PEN 155 Physics Laboratory Report
Title Experiment: Force Table
Date: 22 October 2025
Instructor: Özgür Çıldıroğlu, Yunus Emre Özen
Group Number: 5
Lab Partner(s): Beliz Öztürk, Kardelen Güven, Elif Sıla Girgin, Ayşenaz Alcıl, Muhammed Kerim
Akçin
Responsible Student: Ayşenaz Alcıl
1.Objectives and Expectations
1.1. Objective:
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The purpose of this experiment is to learn how vectors are used to represents forces.
Also to learn how to sum vectors both algebraically and graphically.
1.2. Expectations:
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In this experiment we expect to see that the resultant and the equilibrant vector are equal in
magnitude but opposite in direction.
2. Introduction(Theoretical Background)
Force is the effect of one object on another , it can be the energy or cause of motion[3]. Force is a
vector quantity that can affect the velocity, direction and shape of an object[2].It can move a stationary
object, change its direction, or change its speed. Having both direction and magnitude makes it a vector
quantity[1]. The resultant vector represents a single force calculated from the direction and magnitude of
the force vector on the object. The equilibrant vector is a single force that balances two or more forces
. The equilibrant vector and resultant vector have the same magnitude but opposite direction . These
calculations can be proven using the tail to tip method and graph analysis method. All the vectors to
be processes must have the same units. This is a rule that applies both methods[2]. For tail to tip
method first the first vector must be drawn secondly you have to draw the other ones tail starting from
the tip of first one. And the resultant will be start with first ones tail and end with second ones tip [1].
For the graph analysis method first draw a cartesian plane. Then draw the vectors starting from the
origin. Draw their components using trigonometry. Then add the ones with the same direction and
subtract the ones with opposite directions on the axes. Draw the resultant vector.
Today, in our experiment, we will learn to draw force vectors and make related calculations using
these methods. First we will use two masses that will represent the forces after that we will find the
resultant vector of the first and second forces. Then we will place a third mass ,that will represent the
equilibrant vector, approximately. And we will calculate the mass at the correct angle and magnitude.
We will record the angles and errors while doing these.
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3. Experimental Setup
3.1 Equipment:
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Force Table
Masses
Ruler
Protractor
Centimeter-ruled Graph Paper
Figure.1. A Picture of Force Table
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Figure.2. A Picture of Protractor
3.2 Experimental Procedure:
1-) Setting the Force Table: First set up two vectors to be added on the force table. Do not need to
convert them gram to Newton.
2-) Attaching Pulleys: Attach two pulleys just like the way you set up the vectors. They will be
represents of the forces to be added.
3-) Guessing Equilibrant: The third one will be represent of the equilibrant vector. So position it
approximately for now.
4-) Attaching Masses: Place the three stringed ring over the center. Pass each one over a pulley.
Attach a mass hanger to each one. Place additional mass on the two strings. They are representing the
magnitudes of vectors that drawn.
5-) Adjusting the Strings: Move the string that represents the equilibrant to the right on left until the
ring is centered on the post. Hang the third pulley in the designed position.
6-)Measuring Angles with Protractor: Place additional mass on the third string. This mass will
balance the other ones. Make sure you set the angle and force correctly. Measure the angles carefully
and use the inner circle.
7-) Recording the Results: When the system is in balance, record this on the measurement table.
Record the measured value of “θ= Φ-180° ”
8-) Calculating: Calculate the magnitude and direction of the resultant vector using trigonometry. Calculate
the x and y components for each vector. Calculate the sum of the forces along the axes. Use these to
find the direction and magnitude of the resultant vector. Also calculate the “Φ = θ + 180° ”
9-) Adding Vectors using Centimeter-ruled Graph Paper: To add vectors graphically use these steps:
9.1-) Using a centimeter-ruled graph paper draw a cartesian plane then draw the vectors by following
“1cm=10g”
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9.2-) Draw the first one using a protractor, then draw the second one starting from the end of the
first one. Draw the arrow indicating the direction of the vector in middle, not its tip. This prevents
misunderstandings.
10-) Converting: Draw the resultant vector, measure its magnitude with a ruler. Then convert its units
to grams. Measure the angles.
4. Data and Analysis
4.1. Collected Data
Force
Magnitude(g)
������
��(°)
130g
�� = ��−180°(°)
21°
41°
Table 1 :Experimental data showing the force ,magnitude and directions forFinding the resultant vector.
There are 3 variable in this experiment.Force,magnitude and direction.We will use and we can find the
results of our experiment. ����(��) and ����(��) are our vector Componenets .First of all we
should formulas because formulas are show to us result of calculations.First force: magnitude which is
pull or push a object and there are two inportant things in this formula mass and accelereation .Also
acceleration have a formula .We can find accelereation in this shape :accelereation is speed divided By
time .Speed is distance divided by time.
F=m×a
a=v/t
v=x/t
4.2. Calculations
Force
��1
��2
Magnitude(g)
Direction, ��(°)
����(��)
100g
0°
100g
150g
120°
-75g
0g
∑���� = 25g
��
130g
221°
����(��)
∑���� = g
�� = ��+180° = 121°
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Result of experiment showing data in table :3 . This information that has been found after
measurement .Firstly there are 2 vectors F1 and F2.Magnitude (g) F1 is 100g and its direction is
0°.Then F2 have 150 magnitude (g) ,its direction 120°.Also knowing F1 and F2 have Fx and Fy
each other . Fx and Fy is calculated and finding equilibrium of a point. Kowing this point which
was chosen is not perfectly equilibrium for some reason .This result can know due to �� =
��−180°(°) this formula .
table
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Table
Graph
5. Discussion and Conclusion
1. Discussion: The purpose of this experiment was to understand how vectors work and to see how
the changes we made affected the result. Overall, this experiment shows that both magnitude and
direction of the vectors are necessary for physical descriptions.
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2. Consistensy with Theory: The results almost aligned with the theory because the tool used did not
have a perfectly distributed density as it should have. Despot this, the results were very close.
3. Data Analysis: Experimental data shows the relationship between the components of the weight
vectors and the resultant vector, as seen in figure 1 and figure 2.Calculated angles from the force
table confirms that The sum of vectors 1 and 2 has the same magnitude but opposite direction as the
resultant vector.
4.Graphical Interpratation: The 0.34 degree error observed in the graph shows that there is a margin
of error in the measurement, but this margin of error does not significantly affect the result.
5. Experimental Considerations: The force table has angle measurements to make it easier to see the
angles between masses. However, since the weight of the central disc used is not equal at every point,
some errors occurred in angle measurements. Still, the experiment turned out almost ideally.
6. Conclusion: In this experiment the results shows that, vectors have magnitudes and directions,
moreover adding two vectors produces a resulting vector. The magnitude and direction of the resulting
vector depends on the magnitude and direction of the component vectors.
6.References
[1] Douglas C. Giancoli, Physics Principles with Applications 7th edition,2014
[2]Raymond A. Serway,Physics for Engineers and Scientists,3rd edition, 1990
[3]https://languages.oup.com/google-dictionary-en/
Accessed on:22.10.2025
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