An experiment to determine the acceleration
due to gravity using a pendulum bob
in the school physics lab
Done by China Suetani Year 12i
06/09/2012
IB Higher Level Physics Internal Assessment
An experiment to determine the value of the acceleration due to
gravity using a pendulum bob in the school physics lab
★Research Problem
There is gravity on the earth. It causes thing are pulled downward. The definition of
gravity is said that the natural force of attraction exerted by a celestial body, such as
Earth, upon objects at or near its surface, tending to draw them toward the center of the
body. And which is about 9.8m/s². However gravity changes depend on where you are
(latitude and altitude) on the earth. The aim of the experiment was calculating
acceleration due to gravity in our school in Malaysia at. To solve the problem I made an
experiment with a pendulum bob.
★Hypothesis
I hypothesised that gravity will be lower than 9.8m/s², because Malaysia locates low
latitude which means that gravity would be lower. Also Uplands school located higher
than sea level and I made this experiment in the class room on the 3rd floor which
means that gravity would be lower as it is further from the middle of the earth.
★Variables

Independent Variable – total length and time
The length of tread was measured with a metre ruler which has 0.1cm as the smallest
scale. Therefore the result is put nearest 0.05cm

Dependent Variable – acceleration due to gravity
The formula for acceleration due to gravity is

Controlled Variables – use same pendulum bob, same type of thread, same
metre ruler, same retort stand and digital stopwatch, make experiment in
same surrounding and location, and same person to time and push the
pendulum bob
Same tools, surroundings and persons for more accuracy

Same pendulum bob must be used to keep the radius, the air resistance and friction
between the bob and thread, same the mass of it might affect the result

Same type of thread must be used to keep the air residence, and friction between
the bob and thread and between thread and the retort stand, same

Same metre ruler must be used to keep the measuring scale exactly same

Same retort stand must be used to keep the friction between the thread and the
stand same and make sure that the stand does not move when the pendulum is
moving

Same digital stopwatch must be used for same sensitivity of the stopwatch

Same surrounding must be kept as wind from fan or air conditioner or just people
pass behind, would change the time taken.

Same location for the experiment as latitude and altitude change the result

Same person to time as reaction time is different by other person

Same person to push the pendulum bob as the releasing timing affect to the result
For more accuracy…..

Took the time for 20 times and calculate the average to make human error smaller

Do the experiment 5 times for each length and calculate the average for each length
to make human error smaller

Do the experiment with 5 different length to take 5 different types of data

Made sure that the pendulum is not turning when it is swinging as it affects the
result

Made sure that the centre of gravity on the pendulum bob should be on the
extension of the threat
★Apparatus

Pendulum bob

Thread

Retort stand

Metre ruler (smallest scale - 0.100cm, accuracy ±0.050cm)

Stopwatch (smallest number – 0.010seconds, accuracy ±0.010seconds)

Vernier calliper(smallest scale – 0.010cm, accuracy ±0.001cm)
★diagram
★Method
1.
Firstly check tools you use. For example the retort stand should be balances on the
horizontal. Also set tools as u can u them easily.
2.
Secondly measure the radius of the pendulum by using vernier calliper and record
the value.
3.
Then take about one metre of the thread. Attach one side of the thread with the
retort stand and another end with the pendulum bob, then record the length
4.
Next stand in front of the stand and push the bob to right/left side by using the
metre ruler. Put ‘start’ on the stopwatch and remove the ruler at the same time.
5.
Count 20 times the bob comes to the one side which you started with and record the
time it spend to swing for 20 times.
6.
Repeat same experiment 5 times and record them as you did in process 5.
7.
You roll the thread around the stand to make the thread shorter and record. Now do
same things from process 4 and repeat that 5 times to take 5 different data.
★Data collection

Diameter (D) = MSR + (LC
Pendulum bob radius
VSR)
Main scale reading (MSR)
D = 2.5 ＋ (00.1 × 3)
= 2.500cm ± 0.050cm
List count (LC) = 0.01cm ± 0.050cm
Vernier scale reading (VSR) = 3

= 2.53 ± 0.050cm
Radius (R) = Diameter (D) / 2
2.53 / 2 = 1.265
Raw data
Test
Length of thread
Radius of Pendulum
number
(l) / cm /±0.05cm
bob (r) / cm / ±0.005cm
Radius (R) = Diameter (D) / 2
Total length (L) / Time for 20 oscillations (T₁)
2.53 / 2 = 1.265
cm / ±0.055cm
/ seconds / ±0.01 seconds
38.13
38.03
1
91.00
1.265
92.265
38.50
38.15
38.75
35.43
35.60
2
76.80
1.265
77.065
35.50
35.63
35.46
32.75
32.75
3
65.50
1.265
66.265
32.71
32.62
32.71
31.21
31.22
4
58.70
1.265
59.965
31.35
31.15
.31.16
28.78
28.63
5
49.50
×
1.265
50.765
28.41
28.84
24.90
★Data analysis
Time for 1
Average time
Uncertainty
Test
oscillation for
for 1 oscillation
of T /
number
each time (T₀) /
(T) / seconds
seconds
seconds (2d.p.)
(2d.p.)
(2d.p.)
1.92
±0.02
3.69
±0.07
25.00
(*2)
(*3)
(*4)
(*5)
(*7)
1.78
±0.01
3.17
1.64
±0.01
2.69
±0.03
24.63
1.56
±0.01
2.43
±0.03
24.68
1.44
±0.02
2.07
±0.05
24.52
T² /
seconds²
(2d.p.)
Uncertainly
of T² /
L /T²
seconds²
(2d.p.)
(2d.p.)
Average
of L /T²
(2d.p.)
1.91 (*1)
1.90
1
1.93
1.91
1.94
1.77
1.78
2
1.78
1.78
±0.04
(*6)
24.31
1.77
1.64
1.64
3
1.64
1.63
1.64
1.56
1.56
4
1.57
1.56
1.56
1,44
1.43
5
1.42
1.44
1.45
24.63
(*8)
 Calculation
Time for 1 oscillation for each time (test number 1, 1st experiment)
Time for 1 oscillation = time for 20 oscillation / 20
X
=
38.13
/ 20
X
=
1.91 ( 2 decimal points ) ⇠(*1)
Repeat the calculation with other figures
Average time for 1 oscillation (test number 1)
Average time for 1 oscillation
= (time for 1 oscillation for 1st experiment ＋ 2nd ＋ 3rd ＋ 4th ＋ 5th) / 5
X = (1.91 ＋ 1.90 ＋ 1.93 ＋1.91 ＋
X = 1.92 (2 decimal points) ⇠(*2)
Repeat the calculation with other tests
Uncertainly of Average time for 1 oscillation (test number 1)
Uncertainly of Average time for 1 oscillation
= (biggest figures for 1 oscillation in experiment 1 － smallest figure) / 2
X
=
( 1 . 9 4
－
1 . 9
X
=
0 . 0 2
( 2 decimal points )
Repeat the calculation with other tests
Square of average time for 1 oscillation (test number 1)
1 . 9 2 ²
=
3 . 6 9
( 2
d e c i m a l
Repeat the calculation with other tests
0
1.94)
)
⇠
p o i n t s )
(
/
*
/
5
3
2
)
⇠ ( * 4 )
Uncertainly of Square of average time for 1 oscillation (test number 1 and)
If the longest time for 1 oscillation for each time in the test has the biggest difference with the
average for 1 oscillation is….(like test number 1)
Uncertainly of Square of average time for 1 oscillation
= (longest time for 1 oscillation for each time)² －Square of average time for 1 oscillation
=
(1.94)² − 3.69
=
0.07 (2 decimal points) ⇠(*5)
If the shortest time for 1 oscillation for each time in the test has the biggest difference with the
average for 1 oscillation is….(like test number 2)
= Square of average time for 1 oscillation − (shortest time for 1 oscillation for each time)²
=
3.17
− (1.77)²
=
0.04 (2decimal points) ⇠(*6)
Repeat the calculation with other tests
Total length per square of average time for 1 oscillation (test number 1)
92.265
/
3.69
=
25.00 (2 decimal points) ⇠(*7)
Repeat the calculation with other tests
Average of the value of total length per square of average time for 1 oscillation (test number 1)
= (total length per square of average time for 1 oscillation for 1st experiment ＋2nd ＋3rd ＋4th
＋5th) / 5
= ( 25.00 ＋ 24.31 ＋ 24.63 ＋24.68 ＋ 24.52 ) / 5
=
24.63 (2decimal points) ⇠(*8)
Repeat the calculation with other tests

Calculation of acceleration due to gravity
We use T = 2π√L/g to know the relationship between length of pendulum, gravity and time in the
pendulum experiment.
This time I want to solve the gravity, so rearrange the formula to g/4π² = L/T²
I use average figure of L/T² for the calculation
g/4π² = L/T²
g/4π² = 24.63
g = 24.63×4π²
g = 972.3534
g = 972.3534 / 100
g = 9.72m/s² (2decimal points)

Graph
★Conclusion
From the graph, the best fitted line shows that the slope (the value of L/T²) is 25.23. As the value is
the answer of divided by 4π²(g/4π² = L/T²), we have to multiply it with 4π².
25.23 × 4π² = 996.04048
996.04048 / 100 = 9.96 (2 decimal points)
Again, from the graph, calculate the maximum and minimum.
Maximum
Minimum
(3.65 92.25)
(3.73 92.25)
25.27 × 4π² = 997.7764
24.73 × 4π² = 976.3013
997.7764 / 100 = 9.98 (2 decimal points)
976.3013 / 100 = 9.76 (2 decimal points)
Uncertainty is (9.98 － 9.76) / 2 = ±0.11
My final result is…9.96 ±0.11
Even if I got acceptable answer (9.96 ± , there should be some errors that the final value of the
experiment became bigger than 9.8m / s².
 Percentage error
Error from my final value
(9.96 － 9.8) / 9.8 × 100% = 1.63% (2 decimal points)
Error from my calculated value
(9.96 － 9.72) / 9.8 × 100% = 2.45% (2 decimal points)
★Errors and improvements
Errors
How it could have affected the
result of the experiment?
Possible improvement
They caused making wind. And
the wind might change the time
of the oscillation.
Doing the experiment alone in
the room, and close the door,
turn off the air conditioner and
fan if there is any.
The result change depends on the
person who do the experiment.
Time for more than 20
oscillation, then the error
would be smaller
or
Use software which can
recognise when the pendulum
reach the determined degrees
where the pendulum bob was
released, and take time
Air conditioner was on
Students walked pass just
behind the table where the
experiment was carried
There must be human error
when I started and stopped
stopwatch.
The gravity changes depend on
the time I make the experiment
as the earth I rounding (the
distance between the moon / sun
change)
I did the experiment in two
classes on the different day
and time.
Temperature rising causes
particles in the air move quicker
which means more air resistance
will be occurred.
Difference of atmospheric
pressure causes deferent air
resistance (lower atmospheric
pressure → lower air resistance)
The experiment had to be done
on the same day and within
shorter time.
The experiment had to be done
in night time as the
temperature will not change a
lot.
Use of threat and not heavy
pendulum bob.
Threat might stretch when bob is
attached. That means the total
length change.
Use stronger and not stretchy
line such as piano wire.
Light pendulum bob gets bigger
effects by air resistance.
Use heavier pendulum bob
There must be the friction
between stand and threat,
and threat and pendulum
bob.
Friction between them makes the
pendulum bob swing slowly,
especially when the bob reaches
the highest points, the friction
works more and it causes total
time become longer.
It is impossible to make it no
friction but we can make it
smaller by using smoother line
like fishing line or make the
surface of stand and pendulum
bob smoother by filing.
Although I tried hard to not
the bob turning, it did not
perfectly swing. It should
have been turning a little.
Turning makes the friction bigger
and it makes difficult to see
whether the bob reaches the top
or not.
I did not measure the degree
when I leave the pendulum
bob.
The bigger angle when it is
released, makes more air
resistances
We can use two
stands and two
pieces of threat
for supporting
the bob
Provide the
perpendicular
top of the stand.
Decide the angle
(less than 4°is
better as dropping from more
than 5°makes more than 0.1%
error.)