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Verification of the earth's gravitational field strength

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Introduction

Challenge 5- Verification of the earth’s gravitational field strength.

Design

Research Question: Is it possible to verify the earth’s gravitational field strength at Istra and get results that are close to the text book result (9.8ms-1)?

Hypothesis: I believe that it is possible to verify the earth’s gravitational field strength at Istra just like you can verify it wherever you are in the world. There are several ways in which this can be done due to the fact that g (gravitational field strength) is met in various equations. However, the most valid experiment in which we can find g is the pendulum one due to the fact that it is possible to do it at Istra and at the same time get a fairly accurate result. A pendulum is made up of a mass (bob) attached to a string that is fastened so that the pendulum can swing (oscillate) in a plane.  In a simple pendulum, all the mass is considered to be concentrated at a single point at the centre of the bob.  Physical quantities of the pendulum include length L, mass m, angle through which the pendulum swings θ, and the period T of the pendulum (which is the time it takes for the pendulum to swing through one complete oscillation).

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Middle

Time for 20 oscillations (T)/s  (±1s)

Trial 1

Trial 2

Trial 3

0,5

29,93/29,94

29,87/29,97

29,93/29,87

1,0

41,08/41,14

41,23/41,26

41,25/41,13

1,5

49,93/50,16

49,97/49,88

49,87/49,53

2,0

57,13/57,32

57,62/57,43

57,48/57,54

We have two readings for each trial because we had to stopwatches going at the same time. Our next step is to find an average for each reading.

Table showing the Period for 20 oscillations obtained at different lengths. (All time readings to two decimal places).

Length of pendulum string (L)/ m (±0.01m)

Average Time of each trial (T)/s  (±1s)

Trial 1

Trial 2

Trial 3

0,5

29,94

29,92

29,90

1,0

41,11

41,75

41,19

1,5

50,05

49,93

49,70

2,0

57,23

57,53

57,51

Data processing:

Our next job is to actually find an average for the 20 oscillations and then find the time for 1 oscillation. To find the average for the 20 oscillations we will add the three trials for each length and divide them by 3. To find the average oscillation we will divide our answer by 20.

E.g. for 0.5m average for 20 oscillations →(29.94+29.92+29.90)/3=29.92

Average for 1 oscillation= 29.92/20= 1.50 (All results to two decimal places).

Table showing the average time for 20 oscillations and then the period.

Length of pendulum string (L)/ m (±0.01m)

Average Time for 20 oscillations (T)/s (±1s)

Average Period (T)/s

0,5

29,92

1,50

1,0

41,35

2,07

1,5

49,89

2,49

2,0

57,42

2,87

Our final step is to find the constant in order to then find g.

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Conclusion

Evaluation: There were several weaknesses in our experiment. First of all, it was very hard to keep the angle the same all the time. This may affect the readings because it can affect the period. Also, it was hard to keep the bob moving symmetrically which again affects the period of an oscillation. Finally, it was hard to make sure that both people with the stopwatch started at the same time and therefore this distorted our readings for the period a little bit.

In terms of limitation, we couldn’t use a longer string because of the space and as a result our data may be insufficient to accurately show the earth’s gravitational field strength.

Improvements: Realistic improvements that could cut some weaknesses of the procedure could include using greater lengths of string and doing the procedure in a greater space.  This would help to get more results and hence get an even closer answer to g. Moreover, I believe the more trials done, the better chance you will get of obtaining the best average value: perhaps 10 trials would be a good idea. Finally, we could use technology to get precise timing. It is possible to set a beam of light with a sensor that starts the stopwatch every time the bob cuts the beam and stops the stopwatch when the bob cuts the beam on the way back. That way we can get an exact value for the period.

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