M3.0 Laboratory Report 2 Worksheet22 (1)
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Feb 20, 2024
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Name: ______Demauri Simpson____________________________________ M3.0 Laboratory Report 2 Worksheet
PhET Simulation: Vector Addition
Instructions
Before you start to work on this worksheet, review the M3.0 Laboratory Report 2 Instructions
Submit your completed work to the M3.0 Laboratory Report 2 dropbox. See the Schedule and Course Rubrics in the Syllabus Module for due dates and grading information.
.
Pre-Lab Activities:
1.
Open the simulation using the link to PhET Interactive Simulations at the University of Colorado Boulder:
https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html
2.
Explore the four options available in the simulator
3.
Select the option (Explore 2D).
Part I: Vector Addition – Component (Analytical) Method.
Part 1.1 Use the components method to add the following 2 vectors: 𝑎⃗
= 29.2, @31.0° and 𝑏⃗
= 16.2, @68.2°
Procedure:
1.
Click on vector segment 𝑎⃗
and drag it so the tail positioned at the origin of the graph. Adjust the vector to the given magnitude (drag the head of the vector to adjust the length) and rotate the vector to adjust the angle.
2.
“Break” the vector into components (see Sample 1 below) and input the components into Table 1.
3.
Insert a screenshot of your vector 𝑎⃗
and its components (as shown in Sample 1)
Table 1
Vector
Magnitude
Direction
(degree)
x-component
y-component
𝑎⃗
Cos 31o
29.2=25
31
29.2
a
𝑏⃗
Cos 68.2
68.2
16.2
b
𝑠⃗
Cos(-13.6 36o)=11
36-
13.6
s
4.
Complete steps 1-3 for vector 𝑏⃗
.
5.
Drag the 2 vectors with their tails positioned at the origin of the graph, as shown in Sample 2 below.
6.
Click on the sum vector where 𝑠⃗
= 𝑎⃗
+ 𝑏⃗
. 7.
Record the magnitude and the angle for the resultant vector 𝑠⃗
in Table 1.
Part 1.2 Using the theoretical equations calculate the resultant sum of the same two vectors (
𝑎⃗
= 29.2, @31.0° and 𝑏⃗
= 16.2, @68.2°) and insert your calculations in the lab report. Compare your calculated resultant to the one obtained with the simulator. Is it different from the experimental one? Explain.
Part 1.3 Use the components method to add the following 3 vectors:
𝑎⃗
= 22.4, @26.6° 𝑏⃗
= 11.3, @ - 135.0°
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c
⃗
= 13.6, @ - 36.0°
Y-componet
degree
Magnitude
vector
Sin 26.6o
Cos 22.4
26.6o=20
26.6
22.4
A
Sin -135o=-11.3 8
Cos (-11.3
135o)=-8
135-
11.3
b
Sin (-36o)=-8 13.6
Cos(-13.6 36o)=11
36-
13.6
s
Use the same steps as in Procedure in Part 1.1. Create a new table (Table 2) adding another row
for vector c
⃗
and populate the table. Insert the screenshots from the simulator for all 3 vectors and their components and a screenshot for the resultant (as listed in the steps in Part 1.1)
Part 1.4 Using the theoretical equations calculate the resultant sum of the three vectors and insert your calculations in the lab report. Compare your calculated resultant to the one obtained with the simulator. Is it different from the experimental one? Explain.
Part II Vector Addition – Head-to-Tail (Graphical) Method.
Vectors can be added together graphically (Head-to-Tail) by drawing them end-to-end. A vector
can be moved to any location; so long as its magnitude and orientation are not changed, it remains the same vector. When adding vectors, the order in which the vectors are added should not change the resultant.
In the graphical addition
process known as the polygon method one of the vectors is first drawn
to scale. Then each successive vector to be added is drawn with its tail starting at the head of the preceding vector. The resultant vector is then the vector drawn from the tail of the first arrow to the head of the last arrow.
Firstly, we draw the vector A with the same angle that it makes with the positive x – axis choosing the appropriate and the same scale for all vectors. Then B is drawn at the proper angle (α) relative to A. Finally, the resultant R is the vector connecting the tail of vector A and the head of vector B as shown in the figure below:
Part 2.1 Add the given vectors 𝑎⃗
= 29.2, @31.0° and 𝑏⃗
= 16.2, @68.2° in Part I using the “Explore
2D” or “Lab” option in the simulator.
Compare the resultant (magnitude and direction) with the one found in PartI. Are the two resultants the same? Follow the instructions in Writing a Lab Report – Guidance, and refer to the Rubric for Laboratory Report, complete and submit your file in the corresponding folder.
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