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Measuring Acceleration due to Gravity using a simple Pendulum.

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Introduction

Measuring Acceleration due to Gravity using a simple Pendulum


Simple Harmonic Motion is very similar to the motion of a bob of a simple pendulum. A simple pendulum is made of a metallic bob suspended by fine string. Using these apparatus the acceleration due to gravity had to be measured. The acceleration due to gravity on earth is 9.81ms-2, therefore every second the particle will increase it’s speed by 9.81ms-1. Although, this may not be the case, due to air resistance.

Acceleration is directly proportional to force and acts towards a fixed position.


Planning


To derive a value for g, the S.H.M. equation was used:

image01.png

For calculating ‘g’ the formula had to be rearranged:

T2 = 4π2l

         g

Therefore:

g = 4π2 l

         T2

Where: g is the acceleration to gravity; T is the period & l is the length.

Out of the above, the length of the pendulum had to be measured and then the period with that information. Instead of using the formula, a graph could be drawn of length against T
2, calculate the gradient, invert it then multiply by 4π

g =
4π2 l

         T2


“”””“””””..

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Middle

1.200

47.49

2.38

1.000

44.09

2.21

0.800

40.10

2.01

0.600

35.19

1.18

0.400

29.20

1.46

0.200

21.11

1.06

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.

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Conclusion

th 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:

Resolution

Length (m)

0.001

Time (secs)

0.01

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

...read more.

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