An Experimental Investigation of

the Acceleration Due to Gravity

❑ Student Names & ID Numbers
Blessing Mayer PMBChB25151730
Nathan T Mauwa BSN25152091
Course Code: BMPH120(Group B5)
Instructor: Mr S Banda
Dates Of Experiment: 26 August , 2025-August 25,
2025
 Abstract

This experiment was designed to determine an experimental value for the acceleration due
to gravity, g, by analysing the motion of a simple pendulum. A pendulum with a length of
0.486 meters was set up and allowed to oscillate at a small angle. The time for multiple sets
of oscillations was recorded using a stopwatch to accurately determine the average period of
one oscillation, which was calculated to be 1.346 seconds. By applying the formula for the
2
4𝜋 𝑙
period of a simple pendulum, 𝑔= 2 , the experimental value for the acceleration due to
𝑇
gravity was found to be 10.6 m/s². This result is slightly higher than the accepted standard
value of 9.81 m/s², with the difference likely resulting from experimental errors such as
reaction time during measurement or parallax error.
 Introduction

Gravity is a fundamental force of nature that pulls objects towards the centre of the Earth.
When an object is in free fall, it accelerates downwards at a constant rate, known as the
acceleration due to gravity (g). This value is a crucial constant in many areas of physics and
engineering. While the accepted standard value for 'g' at the Earth's surface is approximately
9.81 m/s², the actual value can vary slightly with location.

One of the most classic and effective methods for measuring 'g' in a laboratory setting is by
using a simple pendulum. A simple pendulum consists of a mass (often called a bob)
suspended from a fixed point by a lightweight string. When displaced from its resting
position and released, the pendulum swings back and forth in a predictable motion. The
time it takes to complete one full oscillation (one swing back and forth) is called the period
(T).

For small angles of displacement, the period of a pendulum is determined almost entirely by
its length (L) and the local acceleration due to gravity (g). This relationship is described by
the formula:

𝑇 =2 𝜋
√ 𝐿
𝑔

By rearranging this formula, we can solve for 'g':

2
4𝜋 𝐿
𝑔= 2
𝑇

Therefore, by accurately measuring the length of the pendulum and its period of oscillation,
we can calculate a reliable experimental value for the acceleration due to gravity.
 Materials

The following equipment was used to conduct the experiment:

 A pendulum bob

 Lightweight string
 A retort stand with a clamp and boss head

 A digital stopwatch
 A meter rule
 Methodology

 Apparatus Setup:

The apparatus was arranged as shown in the diagram. A pendulum bob was attached to a
string, and the string was suspended from a clamp stand.

 Length Measurement:

The length of the pendulum (L) was carefully measured from the point of suspension to the
center of the mass (the bob) and this value was recorded.

 Initiating Oscillation:

The pendulum bob was pulled to the side at a small angle (less than 15 degrees) from its
resting vertical position and then released smoothly to allow it to swing back and forth.

 Timing the Oscillations:

A stopwatch was used to measure the total time taken for the pendulum to complete a
specific number of full oscillations. A full oscillation is one complete swing back to the
starting point.

 Data Collection:

The experiment was conducted three times (three trials). In each trial, the time was
recorded for a different number of oscillations: 5, 10, and 15 oscillations.

 Calculating the Period:

For each trial, the period (T), which is the time for one single oscillation, was calculated by
dividing the total time measured by the number of oscillations.

 Determining the Final Value:

The average period from the three trials was calculated. This average period and the
measured length (L) were then used in the formula g = 4π²L / T² to determine the
experimental value for the acceleration due to gravity.
 Results

Given Data:

Length of the pendulum (L) = 0.486 m

Data Table:

Trial Number of Time taken (s) 𝑡

Period (𝑇 = ) (s)
oscillations 𝑛

1 5 6.68 1.336
2 10 13.46 1.346
3 15 20.34 1.356

Calculations:

 Average Period (T)

(1.336 +1.346+1.356 )
𝑇=
3

4.038
𝑇=
3

𝑇 =1.346 𝑠

❑ Acceleration due to Gravity (g)

 2
4𝜋 𝐿
Using the formula 𝑔= 2
𝑇
2
4 𝜋 ( 0.486 )
𝑔=
( 1.346 )2
19.186
𝑔=
1.8117

g = 10.6 m/s²

Comparison:
 Standard Accepted Value of g:

The commonly accepted value for the acceleration due to gravity on Earth is 9.8 m/s².

 Experimental Calculated Value of g:

Based on the data and calculations: 10.6 m/s².

 Absolute Difference:

The difference between the experimental and standard values is:

∣10.6 m/s2− 9.8 m/s2∣

=0.8 m/s2

The experimental value is 0.8 m/s² higher than the standard value.

Percentage Error:
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒− 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 = ⋅100 %
𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
10.6 −9.8
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 = ⋅100 %
9.8

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 ≅ 8.16 %

 Discussion

The goal of this experiment was to calculate the acceleration due to gravity, g. Based on
our measurements, the experimental value for g was found to be 10.6 m/s². The accepted
standard value for acceleration due to gravity on Earth is approximately 9.8 m/s². Our result
is higher than this accepted value. The percentage error for our experiment is calculated as:
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒− 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 = ⋅100 %
𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
10.6 −9.8
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 = ⋅100 %
9.8

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 ≅ 8.16 %

Interpretation of Comparison:

The experiment yielded a value for the acceleration due to gravity (g) that is 8.16% higher
than the standard accepted value of 9.8 m/s².

This level of error is common in introductory physics experiments due to various factors.
While the experimental value is in the correct order of magnitude, This difference between
our result and the standard value can be explained by a few potential sources of error.

 Human Error in Timing the Oscillations:

The most significant source of discrepancy is likely human error in timing the
oscillations. Reaction time when starting and stopping the stopwatch can affect the
"Time taken" measurement. If the stopwatch was consistently started late or stopped
early, the recorded total time (t) would be shorter than the actual time taken. A
shorter 't' would, in turn, lead to a shorter calculated period (T) for each trial. Since
2
4𝜋 𝐿
'g' is inversely proportional to T (𝑔=
2
2 ) an underestimation of 'T' would result
𝑇
in an overestimation of 'g', aligning with our experimental result of 10.6 m/s² being
higher than 9.8 m/s². Measuring a larger number of oscillations, as done in trial 3 (15
oscillations), helps to reduce the relative impact of a fixed reaction time error
because the error is averaged out over a longer duration, making the calculated
period more accurate. However, if the bias is consistent, it still affects the overall
average.
 Inaccuracies in Measuring Pendulum Length (L):
Another critical factor is the accurate measurement of the pendulum's length (L). The
 effective length of a simple pendulum is defined as the distance from the pivot point
to the centre of mass of the bob. Errors can arise if:

The measurement doesn't precisely account for the centre of the bob, the exact pivot point
is not clearly defined or consistently measured, the string itself has some mass, slightly
shifting the centre of mass.
If the measured length of 0.486 m was slightly longer than the true effective length of the
pendulum, this would directly lead to a higher calculated value of 'g' (as g∝L), which again
aligns with our experimental outcome.

 Other Potential Sources of Error:

Air Resistance: The presence of air resistance would dampen the oscillations and slightly
increase the effective period, which would contribute to a lower calculated 'g'.

Friction at the Pivot: Friction at the point where the pendulum is suspended would also
slightly lengthen the period, similarly leading to a lower calculated 'g'.

Non-Ideal Pendulum: The theoretical model assumes a massless string and a point-mass
bob. In reality, the string has a small mass, and the bob has a finite size, which slightly alters
the true center of mass and the moment of inertia, leading to deviations from the ideal
simple pendulum behavior.

Parallax Error: When reading measurements from a ruler for length or a protractor for angle
of release, parallax error (observing from an angle rather than directly perpendicular) can
lead to inaccuracies.

 Future Improvements:
The 8.16% percentage error, while notable, is acceptable for a basic laboratory
experiment. It indicates that the experiment was able to qualitatively demonstrate
the principle of a simple pendulum's relationship to gravity. To improve the accuracy
and reduce the percentage error in future experiments, several steps could be taken:

Automated Timing: Employing automated timing devices such as photogates connected to a

data logger would eliminate human reaction time errors, providing a much more precise
measurement of 't' and 'T'.

Precise Length Measurement: Using a plumb bob and a more accurate measuring tape,
along with careful consideration of the bob's center of mass, would refine the measurement
of 'L'.

Increased Trials: Conducting more trials and averaging the results would further minimize
the impact of random errors.

Minimizing External Factors: Ensuring the experiment is conducted in an environment free

from drafts and minimizing friction at the pivot point could also contribute to greater
accuracy.
 Conclusion

In this experiment, the acceleration due to gravity was determined using a simple pendulum.
Our calculated value for g was 10.6 m/s². While this value is reasonably close to the
accepted value of 9.8 m/s², the 8.16% error shows there were some inaccuracies in the
measurement process. The experiment successfully demonstrated the relationship between
the period of a pendulum and the acceleration due to gravity.

References

1. Bell, J. (2018) Doing Your Research Project: A Guide for First-Time Researchers. 7th
edn. Maidenhead: Open University Press.
2. Department for Education (2016) The Prevent duty: guidance for further education
institutions in England. London: Department for Education. Available at:
www.gov.uk/government/publications/the-prevent-duty-guidance-for-further-
education-institutions-in-england (Accessed: 23 October 2023).
3. Giddens, A. (2013) Sociology. 7th edn. Cambridge: Polity Press.
4. Patel, A. (2020) Challenges of Online Learning. Journal of Educational Technology,
4(2), pp. 15-28.
5. Smith, J. and Jones, P. (2019) 'Impact of Climate Change on Coastal Regions', in
Thompson, L. (ed.) Environmental Science Today. New York: Academic Press, pp. 112-
135.