Measuring Acceleration due to Gravity using a simple Pendulum.

Apparatus

To measure ‘g’ using simple harmonic motion the following apparatus were used:

• Metre Rule
• Metallic Bob
• Fine string
• Clamp stands & clamps
• Split Cork (to hold string)
• Digital stopwatch
• Linear graph paper

They were set up in the following way:

The pendulum should have swung no further than 10° from the vertical.

The experiment was repeated three times to retrieve a more accurate result and twelve readings were recorded over 1.2m.

Preliminary experiment

The preliminary experiment was to check the right equipment was used and to confirm that the experiment was being conducted in the correct way to measure what needed to be deliberated. This was also a good opportunity to see what range of measurements was to be taken. In the preliminary experiment a range from 0.2m to 2.4m was used. This gave a better understanding of what measurements to use in the final experiment.

With the preliminary experiment there was only a need to include one set of results, but in the final experiment three sets of results will be collected for more accuracy. A problem rose whilst trying to measure the length of the pendulum. It was unknown whether to measure the whole length of the bob, only to the top of the bob or to the middle of the bob. A final decision was made to measure to the middle of the bob, as this is where an assumption can be made that all the weight acts in the centre. This is why the bob being small and dense was made important. A piece of string was used in the preliminary experiment although this would carry extra weight compared to a piece of cotton. By using cotton the overall weight of the pendulum was reduced. A stopwatch was used to measure the swinging motion but this may have led to random errors.

Fair Test

To make the experiment as fair as possible the same bob and equipment were used for each experiment. The length of pendulum was measured from the base of the split cork to the middle of the metallic bob. The angle at which the bob swung also had to be the same. This was

Conclusion

The value for g calculated is not the exactly the same as the theoretical value. The inaccurate measurement would have come from inaccuracies within the experiment. Some of those reasons are as follows:

• Length of pendulum or period of pendulum incorrectly measured.
• Metre rule or stop watch not calibrated properly.
• Low resolution of measuring, less precise.
• Pendulum may have been rotating when swinging.
• The weight of the string wasn’t taken into account; a weightless string would have been ideal.

References

Advanced physics by M. Nelkon & M. Dethereidge

”S.H.M. is acceleration is directly proportional to displacement and directed (acts towards) a fixed point.”

Evaluation

From my graph I have realised that I only have 2 anomalous results, these results are at the points: length = 0.900 and 1.000

These anomalous results have occurred because of the errors.

Percentage errors

Percentage error of the length =   0.001     x  100

                                                 length

Percentage error of the period =    0.01      x  100

                                                 period

 

Percentage error of g = (percentage error of length) + 2(percentage error of period)

The maximum percentage error of g = 3.92

8. × 0.0392 = 0.37

9.43 + 0.37 = 9.80

9.43 – 0.37 = 9.06

My result was 9.43 and as you can see it is fairly accurate because it is just outside the range of values for the percentage error. The theoretical value for ‘g’ is 9.81 and my experimental value for ‘g’ is 9.43, when I add the percentage error value to this I am exactly 0.01 out from the theoretical value. The highest percentage error is 3.92 and this could have occurred because of two main sources of error:

1. Reaction time: this was occurring when a person was using a stopwatch to find the period. If your reaction time is slow, then the overall period will increase because it would take extra milliseconds to stop the clock.

2. The angle: the angle between the vertical and the pendulum should have been 10o, although it would have been very easy to misjudge the 10o between the normal and the pendulum.

The resolutions of the equipment were also to blame for an inaccurate result. For example, the stopwatch only measures to the nearest 100th of a second. If stopwatches were used which were more accurate, i.e. 1000th of a second a more precise result could have been gained.

Resolutions:

Improvements

To improve the experiement:

* Light gate :

1. You can use a Distance Sensor Metre; you will use this by using the pendulum except you will swing the bob back and forth towards and away from the DSM. The DSM will be linked to a computer and by using a certain program you are able to produce a graph of the information collected. From the graph you can work out a value for ‘g’.

2. You can also use a light gate, by doing this you will put a light gate about halfway across the pendulum. You will then use a computer program to measure the time it takes for the pendulum to cut the light gate twice. You will have to times the time by two; this will then give you the period for the pendulum.

Accuracy improvements

For an improvement of accuracy:

• More repeat readings; this will cancel out any anomalous results.

• Equipment; could have used equipment of more accuracy, i.e. a computer programme & light gates