Experiment #6
The Addition and Resolution of Vectors: The Force Table
Physics 1101 – 1L3 General Physics I Laboratory
Fall 2020
Professor: Dr. Juan Homero Hinojosa
09/28/2020

____ out of 3
Purpose
The objective of this experiment is to find the resultant or vector sum of two or more vectors. In
order for this experiment to be successful, special methods of the vector addition must be used.
This is done by using graphical and analytical methods. Once the results have been obtained then
the graphical and analytical methods can then be compared with the experimental results that
were obtained from a force table. The experimental arrangements of forces (vectors) will then
physically illustrate the principles of the vector addition. After performing this experiment and
analyzing the data, you should be able to do the following:
1. Add a set of vectors graphically to find the resultant.
2. Add a set of vectors analytically to find the resultant.
3. Appreciate the difference in convenience between using graphical and using analytical
methods of vector addition.
____ out of 20
Theory
The main idea behind this experiment is Vector Addition. What this means is the addition of
different distances at different angels, which are considered magnitude and direction. There are
three methods to calculate the addition of vectors.
The first one talked about in this experiment is the Graphical Method, which is basically
calculating the vectors by drawing and graphing them. The vectors are added by the Triangle
Method. This method is basically drawing the three vectors in a way that they connect each other
so it would facilitate calculations of the vectors. Formula for this method is:
R
=
√
F
x
2
+
F
y
2
The next method is the Analytical Method, which is basically using tested formulas to add the
vectors. The formulas used in this experiment are the following:
F
x
=
F
1
x
cosθ
+
F
2
x
cosθ
F
y
=
F
1
y
sinθ
+
F
2
y
sinθ
For the direction/angle use:
θ
=
tan
−
1
F
y
F
x

Now, for the Experimental method is carrying out the actions of the experiment physically. So, in
this case, it is mainly about adding weights to each hanger of the clamp until they total .2 kg or
200 grams. Then, the data is recorded (angle, weight, etc.) Also, in this section one must make
sure that the strings are stable for chances of error are really high, unlike the other two methods
(Graphical and Analytical).
Equations
Weight = gravitational force
w
=
mg
Law of Cosines
R
2
=
A
2
+
B
2
−
2
ABcosγ
Law of Sines
B
sin
θ
=
R
sin
γ
=
A
sin
β
R
=
√
R
2
x
+
R
²
y
tan
θ
=
Ry
R
ₓ
θ = tan
¹
⁻
Ry
R
ₓ
¿
)
E = 180
E = -R
____ out of 2
Equipment
Force table with four pulleys
Four weight hangers
Set of slotted weights (masses), including three of 50 g and three of 100 g
String
Protractor
Ruler
Level
3 sheets of Cartesian graph paper
____ out of 20
Procedure