(Sample Lab Report)
The Force Table
Physics 221 Section 001
September 22, 2006
Kyle Schmitt
Purpose/Theory
The purpose of this experiment is to verify vector addition. According to
Newton’s second law, an object that is not accelerating must have no net force, i.e. the
sum of the vectors of the forces on that object must be zero. The method for vector
addition includes finding the orthogonal components of each vector and adding so that
the components of the resultant vector R is related to the components of the individual
vectors A, B, etc., in the following way:
Rx = Ax + Bx + ... + Nx
Ry = Ay + By + ... + Ny,
where N is the total number of forces acting on the object. The magnitude of the
resultant vector is
R = R x2 + R y2 ,
and the angle θ between the vector R and the x-axis is
θ = tan −1 (
Ry
).
Rx
The equilibrant vector is the vector E which when added to R returns zero (Parks 35-38).
Procedure
Three masses were used to exert measurable forces on a ring at the center of the
force table. They were placed at measurable angles so that the components of the force
vectors could be calculated. A forth mass was placed so that the net force on the ring was
zero, i.e. the ring was centered on the table.
Data
The forces applied to the ring and the calculated and measured equilibrant forces
are presented in Table 1.
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Forces
Force #1
Force #2
Force #3
Sum of
Components
Resultant Force R
Equilibrant Force E
Measured Force
% Difference
Force #1
Force #2
Force #3
Sum of
Components
Resultant Force R
Equilibrant Force E
Measured Force
% Difference
Force #1
Force #2
Force #3
Sum of
Components
Resultant Force R
Equilibrant Force E
Measured Force
% Difference
Force #1
Force #2
Force #3
Sum of
Components
Resultant Force R
Equilibrant Force E
Measured Force
% Difference
Magnitude
400
Angle
30
X Component
346.4101615
Y Component
200
200
300
-60
135
100
-212.1320344
-173.2050808
212.1320344
234.2781272
238.9269536
334.62267
334.62267
350
4%
45.56
225.6
227
1%
400
200
500
45
-45
270
282.8427125
141.4213562
-9.18861E-14
282.8427125
-141.4213562
-500
424.2640687
-358.5786438
555.49855
555.49855
550
1%
-40.2
139.8
140
0%
350
200
500
20
315
250
328.8924173
141.4213562
-171.0100717
119.7070502
-141.4213562
-469.8463104
299.3037018
-491.5606165
271.8923361
128.5575219
-234.9231552
126.7854785
-153.2088886
-85.50503583
165.5267029
-111.9284459
575.51242
575.51242
570
1%
-58.66
121.3
118
3%
300
200
250
25
310
200
199.81758
199.81758
200
0%
-34.07
145.9
143
2%
Table 1_________________________________________________________
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Results/Conclusions
The results of this experiment are presented in Table 1. All of the measured
forces are within 4 percent difference of the calculated forces, so it can be concluded that
this method of calculating vector addition is accurate. Possible sources or error include
friction and the weight of the string.
Questions
Just give the answers to the questions I give you, if there are any.
Works Cited
Parks, James E. Selected Introductory Physics Experiments. Knoxville: Thomson
Custom Publishing, 2002.
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