G4_Acceleration of free fall by means of a simple pendulum Page 1/3
G4 Acceleration of free fall by means of a simple pendulum
Pendulum bob (e.g. a metal sphere with a hook attached, or with a hole bored through its centre), cotton thread,
stop-watch, metre rule, stand and clamp, protractor, pieces of paper, small improvised vice, vernier caliper
(available upon request), and triple beam balance (available upon request).
The periodic time T of a simple pendulum of length l is given by Length of the
T = 2π where g is the acceleration of free fall.
g Centre of mass
Please read the following suggested procedures critically. There are some mistakes and some of the
procedures may not be good enough to obtain a precise and accurate result in this experiment.
Tie a two-metre cotton thread to the pendulum bob and suspend the cotton thread from the jaws of an
improvised vice, such as two small wooden blocks held in a clamp. Alternatively two coins, two halves of a
cork split lengthwise, or the jaws of a pair of pliers serve equally well for the point of suspension when gripped
in a clamp.
Place a piece of paper with a vertical mark on it behind the pendulum so that when the latter is at rest it hides
the vertical mark from an observer standing in front of the pendulum.
Set the pendulum bob swinging through an arc of about 50°.
Measure the time for 1 complete oscillation with a stop-watch by setting the stop watch go when the pendulum
passes the vertical mark and stop it when it passes the mark in the same direction.
Measure the length L of the cotton thread from the point of suspension to the point of attachment to the bob.
Shorten the length of the pendulum by successive amounts of about l0 cm by putting the cotton thread through
the vice and for each new length take one observation of the time for 1 oscillation.
Plot a graph with values of T2 / s2 as ordinates against the corresponding values of L / m as abscissas to yield a
straight line and then determine the acceleration of free fall from it.
Some reflections you have to include in the experiment
1. Errors in timing occur both when the stop-watch is started and when it is stopped (reaction time). These
errors are unlikely to be less than the interval at which the second hand moves (scale uncertainty). What
type of error they are (random or systematic)? How are they related to the final error in the experiment?
2. The error in the experiment of L is the error inherent in the use of any scale (half the distance between
adjacent markings, doubled because of two ends to the distance measured). What type of error they are
(random or systematic)? How are they related to the final error in the experiment?
3. As the value for g is obtained solely from the slope of the graph it follows that the % error in g is the same
as the % error in the slope. Estimate the difference between the slope of your chosen ‘best’ straight line
through the points and the slope of other possible straight lines drawn through the points and express this
in percentage. State your value for g accordingly.
4. Compare your result with the standard value of g (9.81 ms-2). Discuss whether your experiment is precise
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5. State the physical meaning of the y-intercept of the graph you obtain and try to determine that physical
quantity directly. Compare the results from the graph and from direct measurement.
6. Suggest a method to measure the period of oscillations other than that used in the experiment. Comment
on the two methods.
7. If the experiment is performed with the pendulum suspended from an inaccessible point, e.g. the ceiling
(i.e. you cannot measure the length of the pendulum), suggest a modification to the experiment to find the
value of g.
Student should be able to
1. follow experimental procedures critically and
2. write a full lab report with suitable and appropriate format, organization and contents.
Before the Practical Session
1. Read the lab menu carefully and critically
2. Write the Objective, Theory and Method of the Lab report
During the Practical Session
1. Perform the experiment
2. Take data accurately and record them in an organized way
3. Analyze the data to obtain the result
After the Practical Session
1. Complete the full lab report
2. Hand in the full lab report the school day after the practical session or the date arranged
by your subject teacher.
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Guidelines for Full Reporting
(G4_Acceleration of free fall by means of a simple pendulum)
1. General Comments:
(a) Passive voice and past tense in reporting in general. You may use present tense in the theory part.
(b) Conclusion should be included.
(c) No point form is used and appropriate paragraphing is needed.
(d) Suitable graphs or diagrams to illustrate your description is expected.
(e) Better hand-writing is required but not necessarily printed.
2. Comments on each sections:
* Concise and usually start with “To ……..”
* the method is stated “…… by means of a simple pendulum.”.
* no setup is shown but the simple pendulum to illustrate
1. it is an approximated s.h.m.
2. how the period related to the length and the period of oscillation.
* Setup should be shown to illustrate how it is set and how the experiment is carried out.
* Measuring instrument should be stated : meter rule for the length L and stop watch for the time of several
oscillations (10 T or more).
* state what L is. What graph should be plotted? How g can be found?
(e) Data and Data Analysis
* Table should be used to represent your data and data analysis.
(f) Result with error and accuracy
* Give the scale uncertainty of measuring L and T and state the % error.
(Justify it is acceptable or not.) ! or put it in discussion!!
* Combine the two errors to see if the total errors is acceptable.
* State the graphical error and discuss the precision of the experiment.
* Give the answer with precision : g = _______ ± ________ ms-2.
* Compare the result with the expected value 9.81 ms-2
“The experiment value of g is _______% smaller / larger than the expected value 9.81 ms-2. ” State if it
is accurate or not.
(i) Random Error
" Discuss % Error due to scale uncertainty. i.e. justify if it is acceptable and state which
measurement is more significant. Is it the major source of error??
" Discuss % Error due to external factors, say the reaction time, elliptical oscillation and all
that. i.e. justify if it is acceptable and state which measurement is more significant. Is it
the major source of error??
(ii) Systematic Error
Discuss the error due to the design of experiment including the set up, say the extensible string,
oscillation of great angle and all that.
" How the systematic error affect the determination of g (over- or under- estimated??)
" Is the error acceptable? If not, how to tackle it? What is the corresponding improvement?
(iii) Implications, suggestions and improvements
Discuss the setup and the whole experimental design, i.e. questions of reflection stated in lab menu.
Simple state what result was found in this experiment and how accurate and precise it is.
“By means of a simple pendulum, the acceleration of free fall was found to be _______ ± _______ms-2
which is _____ % smaller or larger than the expected value of ____ ms-2.”