Valenzuela City School of Mathematics and Science
A. Pablo St., Malinta, Valenzuela City
The Sway of Time: An Experiment Investigating the Acceleration Due to Gravity Using a Simple Pendulum
12-Hobbes SOLIVIO, James Jastine E.
Proponent Quitalig, Lance Jasper A.
Lab Partner
Chapter I Description of the Physics Being Investigated
The gravity (or the gravitational force) is the natural force of attraction that tends to draw bodies together and that occurs because of the mass of the bodies. It was first discovered by Sir Isaac Newton when he witnessed the fall of an apple from a tree in the 17th Century. Newton’s curiosity on why does the apple fell lead him to discovering that it is the same force that caused the apple to fall and the moon to orbit the Earth. This first was called gravitational force of attraction, and in honor of his great contribution to this field, the unit of force newton (N) is named after him. Newton described gravitational force as having these three characteristics: (1) All masses attract one another with gravitational force; (2) The larger the masses, the stronger the force; and (3) The smaller the distance between the masses, the stronger the force. Gravity, denoted by g , is a constant. This idea was discovered by Galileo when he challenged the claim of the famous philosopher Aristotle and led this curiosity to his discovery that the acceleration of the all objects, regardless of its size or mass, due to Earth’s gravitational force is the same. This discovery is the core scientific knowledge today. The aim of this experiment is to calculate the acceleration due to gravity of a body, and to prove Galileo’s claim that the gravitational force is constant to any body of different size or mass,. To test this idea, the proponents used a pendulum, a body that swings freely from a fixed point. Using the Simple Harmonic Motion (SHM) equation
=2√ ,
the proponents can calculate the value of g with the given lengths and time the pendulum completed a specific number of oscillations. Chapter II The Procedure
In this experiment, the proponents used a simple pendulum to measure the a cceleration due to gravity of any object. The materials used were: (1) pendulum bob; (2) string/yarn; (3) iron stand; (4) clamp; (5) ruler; (6) stopwatch; and (7) weighing scale. Two pendulum bobs of different size and weight were used in conducting the experiment. These bobs were tied in a string or yarn of different lengths — 0.1 ± 0.0005 m, 0.2 ± 0.0005 m, 0.3 ± 0.0005 m, and 0.4 ± 0.0005 m — to show the effect of different pendulum lengths to the period of oscillation. Using the weighing scale, the pendulum bobs were then measured their weight, and they measured 64 ± 0.1 g and 26 ± 0.1 g. The pendulum setups with lengths 0.3 ± 0.0005 m were shown in the figure 1.
F igure 1. Pendulum setups of two different pendulum bobs. From left: pendulum bobs of mass 64 g and 26 g. After finishing the setups, eight tests were conducted to each pendulums, where four of them started in the angle and the another four started in small angles (about to ). The proponents let the pendulum to oscillate until it completed 30 oscillations and the time was recorded.
90°
10° 15°
F igure 2. Oscillating pendulum at length 0.3 m. The whole process was repeated for the other setups. The time results of the experiment were recorded in a table and computations followed using the given equation (1) for the Simple Harmonic Motion (SHM) below:
=2√
()
4 =
()
where T is the time for 30 oscillations, L is the length of the pendulum from the middle of the pendulum bob, and g is the gravitational force. But what is needed to be solved is g , so using the equation (1), the resulting equation will become the equation (2) below which will be used in computation:
Chapter III The Results
The results of the experiment were then written in a table for organization. The computations needed were also included in the table. The given variable were L, t , T , and g , where L is for the length of the pendulum from the center of the pendulum bob, t is for the time for 30 oscillations, T is for the time for 30 oscillations divided by 30, and g is for the gravitational acceleration. The results for the test in small angles (about to ) were found in the Table 1.
10° 15° ° °
Table 1. Results of the experiment in small angles (about L (in m)
0.1 ± 0.0005 0.2 ± 0.0005 0.3 ± 0.0005 0.4 ± 0.0005 0.1 ± 0.0005 0.2 ± 0.0005 0.3 ± 0.0005 0.4 ± 0.0005
mass (in g)
64 ± 0.1 64 ± 0.1 64 ± 0.1 64 ± 0.1 26 ± 0.1 26 ± 0.1 26 ± 0.1 26 ± 0.1
t (in sec)
19.68 ± 0.01 26.10 ± 0.01 32.90 ± 0.01 38.22 ± 0.01 18.78 ± 0.01 27.13 ± 0.01 33.20 ± 0.01 37.46 ± 0.01
T (in sec)
0.66 ± 0.30 0.87 ± 0.30 1.10 ± 0.30 1.27 ± 0.30 0.63 ± 0.30 0.90 ± 0.30 1.11 ± 0.30 1.25 ± 0.30
to
).
T 2 (in sec2)
0.44 ± 0.60 0.76 ± 0.60 1.21 ± 0.60 1.61 ± 0.60 0.40 ± 0.60 0.81 ± 0.60 1.23 ± 0.60 1.56 ± 0.60 Average:
= .
(in
m/s2 8.96
10.38 9.78 9.80 9.86 9.74 9.62 10.11 9.78
After the conducting the tests in small angles, the proponents repeated the procedures in different angle of . The results of the experiment were found in Table 2.
90°
Table 2. Results of the experiment in L (in m)
0.1 ± 0.0005 0.2 ± 0.0005 0.3 ± 0.0005 0.4 ± 0.0005 0.1 ± 0.0005 0.2 ± 0.0005 0.3 ± 0.0005 0.4 ± 0.0005
mass (in g)
64 ± 0.1 64 ± 0.1 64 ± 0.1 64 ± 0.1 26 ± 0.1 26 ± 0.1 26 ± 0.1 26 ± 0.1
°
angles.
t (in sec)
19.39 ± 0.01 28.90 ± 0.01 36.22 ± 0.01 41.37 ± 0.01 20.83 ± 0.01 28.36 ± 0.01 35.48 ± 0.01 40.16 ± 0.01
T = t/30 (in sec)
T2 (in sec2)
0.65 ± 0.30 0.96 ± 0.30 1.21 ± 0.30 1.38 ± 0.30 0.69 ± 0.30 0.95 ± 0.30 1.18 ± 0.30 1.34 ± 0.30
0.42 ± 0.60 0.92 ± 0.60 1.46 ± 0.60 1.90 ± 0.60 0.48 ± 0.60 0.90 ± 0.60 1.39 ± 0.60 1.79 ± 0.60 Average:
= . m/s2 9.39
8.57 8.10 8.30 8.22 8.76 8.51 8.81 8.58
(in
Chapter IV The Analysis
In the given variables, the independent variable is the t and the dependent variable is the g , since the value of the g will be dependent on the value of the t . After knowing the independent and dependent variables,
