1. 1. Header (5 points)
Include:
● The name of the lab
● Your name
● Your partners’ names
● Your lab instructor’s name and T.A. name
● The submission date
2. Abstract (10 points)
This should be a short statement, no more than 3 or 4
sentences, that summarizes the lab. Please include:
● The purpose of the lab
● Any major concepts/laws discussed or tested
● The results you found (numbers, affirmations, etc.)
3. Introduction (20 points)
Introduce the theory/concepts behind the testing, what was
being tested, and a subsection containing all equations
used in the experiment. Number the equations so they
may be referenced in your “Results” section.
4. Procedure/Methods (15 points)
In your own words and in full sentences, please list all the
steps necessary to conduct this experiment. You must use
at least one figure in your report, so consider using it here
to visually demonstrate part of the procedure. Do not copy
the procedure in the manual word for word.
5. Results (20 points)
This is where all of your recorded data, answers to
equations, and graphs, charts, and diagrams will go. Each
equations used needs at least one referenced sample
calculation. Do not discuss your data here, as this is merely
the section where it clearly needs to be portrayed to the
reader.
6. Discussion, Data Analysis, and Conclusion (25 points)
Discuss the results in detail here. Do not just say WHAT
the answer is, but WHY it is and HOW it relates to the

2. concept being tested. Answer all assigned questions in
Force Table
Lab Partners: Person 1, Person 2, Person 3, etc.
Instructor, T.A.: Your Instructor, Your TA
MM/DD/YY
ABSTRACT
This experiment was conducted to show how vectors affect one
another- in particular,
how opposing vectors can be added up to cancel each other out
to create a system in equilibrium,
which was done by hanging different masses over various
angles on a force table. As a result,
each case showed that when summed all forces added to 0.
INTRODUCTION
Vectors are extremely important in physics, as they provide a
way to show quantity that
has not only a magnitude, but a direction as well, which is
extremely important when explaining
things like motion. Although these vectors are more complex

3. than just a single number, they can
be manipulated by other vectors fairly easily. This makes
combining certain measurements that
could involve a multitude of vectors, as well as manipulating a
single vector as it can be added or
subtracted from itself, fairly simple.
This experiment showed the use of a force table to prove this
manipulability with vectors
by setting mass as forces on certain angles in order to cancel
each other out. This works as an
example because all three of the masses had some sort of force,
in this case being caused by
acceleration due to gravity, being applied to them in the
direction they were angled. It also
helped to demonstrate graphical methods for manipulating
vectors by means of “tip-to-tail”
measurement. This type of measurement aids in the visual
representation of vectors and gives
understanding to how a system of vectors looks when in
equilibrium, in this case a quadrilateral
formed by four vectors of different magnitude and direction. A
number of equations were used in
this experiment, and are as follows:

4. Instructor name
Fx = 0Σ (1)
Fy = 0Σ (2)
Fx = Fcos( )θ (3)
Fy = Fsin( )θ (4)
g = 9.8 m/s2 (5)
F = mg (6)
Equations (1) and (2) show how F x and F y , the horizontal
and vertical components of
force F (Newtons ), when in an equilibrium-system should sum
to 0. Equations (3) and (4) show
how the force F is geometrically related to the horizontal and
vertical components, respectively,
by means of angle (degrees ). Equation (5) is a constant that
states how the acceleration due toθ
gravity, g (meters/second 2 ), is equal to 9.81. Equation (6) is a

5. variation of Newton’s Second Law
that shows that the force due to gravity on an object is
equivalent to g multiplied by mass m
(kilograms ).
PROCEDURE
The force table, which allows a central equilibrium to be
reached by hanging multiple
masses at different angles, was set up with 3 points to be
determined. The force table with a
3-pulley setup is seen in Figure 1. The pulleys were attached
around the circumference with a
ring and three strings that could spin freely placed in the center
of the table. The first trial
included forces in the first quadrant at 0o degrees and 200
grams and 90o degrees and 400 grams,
and one component to be measured based on these. The third
string was then pulled across the
table until the ring was centered on the middle post, and the
angle was recorded. A mass hanger
was then added to the string on this side, and weight was added
until the ring again centered

6. itself in the middle. At this point, all components were put in
equilibrium. This process was
repeated once more, only the 900 angle was
adjusted to 135o with the same weight of 400
grams. The third angle was measured, weight
was added, and equilibrium was reached, and
the results were recorded. Following this, a
procedure to allow for a graphically calculated
equilibrium-system was conducted. An arbitrary
quadrilateral, with a base line on the horizontal
of some graph paper, was drawn. Each side
represented a tip-to-tail vector, with the final tip
touching the tail of the horizontal vector. The angle of each
vector was found using a protractor
and the magnitude of each was found with a ruler using the
conversion 0.25” = 25 grams. These
values were translated to the force table, where 4 hangers and
pulleys were used to represent the
four vectors in the quadrilateral. Small adjustments were made
until equilibrium was established.

7. RESULTS AND CALCULATIONS
The following table shows angles, mass, and force for the first
setup in the experiment,
which involved starting angles that were orthogonal. Following
the table are sample calculations
demonstrating how the results were found.
Table 1: Orthogonal Starting Forces, Resultant Force
Angle (o) Mass (kg) Force (N)
0 0.200 1.96
90 0.400 3.92
246 0.450 4.41
F = mg (6)
g = 9.8 m/s2 (5)
450 g 10-3 = 0.450 kg×
0.450 kg 9.8 m/s2 = 4.41 kg = 4.41 N× m
s 2

8. A table for the vertical and horizontal components is shown
below, with sample
calculations following:
Table 2: Orthogonal Starting Forces, Components
Angle (o) Force (N) X-component (N) Y-component (N)
0 1.96 0.200 0.000
90 3.92 0.000 0.400
246 4.41 -0.183 -0.411
Sum 0.017 -0.011
Fx = Fcos( )θ (3)
Fx = Fcos( ) = (.450)cos(246) = -0.183 kgθ
Fy = Fsin( )θ (4)
vy = vsin( ) = (.450)sin(246) = -0.411 kgθ
Fx = 0Σ (1)
Fx = 0.200 + 0.000 + -0.183 = 0.017 0Σ ≈
Fy = 0Σ (2)

9. Fy = 0.000 + 0.400 + -0.411 = -0.011 0Σ ≈
The following table shows angles, mass, and force for the
second setup in the experiment,
which involved starting angles that were in the first and second
quadrants.
Table 3: First and Second Quadrant Forces, Resultant Force
Angle (o) Mass (kg) Force (N)
0 0.200 1.96
135 0.400 3.92
285 0.330 3.23
A table for the vertical and horizontal components in this
section of the experiment is
shown below.
Table 4: First and Second Quadrant Forces, Components
Angle (o) Force (N) X-component (N) Y-component (N)
0 1.96 0.200 0.000
135 3.92 -0.283 0.283

10. 285 3.23 .085 -0.319
Sum 0.002 -0.036
The following page consists of the graphs of Force and
components for each of the two
trials. They are based on the data in Tables 1, 2, 3, and 4:
The following table shows the angles, magnitudes, and forces
for the quadrilateral system
of vectors that was drawn on the graph paper. Again, the
magnitudes are based on 0.25” = 25 g.
Table 5: Quadrilateral System, Forces

11. Angle (o) Mass (kg) Force (N)
0 0.25 2.4525
116.57 0.1118 1.0968
180 0.15 1.4715
243.43 0.1118 1.0968
A table for the vertical and horizontal components in this
section of the experiment is
shown below. This is the data the was calculated before being
put on the force table.
Table 6: Quadrilateral System, Components, Theoretical
Angle (o) Force (N) X-component (N) Y-component (N)
0 2.4525 2.4525 0
116.57 1.0968 -0.4905 0.9810

12. 180 1.4715 -1.4715 0
243.43 1.0968 -0.4905 -0.9810
Sum 0 0
DISCUSSION, DATA ANALYSIS, AND CONCLUSION
In total, the data was fairly accurate in portraying systems in
equilibrium. Each case
showed fairly close results, meaning each mass system tested
ended with the ring being centered.
In the first setup, where the starting angles were orthogonal, the
resultant force was in the
quadrant opposite, which is expected. When considering the
vectors in terms of parallelograms,
the resultant of those two forces would be on a line somewhere
in between them, which when
applied to create equilibrium would be in the opposite direction,
For the case where the angles
were in different quadrants, the resultant was more difficult to
predict. In the case of creating a
resultant force that will put a two-force system into equilibrium,
it can be judged that the applied
resultant force will tend to be directed more in parallel to the
strongest of the two forces already

13. in the system; in other words, the angle between the resultant
vector and the strongest
pre-existing vector will be the closest to 180 degrees. This
proved true in the case of this
experiment, as the third force applied created a much more
obtuse angle with the hanger
producing a greater force out of the two forces already on the
table.
The quadrilateral equilibrium system was a way to demonstrate
differences in
tip-to-tail/graphical versus component methods of vector
computation. As the data shows, while
graphical representation can be useful for visualization,
component methods give much better,
more precise theoretical values that are better suited for further
calculation as these attributes
have much less error. They are also more easily organized and
are more efficient to use, which is
why they are preferable. Like the two previous sections of the
experiment, the quadrilateral that
was conceived demonstrated a system of equilibrium; however,
it gave more rise to sources of
error due to the discrepancies and variations between the

14. computed model and the force table
model.
One possible source of error that created some of these
unexpected results was that the
angles were all measured by eye. Obviously depending on the
perspective each angle can look
different, so this could have resulted in some inaccuracies when
measuring not only the
components, but the masses as the qualifications for equilibrium
would have changed. Another
source of error is that the force table had not been calibrated.
Similar to the source above, this
error may have caused an imbalance in the equilibrium, thus
producing inaccurate component
measurements. Another source of error may have been the
strings on the center ring, and the
friction in the pulleys. It was noted after the experiment that
they were not freely sliding around
as they should and were sometimes catching on certain portions
of the ring. This was also the
case with the pulleys. This means that some of the results may
be off as the angle may not have
been accurately measured after adding mass to the first two
strings.

15. Overall, this experiment showed how important vectors are and
how their angles and
magnitudes significantly affect their behavior and interaction
with one another. It demonstrated
not only how to solve equilibrium systems, through components
as well as graphical
representation, but how to calculate, create, and check
equilibrium systems.