Experiment 3: Resolving & Adding Vectors
Student Name:
Chao Lee
Section Number:
PHYS 2425 P1L
2/11/22
REPORT
Instructions
1)
Follow all of the lab activity steps given in the Lab Procedure.
2)
Attach your completed data tables to this page.
3)
TYPE YOUR ANSWERS IN THE PROVIDED SPACES below & in your data tables.
4)
Attach additional sheets of paper that clearly (NEATLY) show all of your calculations performed
during this experiment.
Results
1)
What is the principle source of error in each of the methods used for vector resolution and addition
(graphical, analytical, and experimental)? Which of these methods is most accurate? Why?
Write out your answer in a clear and well supported paragraph.
1.Graphical: Because in graphical method, I measure R length with divider or a ruler and measure its direction with a
protractor, and such measurements have low precision and low accuracy. 2.Analytical: Analytical method is more
accurate than graphical method. Because this method gives exact equations that enable to find the magnitude and
direction of the resultant of vector, but analytical method can not add vector forces. 3.Experimental: Using experimental
method first need to know the magnitude and direction of the vector, then apply vector to the ring by hanging the
appropriate mass from a properly located pully. But that leads to mass and location is not accurated.
2)
You measured the direction of the analytical resultant relative to the x axis. Would the vector
components change if you had used a different reference axis? Would the magnitude of the resultant
change? Would its direction change? Explain. Write out your answer in a clear and well
supported paragraph.
Yes, it is goning to change if I used a different reference axis. The magnitude of Vx and Vy are found by
using trigonometry of a righe triangle. Therefore, Vx=Vcos(theta), Vy=Vsin(theta), theat=arctan(Vy/Vx),
where V is the magnitude of the vector V and theta is the angle between the vector and Xaxis. If I change to
Yaxis, then Vx and Vy is opposite, and direction is also changed.
3)
Although vector A makes an angle of 40° with the x axis, you placed the pulleys to determine
its x and y components at the 180° and 270° positions, respectively. Explain why.
Write out your answer in a clear and well supported paragraph.
Because, rather than put a single equilibrant force B to the ring to against the Vector A at 220 degree. I
apply two perpendicular force to it that the ring is in equilibrium. The two perpendicular forces are the
equilibrants of Ax and Ay -their magnitudes are equal to the magnitudes of Ax and Ay,Since the magnitude of
B is equal to the magnitude of A, the magnitudes of there two perpendicular blancing forces are equal to the
magnitudes of the experimentally-determined x and y components of B.
1
2
Experiment 3: Resolving & Adding Vectors
Student Name:
CHAO LEE
DATA
PHYS 2425 P1L
Section:
A. Components of a Vector
Table 3.1: Vector Forces
Force
Vector
A
B
C
Total Mass
50g
70g
100g
Magnitude
0.49 N
0.69 N
0.98 N
Direction
40°
120°
230°
Table 3.2: Graphical Components
Vector
A
B
C
Scale
1CM=0.1N
1CM=0.1N
1CM=0.1N
Components
x
y
0.37
0.35
-0.375
0.65
-0.63
-0.73
% Error
x
2.6
7.14
0
y
9.3
8.33
2.67
Table 3.3: Analytical Components
Components
Vector
x
y
A
0.38
0.32
B
-0.35
0.6
C
-0.63
-0.75
Table 3.4: Experimental Components
Force
Component
Ax
Ay
Bx
By
Cx
Cy
Hanger Mass
5g
5g
5g
5g
5g
5g
Added Mass
33g
27g
30g
56g
61g
70g
Magnitude
0.37N
0.31N
0.34N
0.60N
0.65N
0.74N
% Error
2.6
3.1
2.8
0
3.2
1.3
B. Adding Vectors
Table 3.5: Graphical Addition
Scale
1CM=0.1N
Length
6.3CM
Resultant
Magnitude
0.68N
Direction
139°
1
% Error
Magnitude
Direction
8.9
15.33
Table 3.6: Analytical Addition
Components
Vector
x
y
A
0.38
0.32
B
-0.35
0.6
C
-0.63
-0.75
R
-0.6
0.17
Magnitude
0.624
Direction
164.18
Table 3.7: Experimental Addition
Force
Vector
A
B
C
E
R
Total Mass
50g
70g
100g
66g
Magnitude
0.49
0.69
0.98
0.64
0.68
Direction
40
120
230
345
139
2
% Error
Magnitude
Direction
8.9
15.33
2/11/22
DATA
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4