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Determination of the acceleration due to gravity using a simple pendulum.

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Introduction

AS Physics Coursework                Page  of

Hannan Shah

AS Physics Coursework

HANNAN SHAH

Determination of the acceleration due to gravity using a simple pendulum

Method

Front viewSide view

First a long piece of string (approximately 1.5m long) was tied to a bob.  A metre rule was used to measure a length of 1.2m from the centre of mass of the bob to the string.  The remaining length of string was placed between the wooden blocks and clamped to the retort stand, as shown above.  The wooden blocks were used to define the right angles to help when measuring the displacement and also to measure the string again to ensure it is still the same as the original measured length.  

Once the equipment was set up the bob was given a displacement of approximately 10 degrees and let go.  The displacement has to be of this magnitude or else the error when calculating 'g' using (T = 2π√l/g) will be greater.  The stopwatch was started once the bob passed the fiducial marker (this is used to indicate the beginning of an oscillation).  The timing was stopped once twenty oscillations were complete.  Twenty oscillations were used to try and minimise the error that arises through the reaction times in stopping and starting the stopwatch.

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Middle

±0.5 degrees as each measurement is given to the nearest degree.Parallax error: Mistakes can be made when making measurements or when choosing the moment start/stop the stopwatch as the bob arrives at the fiducial marker.  This can cause errors, especially if the pendulum is swinging quickly.Random error: These are associated with nearly all measurements and can never be completely eliminated.
  • Take three sets of readings and then take the average of those readings.  I will do this to eliminate any anomalous results.  If I only take one reading it could be an anomalous result but I won’t know this unless I have more sets of results to compare my data with.  Multiple readings ensure that anomalous results are spotted and eliminated.

Results

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Conclusion

To make my calculation I plotted a graph of T2 (y axis) against length (x axis).  This allowed me to calculate 'g'.

T = 2π√l/g it would be more complicated to work out 'g' if T was plotted against length as the graph produced wouldn't be a straight line.  By squaring the whole equation you get T2=4π2(l/g) or T2=(4π2/g) x l.  Compare this to y=mx+c.  By plotting T2 against length the line should pass through the origin (because the c=0) with gradient=4π2/g.  By simply rearranging this g = 4π2

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Conclusion

The experiment could be improved by either improving the reliability of the existing procedure.  Increasing the number of oscillations to further reduce the error caused during the timing could do this.

The value 9.84ms-2 is very close to 9.81ms-2.  Considering that the percentage errors in time seem to be the largest I predict that I could further increase the accuracy of the value obtained by eliminating the reaction times.  

A more sophisticated experiment would definitely increase the accuracy in the timings.  Light gates would remove the error caused by reaction times as they will accurately time the moment the bob passed over the point to complete an oscillation.  In the current experiment the fiducial marker was only used as a guide to a complete oscillation.  Also using a more rigid pendulum would further reduce the error.

There is a limitation with the graph paper used to calculate the gradient as its gridlines are only spaced in mm.  If any measurement required accuracy greater than the value scaled to 1mm then this simply wouldn't be possible.  This could be another reason why 'g' wasn't exactly 9.81ms-2.

The effect of air resistance on the pendulum could have been investigated by changing the displacement of the pendulum.  I could prove whether my hypothesis about the effect of air resistance on the pendulum was correct by giving the pendulum a greater displacement and repeating the experiment.

HANNAN SHAH

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