Using a Pendulum to Find Gravity Essay

Published: 2019-10-10 12:20:10
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Category: Gravity

Type of paper: Essay

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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.

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