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Aim:
To find the gravity by finding the period of the oscillations of a pendulum and plotting a graph.
Hypothesis and Prediction:
the gravity from the graph is going to equal the gravity from the formula.
Variables:
The independent variable is the length of the string
The Dependent variable is the period of one oscillation
Controlled variables are: mass of the pendulum
Equipment:
-Brass Ball
-string
-boss and clamp
-stopwatch
-2 metal blocks
-Meter Ruler
-Micrometer
-The diameter of the brass ball was measured using a micrometer. Then the value was divided by 2 to give the radius
-the length of the string was measured
-two metal block were clamped with the string in between, the string was tied to the bob
-the bob was pulled to the side and released
-the time was started when the bob passed the reference line.
-a full oscillation is when the bob passes the reference line forth back and forth again.
the length of the string is increased or decreased in a regular pattern
the time was monitored by reading through the stopwatch.
-the same brass ball was used over the experiment to keep the mass constant.
the length was varied 10 times with a 10 cm difference.
-4 readings were taken for each 10 cm
-the time was taken for 20 oscillations. And then divided by 20 to give one oscillation.
Data Collection:
Table number
Length of String / M
0.05
Number of oscillations
Time Taken/s
0.5
Period/s
0.5
1
1.01
20
39.65
1.9825
20
41.93
2.0965
20
39.82
1.991
20
39.94
1.997
2
0.91
20
37.25
1.8625
20
37.34
1.867
20
37.82
1.891
20
37.35
1.8675
3
0.81
20
35.25
1.7625
20
35.6
1.78
20
35.25
1.7625
20
36.13
1.8065
4
0.71
20
33.37
1.6685
20
33.07
1.6535
20
33.16
1.658
20
33.06
1.653
5
0.61
20
30.53
1.5265
20
30.31
1.5155
20
30.29
1.5145
20
30.75
1.5375
6
0.51
20
28.28
1.414
20
28.29
1.4145
20
27.91
1.3955
20
28.9
1.445
7
0.41
20
25.59
1.2795
20
25.21
1.2605
20
24.75
1.2375
20
24.94
1.247
8
0.31
20
21.94
1.097
20
21.79
1.0895
20
22.09
1.1045
20
21.75
1.0875
9
0.21
20
18.28
0.914
20
18.22
0.911
20
19.19
0.9595
20
18.34
0.917
10
0.11
20
13.44
0.672
20
13.34
0.667
20
13.35
0.6675
20
13.41
0.6705
The table contains the length of the string in meters, the number of oscillations, the time per 20 oscillations and the period of one oscillation.
As the length of the string deceases , the time for 1 oscillation decreases. So the length of the string is directly proportional to the period.
Data Processing and presentation:
Example in working out average period when the string is 1.01 m:
1.9825+2.0965+1.991+1.997=8.067
8.067/4=2.01675
The same procedure is used for the rest.
Length of string/m
0.05
Average Period/s
0.5
Average Period Squared
Gravity
1.01
2.01675
4.067280563
9.803405781
0.91
1.872
3.504384
10.25154778
0.81
1.777875
3.160839516
10.11678008
0.71
1.65825
2.749793063
10.19337669
0.61
1.5235
2.32105225
10.37539536
0.51
1.41725
2.008597563
10.02390591
0.41
1.256125
1.577850016
10.25835856
0.31
1.094625
1.198203891
10.21387892
0.21
0.925375
0.856318891
9.681519102
0.11
0.66925
0.447895563
9.695621703
The graph is plotted with Average period squared against length of string.
Y=3.9244x-0.0087
3.9244=gradient.
3.9244= (4(pi)^2)/g
g = (4(pi)^2)/3.9244
g=10.060 from the graph.
The average gravity from the formula=
100.614/10= 10.614
Conclusion:
the results where very close to the prediction but they werent the same as the graph is a scatter diagram.
-the result from the graph is more accurate as the graph cancels inaccurate measurements.
Evaluation:
-the method had weaknesses.
-the angle of the pendulum to the reference line isnt the same in each reading which might cause a slight error.
-the Air conditional may effect the pendulum; it may change its speed or change its direction.
it is difficult to stop the stopwatch and start it in the reference line exactly which might induce error
sometimes the ball tends to move in a circular motion and the experiment will have to be repeated.
To find the gravity by finding the period of the oscillations of a pendulum and plotting a graph.
Hypothesis and Prediction:
the gravity from the graph is going to equal the gravity from the formula.
Variables:
The independent variable is the length of the string
The Dependent variable is the period of one oscillation
Controlled variables are: mass of the pendulum
Equipment:
-Brass Ball
-string
-boss and clamp
-stopwatch
-2 metal blocks
-Meter Ruler
-Micrometer
-The diameter of the brass ball was measured using a micrometer. Then the value was divided by 2 to give the radius
-the length of the string was measured
-two metal block were clamped with the string in between, the string was tied to the bob
-the bob was pulled to the side and released
-the time was started when the bob passed the reference line.
-a full oscillation is when the bob passes the reference line forth back and forth again.
the length of the string is increased or decreased in a regular pattern
the time was monitored by reading through the stopwatch.
-the same brass ball was used over the experiment to keep the mass constant.
the length was varied 10 times with a 10 cm difference.
-4 readings were taken for each 10 cm
-the time was taken for 20 oscillations. And then divided by 20 to give one oscillation.
Data Collection:
Table number
Length of String / M
0.05
Number of oscillations
Time Taken/s
0.5
Period/s
0.5
1
1.01
20
39.65
1.9825
20
41.93
2.0965
20
39.82
1.991
20
39.94
1.997
2
0.91
20
37.25
1.8625
20
37.34
1.867
20
37.82
1.891
20
37.35
1.8675
3
0.81
20
35.25
1.7625
20
35.6
1.78
20
35.25
1.7625
20
36.13
1.8065
4
0.71
20
33.37
1.6685
20
33.07
1.6535
20
33.16
1.658
20
33.06
1.653
5
0.61
20
30.53
1.5265
20
30.31
1.5155
20
30.29
1.5145
20
30.75
1.5375
6
0.51
20
28.28
1.414
20
28.29
1.4145
20
27.91
1.3955
20
28.9
1.445
7
0.41
20
25.59
1.2795
20
25.21
1.2605
20
24.75
1.2375
20
24.94
1.247
8
0.31
20
21.94
1.097
20
21.79
1.0895
20
22.09
1.1045
20
21.75
1.0875
9
0.21
20
18.28
0.914
20
18.22
0.911
20
19.19
0.9595
20
18.34
0.917
10
0.11
20
13.44
0.672
20
13.34
0.667
20
13.35
0.6675
20
13.41
0.6705
The table contains the length of the string in meters, the number of oscillations, the time per 20 oscillations and the period of one oscillation.
As the length of the string deceases , the time for 1 oscillation decreases. So the length of the string is directly proportional to the period.
Data Processing and presentation:
Example in working out average period when the string is 1.01 m:
1.9825+2.0965+1.991+1.997=8.067
8.067/4=2.01675
The same procedure is used for the rest.
Length of string/m
0.05
Average Period/s
0.5
Average Period Squared
Gravity
1.01
2.01675
4.067280563
9.803405781
0.91
1.872
3.504384
10.25154778
0.81
1.777875
3.160839516
10.11678008
0.71
1.65825
2.749793063
10.19337669
0.61
1.5235
2.32105225
10.37539536
0.51
1.41725
2.008597563
10.02390591
0.41
1.256125
1.577850016
10.25835856
0.31
1.094625
1.198203891
10.21387892
0.21
0.925375
0.856318891
9.681519102
0.11
0.66925
0.447895563
9.695621703
The graph is plotted with Average period squared against length of string.
Y=3.9244x-0.0087
3.9244=gradient.
3.9244= (4(pi)^2)/g
g = (4(pi)^2)/3.9244
g=10.060 from the graph.
The average gravity from the formula=
100.614/10= 10.614
Conclusion:
the results where very close to the prediction but they werent the same as the graph is a scatter diagram.
-the result from the graph is more accurate as the graph cancels inaccurate measurements.
Evaluation:
-the method had weaknesses.
-the angle of the pendulum to the reference line isnt the same in each reading which might cause a slight error.
-the Air conditional may effect the pendulum; it may change its speed or change its direction.
it is difficult to stop the stopwatch and start it in the reference line exactly which might induce error
sometimes the ball tends to move in a circular motion and the experiment will have to be repeated.