will vary, but should confirm. Calculations:

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY Part III: Calculating Resultant Vectors ***GRADED*** 

Use a calculator to find the mathematical sum of each set of vectors below, recording your work in the table.



To add vectors, break each vector into its X an Y components by calculating X = R cosq

Y = R sin q **Remember, the components CAN BE NEGATIVE ( = -x, -y) 

The resultant vector’s X and Y components are the sum of the X and Y ’s of each vector Xr = X1 + X2

Yr = Y1 + Y2 

The resultant vector’s magnitude, R , is found by using the Pythagorean theorem using X r and Yr as the legs of a right triangle, where the hypotenuse is the magnitude.



The angle θ of the resultant vector is found using the tangent ratio: tanq =



Yr Xr Use the simulation to recreate (as closely as possible) the vector sum to check your work. Take a screenshot to support your work and paste it to the right of each problem.

Fill in all available boxes. Graded answers will come from calculations. Please round to the nearest tenth (0.1). Use the sim to check your work and post a sim screenshot of your vector sum to the right of each problem. (Typesetting hint: If you place your cursor directly behind the word “Screenshot”, insert and select your picture, and then select Format, Picture, Layout, Tight, you can resize and move your picture accordingly, keeping your vector tables intact.)

Problem #1 Vector 1

Screenshot:

R

q

X1

Y1

12.2

35

10

7

q

X2

Y2

15.9

7

2

Xr

Yr

17

9

Vector 2 R

7.3

Resultant Vector R q

19.2

27.9

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.

KEY Problem #2: Vector 1 R q

18.7 Vector 2 R

21

X1

Y1

15.5

18

5

q

X2

Y2

-25.3

19

-9

Xr

Yr

37

-4

Resultant Vector R q

37.2

Screenshot:

-6.2

Problem #3: Vector 1 R q

Screenshot:

X1

Y1

35

20

14

q

X2

Y2

81.9

1

7

Xr

Yr

21

21

X1

Y1

70

4

11

q

X2

Y2

-14

8

-2

Resultant Vector R q

Xr

Yr

12

9

24.4 Vector 2 R

7.1

Resultant Vector R q

29.7

45

Problem #4: Vector 1 Screenshot: R q

11.7 Vector 2 R

8.2

15

36.9

When you are finished, submit this document to the Vectors Simulation Assignment on Moodle.