Force Table and Vector Addition of Forces
Student: Jessica
Class: Phy—110
Lab Date: September 25, 2012
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I—Introduction
The purpose of this lab was to learn how to work with different scalars. Scalars are used in
science every day; they could be temperature, mass, volume, and time intervals. There are also
physical scalars which include vectors. In this particular lab we are going to use vectors to
determine the magnitude and direction of certain forces.
2.0-Theory
A vector is a term to represent quantities that have magnitude and direction. Some of the
quantities can be; velocity, acceleration, force, and displacement. In order to have a vector you
must know the direction and so they cannot just simply be added together. There are different
methods to find the resultant or sum of different vectors.
The force table used in the experiments allows the application of forces at any angle. To find
the force one must multiply the mass by the gravitational force (kg*9.8m/s^2). After putting
two different forces on two pulleys we must than find the equilibrant and also find the force of
it.
2.1—Percentage Difference
The percentage difference is when we want to compare two sets of numbers, it could be the
same object being measured but different results and so we can calculate the percentage
difference.
%diff=(m1-m2)(100)
(1)
2.2—Force
Force can be determined in different ways. One of the most know ways is Newton’s Second Law
of Motion, which says force is the mass times they acceleration. There is also the fact that many
confuse weight and mass. When a person steps on the scale the number read is not the weight
but the mass. The weight is a force which is determined by the mass times the gravitational
pull.
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F=m*a
(2)
W=m*9.8m/s^2
(3)
2.3—Parallelogram Method
The Parallelogram Method is a method to find the Fnet of two vectors. You must first take the
measurement of F1 with a protractor and put it at the tip of F2 than you draw a line, you do the
same with F1 but you use F2’s measurement. Both lines will connect and at the point they
intersect is where the next point for the parallelogram is. This method can be used when there
are two forces involved.
2.4—the Polygon Method
The polygon method is methods used when there are three forces involved, and we are trying
to find the Fnet of those three forces. Like the Parallelogram Method we must graph F1, than
take the measurement of F2 and put it at the tip of F1 and draw a line, this is done for F2 and F3
with their consecutive measurements. The last line drawn is the Fnet which we measure with a
ruler; the last image should be one of a polygon.
3—Experimental Procedure and Results
There were two parts of the experiment; the first part only involved two forces. The first two
forces were 200 g at 50° angle, and 300 g at 150° angle. For the second part of the experiment
there were three forces involved. The three forces were; 0.150 kg at 120° angle, .250 kg at 110°
angle, and .100 kg at 155° angle.
3.1—Part 1: Two Applied Forces
For part one of the experiment we are told to place two pulleys, the first is a force of 0.200 kg
at a 50° angle, the second force is at .300 kg at a 150° degree angle. We are than supposed to
find the equilibrant by trial and error, once the equilibrant is found we are supposed to find the
mass by using a scale. After finding the angle of the equilibrant we are supposed to find the
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Fnet which is the angle measure of the equilibrant minus 180°. The force and mass of the Fnet
is the same as the equilibrant.
Data Table I
Mass
Degree
Force
F1
0.200 kg
50°
1.96 N
F2
0.300 kg
150°
2.94 N
FE1
0.3405 kg
295°
3.337 N
FR1
0.3405 kg
115°
3.337 N
Using the Parallelogram Method
The next part of the experiment is to determine the Fnet using a graphical solution, because
there are only two forces involved we must use the parallelogram method. This involves
drawing a scale image of the two forces and then using the scale image using a protractor to
find the Fnet. The scale for the graph can be 1N=3 cm, this can be shown by Graph I.
Graph I
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We are than told to put the geometrical solution on Data Table II along with the experimental
value, we are to compare and then find the percentage difference of the two magnitudes. The
data can be found down below on Data Table II.
Data Table II
Angle
Force
Percentage Difference
Experimental Value: FR1
115°
3.337 N (10.01)
Geometrical Solution: FR2
115°
3.333 N (10 cm)
1%
3.3—Part Two: Three Applied Forces
On part two of the experiment we were now working with three forces. The first force placed
on the pulley was 0.150 kg at a 20° angle, the second pulley was 0.250 kg at a 110° angle, and
the third was 0.100 kg at a 150° angle. After putting the three forces we were supposed to find
the equilibrant by trial and error.
Data Table III
Mass
Angle
Force
F3
0.150 kg
20°
1.47 N
F4
0.250 kg
110°
2.45 N
F5
0.100 kg
155°
0.98 N
FE3
0.3365 kg
278°
3.298 N
FR3
0.3365 kg
98°
3.298 N
Using the Polygon Method
After finding the data of the three forces by trial and error we were to confirm the data with a
graphical solution. Because there were three forces used we had to use the Polygon Method.
This involved using a protractor as well, there had to be a scale image first. Drawing F3 on the
graph was the first step than with the protractor we had to graph F4 at the end of the tip of F3
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this was done for all three forces until the Fnet was found. The scale is 1N=3cm, this can be
shown on the graph below Graph II.
Graph II
After finding the Fnet with a graphical solution the results were to be put in Table IV along with
the experimental results. After putting both results on the table the percentage difference was
supposed to be determined. This last step can be shown below on Table IV.
Table IV
Angle
Force
Experimental Value: FR3
98°
3.298 N (9.89 cm)
Geometrical Solution: FR4
98°
3.2 N (9.6 cm)
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Percentage Difference
9.8 %
4—Discussion
For time we have been studying force, vectors, and mass. This experiments shows us how there
are different vectors, and how in order for a vector to be a vector it must have direction. By
placing different forces on pulleys and finding the Fnet and the direction we were tested on
finding different vectors. Using the force table was not easy because if the right amount of
mass was not added than all of the numbers could be off. Using a graphical solution helps us
see the mistakes made in an experiment.
Using the parallelogram method was easier to use than the polygon method. It is necessary to
know both methods because the parallelogram is mostly used only when there are two forces,
but in many cases we have to deal with more than just two forces, which is when the polygon
method comes in handy. Once the percentage difference was calculated we were able to see
how off the numbers were, and some of the mistakes were seen.
5—Conclusion
After doing the experiment it is interesting how much we need math to explain certain things in
science, they both go hand in hand. They polygon method and the parallelogram method are
proof of how sometimes there needs to be two ways of finding things than just doing
experiments. Though doing trial and error gives us a good opportunity and guess on the
outcome using a mathematical way to show how we found something is proof. There is also the
fact that mistakes are made during an experimental procedure. When comparing the
experimental with the graphic solution the differences are seen, sometimes the differences
aren’t much but on other occasions they are. This experiment teaches us how to find the
resultant vectors in different ways. In case when there are two forces than we can use the
parallelogram method, and when there are more than two the polygon method can be used to
find the resultant vector.
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QUESTIONS
1. Scalars
are
physical
quantities
that
can
be
completely
specified
by
their
_______________magnitude_____________________________.
2. A vector quantity is one that has both ____magnitude___ and _________direction_______.
3. Classify each of the following physical quantities as vectors or scalars:
(a) Volume =scalar
(b) Force =vector
(c) Density =scalar
(d) Velocity = vector
(e) Acceleration = vector
Answer questions 4 to 7 with reference to Figure 3.1.
Figure 3.1 Addition of two force vectors.
4. If A stands for a force vector of magnitude 40.0 N and B stands for a force vector of magnitude
60.0 N acting in the directions shown in the figure, what is the magnitude and direction of the
resultant obtained by the addition of these two vectors using the geometrical (graphical)
method?
Magnitude = ___90___ N.
Direction (relative to x-axis) = ___38_____ degrees.
5. What is the equilibrant force that would be needed to compensate for the resultant force of the
vectors A and B?
Magnitude = __90___ N
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Direction (relative to x-axis) = ___218____ degrees
Two forces, one of magnitude 2.00 N and the other of magnitude 3.00 N, are applied to the ring
of a force table. The directions of both forces are unknown. Which best describes the limitations
on R, the resultant?
(a) 2 N ≤ R ≤ 3 N
(b) R ≥ 3 N correct answert
(c) 1 N ≤ R ≤ 5 N
(d) R ≤ 2 N
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