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The Compound Pendulum

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Introduction

The Compound Pendulum Task: * To confirm that a metre rule behaves as a compound pendulum when oscillating; * To determine the acceleration due to gravity using a compound pendulum. Planning: Sources used in research of the above tasks are: 1. A Text-Book of Practical Physics - William Watson; page 129 2. Laboratory Physics - JH Avery & AWK Ingram; page 69 3. Intermediate Physics - CJ Smith; page 50 4. The Text-Book of General Physics - GR Noakes; page 394 5. Intermediate Mechanics - D Humphrey; page 60 6. Introduction to Physics for Scientists and Engineers (Second Edition) - Frederick J. Bueche; page 222 7. http://www.physics.mun.ca/~cdeacon/labs/simonfraser.pdf 8. http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html 9. http://en.wikipedia.org/wiki/Acceleration_due_to_gravity 10. http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm 11. http://www.gorissen.info/Pierre/maps/googleMapLocationv4.php 12. http://en.wikipedia.org/wiki/Reaction_time Where direct quotation is made from a source, the source number is shown in superscript after the preceding italicised quote, e.g. 'quote' 4 . The compound pendulum is defined as: 'a rigid body of any shape and internal structure which is free to turn about a fixed horizontal axis, the only external forces being those due to gravity and the reaction of the axis on the body' 3. In this investigation a wooden metre rule with holes drilled at various positions down its centre, pivoted on a pin, will act as the compound pendulum. The time period, T, for the oscillations of a compound pendulum is given by: T = 2? k² + h² hg Equation from: 4; 2; 7 Where * 'T' is the time period in seconds - dependant variable * 'k' is the radius of gyration about an axis through the centre of gravity in metres - independent variable (constant)

Middle

Any possible errors were identified and will be explained in the following section, along with information on how the errors will be reduced in the main experiment. * Previous to the preliminary, the possibility of discrepancies with the angle at which the pendulum was released was identified and combated. A piece of card was attached to the retort stand with a line ruled upon it at 40º to the vertical. The pendulum was held at rest upon the line before release to ensure that the angle at which it was released each time, and hence the height at which it was released, remained constant. (See Diagram A) However, it is highly difficult for an observer to stay constantly still for a large length of time. If the observation point is moved, even minimally, the results could be compromised and errors could be introduced due to parallax. For consistent results, the retort stand should line up with a fixed vertical line behind it. This would reduce the parallax errors and therefore increase the reliability of results. * The amplitude of each oscillation is not constant and reduces slightly each time. At the extremes of motion, the pendulum slows down and stops for a split-second as it changes direction. It is difficult to gauge at which point the pendulum chances direction, and - because of this - oscillations will be counted from the centre, where it passes the vertical line of the retort stand.

Conclusion

7. Suspend the metre rule on the pin at 0.05m from the centre of gravity (i.e. at 45 cm along the metre rule) 8. Cover the exposed end of the pin with another cork. Do not push all the way through. 9. Attach the card to the stand with blu-tack ensuring that the vertical timing line is in line with the retort stand. 10. Displace the metre rule so that it lines up with the starting line on the card. 11. Release the pendulum and begin timing as it passes the vertical retort stand. 12. Stop the timer after 15 oscillations as the pendulum passes the retort stand. (One complete oscillation is from when the pendulum passes the stand to it's extreme of motion at one side, back past the stand to the other extreme and then back to the stand [See Diagram B (above)]) 13. Record the time. 14. Repeat steps 10 - 13 for the same length twice. Carry out additional repeats if any values are more than 0.15s from the others. 15. Repeat steps 10 - 14 for lengths of: 0.1m, 0.15m. 0.2m, 0.25m, 0.3m, 0.35m, 0.4m, and 0.45m from the centre of gravity. 16. For each length of the pendulum, h: * Calculate the average time for 15 oscillations (addition of the values then division by 3) * Divide the average time by 15 to give the time period * Calculate T²h * Calculate h² And tabulate the results with these calculated values. 17. Plot a graph of T²h against h².

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Response to the question

The candidate has not completed the work so has not answered the question. However, this is a great start. The explanation of theory is good, an important step that is often left until conclusions or sometimes omitted at A-level and ...

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Response to the question

The candidate has not completed the work so has not answered the question. However, this is a great start. The explanation of theory is good, an important step that is often left until conclusions or sometimes omitted at A-level and should not be. The equation should definitely be in there but doesn't need each stage of rearranging showing, if you feel there is a need to show a proof it should be in an appendix. The method seemed reasonable with a clear understanding of how to limit sources of inaccuracies.

Level of analysis

The text has good, relevant physics throughout. It contains good use of references, though these are usually placed at the end of the report. There was no graph, uncertainties or final answer, which made the report less useful.

Quality of writing

The spelling, punctuation and grammar appear to be perfect or very close. It is pleasing to see good use of relevant scientific terms being used correctly.


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Reviewed by k9markiii 06/03/2012

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