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This is the lab report that correspond to the vector addition lab....

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Physics 220 Name: Matthew Mondragon________________ Date:09-03-2020___________ Lab #2 Vectors Addition by Graphical and Analytical Methods Using Phet Calculation Purpose: In this lab you will learn about vectors in order to express them graphically and analytically. You will be able to apply the concepts that you’ve learned in order to solve problems. And compare the differences between the analytical and graphical outcomes. You will measure the magnitude and direction of each vector. Procedure: You will first Identify what a vector is and become familiar with the equations given in the handout. You will find the magnitude and direction as well as identifying the angle of the vector. In part 1 Using the graphical and analytical method you will be adding two vectors to find their overall magnitude and angle. Using the Phet simulation software you will plot two vectors to form a triangle. The sum of these two vectors will give you the resultant vector which is the overall magnitude. Then identify the angle of this triangle. Using the data from the software you analytically calculate the resultant vector and direction. Then record your data on the table provided. Using the percentage difference equation, you will find percent difference of the magnitude in methods one and two. After you calculate the percent different in magnitude you will then calculate the percent difference of the two angles. In part 2 you will be adding three vectors together. As in part 1 you will be finding the magnitude, direction, and the angle of the vectors. Using the Phet simulation you will plot three vectors to form a polygon shape. The sum of the three vectors will give you your resultant vector. then identify the angle shown on the graph. Analytically calculate the resultant vector using the data on the table provided. Then proceed finding the percent difference of the magnitude and angles. Make sure to answer the questions at the end of the lab. Learn the difference between a vector and a scalar quantity. Data:

Part one: Adding two vectors

Graphical Method

This image shows the graphical representation of adding two vectors. Absolute value “s” represents the sum (overall magnitude) of these two vectors. Theta is the degrees of the resultant vector. 9.4 is the horizontal x component, and 11.4 is the y component. R= 50.6 VR= 14.8m/s Analytical method Vector

Vector (m/s)

Direction

x-component

y-component

v1

10

20o

9.4

3.4

v2

8

90o

0.0

8.0

VR

14.78

50.49

9.4

11.4

These values on Table 1 were derived from the graph above. VR = 14.78m/s R = 50.49 percentage difference magnitudes (14.8m/s-14.78m/s/14.79m/s) x 100 = 0.14

percentage difference in angles

(50.6-50.49/50.5) x 100 = 0.22

Part two: Adding three vectors Graphical Method for three vectors

This image shows the graphical representation of adding two vectors. Absolute value “s” represents the sum (overall magnitude) of these two vectors. Theta is the degrees of the resultant vector. -5.0 is the horizontal x component, and 17.0 is the y component R = 106.4 VR = 17.7m/s Analytical method for three vectors Vector

Vector (m/s)

Direction

x-component

y-component

v1

6

30o

5.0

3.0

v2

8

100o

-1.0

8.0

v3

11

145o

-9.0

6.0

VR

17.2

73.6

-5.0

17.0

These values on Table 2 were derived from the graph above. VR = 17.2m/s R = 73.6

percentage difference magnitudes (17.7m/s-17.2m/s/17.45m/s) x 100 = 2.87

percentage difference in angles (106.4-73.6/90) x 100= 36.4

Sample Calculations:

θ = tan

| R| =

-1

(

Ry

Ry=11.4, Rx=9.4

) R x  = tan^-1(11.4/9.4) =50.49

√( R x )2+( R y )2

√ ( 9.4 ) +( 11.4 ) =14.78 2

2

(Result 1- Result 2/Average Result) x100 = Average = 14.8+14.78/2=14.79 (14.8m/s-14.78m/s/14.79m/s) x 100 = 0.14 (Result 1- Result 2/Average Result) x100 = Average = 50.6+50.49/2= 50.5 (50.6-50.49/50.5) x 100 = 0.22

Discussion: What are vectors? Vectors are quantities that have both magnitudes and direction. In the first part of the procedure I used the Phet simulation program to plot the vectors. This gave me my overall magnitude and x and y components. I used the x and y component to find the overall magnitude represented as the absolute value “s”. component y is represented as Ry and the x component is represented as Rx. I used the equation to find magnitude represented | Ras | = ( R x )2 +( R y )2 Once I plugged in the components into the equation this gave me the resultant vector. I proceed to use this same equation to find the resultant vector using the analytical method.

√

The equation that was used to find the angle for both the graphical and analytical Ry -1 θ = method is tan ( R ) x Again, I plugged in the x and y components into the equation to find the angles. I forgot how to calculate the percent difference, so I looked at the open stax physics textbook to find the equation (Result 1- Result 2/Average Result) x100. I used this equation to find the percent difference between the overall magnitude and angles. I made sure to add the percent symbol at the end.

Conclusion: In this lab I learned how to add two vectors graphically and analytically. I then used this information to find the overall magnitude and angle in both the graphical and analytical representations. I found the percent differences between the magnitudes and angles of both the graphical and analytical methods. Then I used percent difference calculation to give me the overall percentage. One error that I found in this lab was in Part two using the graphical method. The graph states that the overall magnitude is 106.4m/s, and the angle is 17.0, but using the analytical method the magnitude is 17.2m/s and the angle is 73.6. The reason why I believe that this is an error is because we are given the same x and y components. Logically this should give you answer close to the graphical calculations, but the magnitude and angles are very different. This finding exceeded my expectations I thought the angles were going to be relatively close. References: https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html https://openstax.org/details/books/college-physics...