UNIVERSITY OF GAZIANTEP
DEPARMENT OF ENGINEERING OF PHYSICS
EP 135 GENERAL PHYSICS LABORATORY I
REPORT FOR EXPERIMENT 1
MEASUREMENT OF GRAVITATIONAL ACCELERATION
WITH SIMPLE PENDULUM
(do not write this: Repeating Experiments)
Group I
Isaac Newton
Albert Einstein
Werner Heisenberg
Abdus Salam
Date of Experiment :
Date of Submission :
Deadline :
18.11.2011
22.11.2011
25.11.2011
Lab Assistant(s):
Res. Ass. Hüseyin Toktamış
Res. Ass. L. Hasan Çite
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1. OBJECTIVE
The purpose of the experiment is to determine the gravitational acceleration, g, by
measuring the period of a simple pendulum.
2. THEORY
The simple pendulum is an example mechanical system that exhibits periodic motion.
It consists of a particle-like bob of mass m suspended by a light inextensible string of length L
that is fixed at the upper end, as shown in Figure 1. The motion occurs in the vertical plane
and is driven by the gravitational force.
Figure 1. A simple pendulum
The acceleration due to gravity for small angle swings of a simple pendulum (small dense bob
on a light inextensible string) is given by[1]:
𝑔 = 4π2
𝐿
𝑇2
(1)
where T is the period of the oscillation for the pendulum.
3. EXPERIMENTAL SETUP AND EQUIPMENTS
Apparatus: String, stop watch, meter stick, bob, support rods.
The pendulum consisting of the string and
bob is attached to meter stick via support
rods as shown in Figure 2. The bob is
manually pulled such that the pendulum
makes a small angle (such as 5o) with respect
to vertical direction. The time for the
required number of oscillations of the
pendulum is recorded by a stop watch. The
period is calculated by dividing the total
measured time to number of oscillations
counted.
Figure 2: The experimental setup
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4. PROCEDURE
i. Make a simple pendulum by using the support rods, bob, and string as shown in Figure 2.
ii. Construct a data table to record the following data for each trial.
Length (L), Initial angle (θ), Number of oscillations (N), Total time taken for the number
of oscillations (t), Measured period (T=t/N).
iii. Use stop watch to measure the time it takes the pendulum to complete 10 oscillations
iv. For the initial angle 5o, repeat the experiment for the fixed length L = 1.0 m, 15 times.
Record measured time values for each trial
v. Calculate g for each trial, evaluate the mean value, standard deviation and standard error of
Record the result, in the form of g ± σE.
vii. Compute percentage error to compare your result (g in previous case) with the very well
known measured value of 9.80665 m/s2[2].
5. RAW DATA
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6. DATA ANAYISIS
Table 1 shows calculated g values using Eqn (1). Since number of data is enough to find mean
and standard deviation, it is not necessary to compute the error propagation for each
measurement.
Table 1: Measured periods and corresponding calculated values of g.
Measurement
Time for 10
Period
Calculated g (m/s2)
#
oscillations t(s)
T = t/10 (s)
Eqn(1).
1
20.05
2.005
9.8204
2
20.09
2.009
9.7814
3
20.04
2.004
9.8302
4
20.04
2.004
9.8302
5
20.12
2.012
9.7522
6
20.09
2.009
9.7814
7
20.09
2.009
9.7814
8
20.09
2.009
9.7814
9
20.08
2.008
9.7911
10
20.04
2.004
9.8302
11
20.06
2.006
9.8107
12
20.09
2.009
9.7814
13
20.06
2.006
9.8107
14
20.06
2.006
9.8107
15
20.04
2.004
9.8302
Using Excel program or pocket calculator, we can compute the mean value, standard
deviation and standard error of the data above as follows:
𝑔=
∑ 𝑔𝑖 9.8204 + 9.7814 + ⋯ + 9.8302
=
= 9.8016 m/s2
𝑛
15
∑(𝑔𝑖 − 𝑔)2
(9.8204 − 9.8016)2 + ⋯ + (9.8302 − 9.8016)2
𝜎=√
=√
= 0.0245 m/s2
𝑛−1
15 − 1
𝜎𝐸 =
σ
√𝑛
=
0.0245
√15
= 0.0064 m/s2
7. RESULTS
The measured gravitational acceleration is:
9.8016 ± 0.0064 m/s2
The percentage error between the world best value and this measurement is
𝑃𝐸 =
|9.8016 − 9.80665|
× 100% = 0.05 %
9.80665
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8. CONCLUSION
By means of the simple pendulum, the gravitational acceleration was measured as 9.8016(64)
m/s2. To do that, the period of the pendulum was computed from 10 oscillations of the
pendulum. To get standard error, the measurement was repeated for 15 times for the fixed
length of 1.0 m. The measured g was reasonably close to the world’s best accepted value
listed in [2]. The percentage error between our measurements and the accepted value was
found to be 0.05%.
9. REFERENCES
[1]. “Physics for Engineers and Scientist”, Serway, 6th Ed. Chapter 15.
[2]. http://physics.nist.gov/cuu/Constants/index.html - Fundamental Physical Constants.
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