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Measuring g in more than one way

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Introduction

Harry Hussey

Measuring g in More Than One Way

Tasks;

  1. To determine the acceleration due to gravity using various methods
  2. To evaluate the best in consideration of uncertainties.

I will be performing two experiments and comparing the accuracy of the measurement of g i get. I will be assuming a value of 9.8 m s-1 for convenience considering that g differs from place to place.

Experiment 1:

For my first experiment i will need

  • 1 x QED + 1 Light Gate
  • A piece of cardboard cut to required mask size
  • 1 x stand
  • 1x boss

Setup:

Set up the QED and attach the light gate to the stand 30 cm from the desk using a boss. Set the QED up to measure for acceleration using the mask size of the piece of cardboard for the calculation.

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Method:

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Middle

-2 for g. The result for the greater mask size is most likely more accurate as any deviation from the expected mask size due to the angle it’s dropped at will have less effect over a greater mask size. For example if the angle the cardboard is dropped at alters the mask size by 0.3cm then this will affect the calculation for the smaller mask size more than the greater mask size. This effect can be seen in the greater range of value from mask size 8, compared to mask size 10, seen in the graph.

The greatest error for the experiment was contained within this problem. Allowing for an effect on the result of the measurement.

To calculate this error i evaluated the maximum amount a miss-drop could alter the distance read. image08.pngimage07.pngimage09.pngimage10.pngimage09.png

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Therefore error = (82+42)1/2  - 8= 901/2 – 8 = 9.48683 – 8 = 1.49 (3.s.f) or 8 + or – 9.3125%

Or 10.7703 – 10 = 0.770 (3.s.f) therefore + or – 3.85%

In the averages this results in

9.73 + or – 0.957  (3.s.f) for mask size 8cm

9.84 + or – 0.391 (3.s.f) for mask size 10cm

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Conclusion

Other Methods considered:

I also considered performing the first experiment, but with two light gates and a metal ball. The problem with this however was that it would have been hard to ensure that the diameter of the sphere would pass through the light gates. For this reason I chose to adapt the experiment using a piece of cardboard with a mask to reduce the uncertainties.

I also considered the traditional method of measuring g, before QED’s were created, by using what was called an “Atwood’s Machine” involving a pulley with weights on either side and measuring the time taken for one weight to hit the ground. This again introduced human error in the timing of this period and, unlike when using a pendulum, it would be difficult to reduce that uncertainty.

Sources:

1.        http://www.physics.mun.ca/~cdeacon/labs/simonfraser.pdf

2.        http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

3.        http://en.wikipedia.org/wiki/Acceleration_due_to_gravity

4.        http://en.wikipedia.org/wiki/Reaction_time

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