University Physics Lab: Acceleration Due to Gravity Experiment Report

This physics lab report details an experiment to determine the acceleration due to gravity using a simple pendulum. The report includes an introduction to gravity, the apparatus used, and the theoretical background, including the relevant equations for calculating the time period and acceleration due to gravity. The methodology involved varying the length of the pendulum and measuring the time period for multiple oscillations. The results section presents observations and calculations, including a table of string lengths and corresponding acceleration values. The report analyzes the results, discussing potential sources of error and comparing the experimental values with the standard value of 9.81 m/s². Error percentages are calculated and analyzed, and the report concludes with a discussion of the findings, including the average measured acceleration and potential improvements for future experiments, such as using more accurate measurement devices. The report also provides a list of references.

Running head: ACCELERATION DUE TO GRAVITY
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Title: Determination of Acceleration due to gravity
Student Name and Id
Course Name and Id
University
Date: 17/3/2020
Author Note
The current report is presented as part of the requirements to complete the course work.

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Contents
Aim:....................................................................................................................................3
Introduction:........................................................................................................................3
Diagram of the Apparatus Employed for determination of the Acceleration due to
gravity:................................................................................................................................3
Time period and the equation for estimation of the time period:.......................................4
Estimation of acceleration due to gravity...........................................................................5
Detailed Analysis and discusison of the results:................................................................6
Error percentages and possible reasons of uncertainities...................................................6
Results and Discussion.......................................................................................................7

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Aim:
The aim or objective of the current assignment is to investigate the acceleration due to gravity
using simple pendulum method. The finding of the acceleration due to gravity will be
compared with the standard values of acceleration due to gravity and implications of the same
will be made about.
Introduction:
Gravity is one of the important forces that act on the objects on earth. Gravity is the
combined effect of both the mass distributed within the earth as well as the centrifugal force
acting due to the rotation of the earth (Pili and Violanda 2019). Acceleration will be
measured in terms of m/s2. Acceleration due to the gravity is the acceleration induced in any
body due to gravitation of the earth. Acceleration due to gravity is about 9.806651m/s2.
Which mean any body freely falling on earth will be accelerated by acceleration of about ‘g’.
It is also the same force with which an object resting on the surface of a body of one unit
mass will be attracted towards the centre of the earth(Faller 2016).
Diagram of the Apparatus Employed for determination of the Acceleration due to
gravity:
Following is a simple schematic of the arrangement of the simple pendulum employed in the
current laboratory to determine acceleration due to gravity (Trail 2016).
Figure 1 Schematic
The time period of simple pendulum can be determined by using the first principles of
acceleration due to gravity. The time period of the simple pendulum will depend both on the

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length of the simple pendulum as well as the acceleration due to the gravity at the particular
locations. If the length of the simple pendulum is increased, acceleration due to gravity will
increase (Eisnstaedt 2018). Based on this relationship between the simple pendulum length
and acceleration due to gravity, time period of oscillations of the simple pendulum will be
determined for different lengths and from each of these values acceleration due to gravity will
be estimated (Campsie et al., 2017).
Detailed procedure for the same is as follows,
(i) Setting the length of the simple pendulum at 0.2 meters and increasing the same in
the steps of 0.2m till it reaches 1.2m.
(ii) For each length of the simple pendulum, estimating the time it will take for
making oscillations of about 10 in number.
(iii) Determining the average time period for making one oscillation.
(iv) From the values of the time period and the length set for the string of the simple
pendulum, acceleration due to gravity can be estimated using the following
equation (Garland 2016).
T = 2π* Sqrt (L/g)
Acceleration due to gravity (g) = (4* π2 * L)/T2
L is the length of the string of the simple pendulum
T is the time period of oscillation of the simple pendulum
Time period and the equation for estimation of the time period:
From Figure-1, simple pendulum restoring force can be estimated as mgsinϴ
Suppose the bob has travelled through a distance of s during the process of regaining its
original mean position, restoring force will be related by the following equation,
Spring constant of the simple pendulum can be determined using the equation
k = (mgsinϴ)/Lϴ

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The limiting value of K from the above equation will be equal to mg/L.
K=mg/L
Hence from the first principles for determination of the time period for simple harmonic
objects, (Kavitha et al 2013).
T = 2*π*sqrt (m/k)
Which mean that Time period
(T) = 2* π* Sqrt(L/g)----------------------(2)
Above equation is the basic equation employed for estimation of acceleration due to the
gravity of the simple pendulum (Krisnanda et al 2020).

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Estimation of acceleration due to gravity
Following are the observations for the each string length for time period of about 10
oscillations:
Table 1 Observations and calculations
S.No Length
of the
string
(m)
Time measured for about 10 oscillations 4* π2* L T2 Acceleration
due to
gravity(g)
m/s2
1
measure
2
measure
Average
time
period
(seconds)
Time
perod for
one
oscillation
(seconds)
1 0.2 9.2 9.59 9.4 0.94 7.8957 0.98827 8.945326
2 0.4 10.53 11.5 11.02 1.102 15.7914 1.2133 13.0152
3 0.6 14.68 14.22 14.45 1.445 23.6871 2.0880 11.34424
4 0.8 16.32 16.94 16.63 1.663 31.5627 2.7656 11.41998
5 1.0 17.03 17.10 17.07 1.707 39.4784 2.9121 13.56649
6 1.2 16.90 16.50 16.70 1.670 47.3741 2.7889 16.98666
Average acceleration due to gravity 12.54465
Acceleration due to gravity as determined in the experiment for different string lengths is
depicted in the following figure,

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Figure 2 Acceleration due to gravity
From the above figure, it is evident that the acceleration due to gravity is changing as per the
variations in the string lengths of the simple pendulum (Pierratos and Polatoglou 2017). The
values found have increased first and decreased for the third reading and later on
continuously increased till it took a maximum value of 16.9866m/s2.
Detailed Analysis and discusison of the results:
(i) Acceleration due to gravity value should not actually change from observation to
observation since principally acceleration due to gravity is fixed and will not
change (Pili and Violanda 2019). However still based on the first reading
obtained in the experiment, it is found to be 8.94m/s2, which is less than the
standard value. The reason for this deviation from the actual result of the
acceleration due to gravity can be mainly due to the measurement error in the time
period. Since the time period is too less for this length, it is possible that it might
have measured larger than the actual value. At the same time, the actual string
length measured might be smaller than the actual value. Due to these concerns,
the measured acceleration due to gravity value found to be smaller than the actual
value (Schlamminger, Gundlach and Newman 2015).
(ii) The second measurement of the acceleration due to gravity is higher than the
actual value of 9.81 m/s2. This might be due to the fact that the length measured is
higher than the actual or alternatively the time period might be erroneously
measured as lower than the actual value(Traill 2016).

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(iii) Readings 3, 4, 5. 6 all gave the value at higher side than the actual standard value
of the acceleration due to gravity. However the variation of these time periods is
actually found to have increased gradually at higher rate. Hence it is more likely
that the error is in time period estimation. Since the time period estimation is
measured lower than the actual value, the acceleration due to gravity measured in
the current case is lower than the actual values and hence the values are not
correct.
Error percentages and possible reasons of uncertainities
Assuming that the error in the acceleration due to gravity = (g-g’)/g
Following are the set of acceleration due to gravity values and their corresponding
error percentages
Table 2 Error percentages
S.No g Error %
1 8.945326 -8.81421
2 13.0152 32.67278
3 11.34424 15.63955
4 11.41998 16.41162
5 13.56649 38.29246
6 16.98666 73.15657
Error values are negative in the first reading and gradually has increased from the
second reading to as high as 73%. Percentage difference from the actual value has
increased drastically as both the length and the time periods have increased.
This error might be due to the fact that the length of the string might have
measured larger than the actual and also the time period of the pendulum might
have measured lower than the actual values.
This uncertainty can be further reduced by improving the accuracy of the devices
employed for measuring as well by introspecting the actual methods employed for
measuring the length and the time period value of the simple pendulum
oscillation.

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If the length is measured by a measuring tape, it needs to be verified by other
standard measuring tape. Also the time period can be checked with an another
stop watch to eliminate the likelihood of error associated with the first stop watch.
Cummulatively the determination of the Timeperiod of the length accurately will
make sure that the measured time period values are accurate.
Results and Discussion
The actual acceleration due to gravity measured in this particular experiment at an average
value of 12.54 m/s2.This value is higher than the actual standard value of acceleration due to
gravity of about 9.81m/s2. This is about 33% higher than the actual acceleration due to
gravity measured. The higher value of the acceleration due to gravity might be due to the
measuring errors as well as experimental errors too. One possible scope of repetition of the
experiment is to employ other devices of measurement of the string length as well as the time
period and the values determined so can be cross verified to get more accurate findings from
the experiment.

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References
Campsie, P., Hammond, G.D., Middlemiss, R.P., Paul, D.J. and Samarelli, A.,
2017. Measurement of acceleration.
Eisenstaedt, J., 2018. The curious history of relativity: how Einstein's theory of gravity was
lost and found again. Princeton University Press.
Faller, J.E., (2016), August. The Measurement of the Acceleration Due to Gravity.
In Heiskanen Symposium Proceedings (No. Heiskanen Symposium
Proceedings).
Garland, G.D., 2016. The Earth's Shape and Gravity: The Commonwealth and International
Library: Geophysics Division. Elsevier.
Kavithaa, R., Babu, R.U. and Deepak, C.R., 2013, July. Simple pendulum analysis—A vision
based approach. In 2013 Fourth International Conference on Computing,
Communications and Networking Technologies (ICCCNT) (pp. 1-5). IEEE.
Krisnanda, T., Tham, G.Y., Paternostro, M. and Paterek, T., (2020). Observable quantum
entanglement due to gravity. npj Quantum Information, 6(1), pp.1-6.
Pierratos, T. and Polatoglou, H.M., 2017. Study of the conservation of mechanical energy in
the motion of a pendulum using a smartphone. Physics Education, 53(1),
p.015021.
Pili, U. and Violanda, R., (2019). Measurement of the gravitational acceleration using a
simple pendulum apparatus, ultrasonic sensor, and Arduino. Physics
Education, 54(4), p.043009.
Schlamminger, S., Gundlach, J.H. and Newman, R.D., (2015). Recent measurements of the
gravitational constant as a function of time. Physical Review D, 91(12),
p.121101.
Traill, D., (2016). An Explanation for Gravitational Acceleration. Global Journal of Physics
Vol, 4(2).