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uncertainties with marbles

Extracts from this document...

Introduction

Marble Experiment

In this experiment, I will be measuring the diameter of six medium sized marbles, with strings and micrometer to find out the differences in measurements I get with measuring with strings and micrometer. In addition, I will also be investigating if all medium sized of marbles have different measurements.

I predict that, by using string and measuring the string by a ruler in centimeters, the measurement I make won’t be as accurate as by using a micrometer. This is because when you use the string method, therefore it moves around or keeps slipping off the marbles. It would be really hard to get a perfect measurement, and this might have an effect when comparing the sizes of medium marbles. As well as that, measuring with a ruler the accuracy is only 0.1cm (*10-2m) compare to measuring with a micrometer which it keeps the object in place, and its accuracy is 0.01mm (*10-3m). In addition, I think six different marbles will have different diameters which mean they won’t all be the same due to the process of making the marbles.

 Circumference using string method Measured in cm using ruler (*10-2m) Marble 1 Marble 2 Marble 3 Marble 4 Marble 5 Marble 6 Uncertainty 1 5.1 5.2 5.0 5.4 5.4 4.8 ±0.05 2 5.1 5.0 5.4 5.4 6.0 5.0 ±0.05 3 5.2 5 5.2 5.2 6.4 5.8 ±0.05 4 5.1 5.0 5.5 5.2 4.8 4.6 ±0.05 5 4.9 5.3 5.5 5.0 4.4 4.4 ±0.05 Average 5.0 5.1 5.3 5.2 5.4 4.9 ±0.05

The outliers from the results I got.

This is measured in cm by using string, since we can’t measure diameter with string, this is how we find out diameter. Diameter=Circumference/

Middle

1.57

1.67

-0.02

3

1.69

1.64

1.74

+0.05

4

1.64

1.59

1.69

0

5

1.72

1.67

1.77

+0.08

6

1.57

1.52

1.62

-0.07

Average

1.64

1.59

1.69

Changes in uncertainty after they are calculated:

• There is an anomaly in this data, because for the average for marble 5 and 6 there is a lot different compare to the overage that is calculated out from all six marbles. One has +0.08 compared to the average and another has -0.07.

Diameter using Micrometer method

Measured in mm (*10-3m)

 Micrometer Mable 1 (*10-3m) Mable 2 (*10-3m) Mable 3 (*10-3m) Mable 4 (*10-3m) Mable 5 (*10-3m) Mable 6 (*10-3m) uncertainty 1 16.21 16.80 16.13 16.6 16.09 16.12 ±0.05 2 16.19 16.80 16.13 16.12 16.09 16.18 ±0.05 3 16.19 16.80 16.12 16.9 16.08 16.84 ±0.05 4 16.17 16.80 16.11 16.11 16.1 16.82 ±0.05 5 16.24 16.80 16.13 16.11 16.12 16.82 ±0.05 Average 16.20 16.80 16.12 16.37 16.10 16.56 ±0.05
• The marble 2 that is measured by a micrometer, I think that the measurement is abnormally perfect. I think that it should not be absolutely the same even though I repeated it for 5 times.

The uncertainties:

 Marbles Average Minimum Maximum Differences 1 16.20 16.15 16.25 -0.16 2 16.80 16.75 16.85 +0.44 3 16.12 16.07 16.17 -0.24 4 16.37 16.32 16.42 +0.01 5 16.10 16.05 16.15 -0.26 6 16.56 16.51 16.61 +0.20 Average 16.36 16.29 16.41
• The one with micrometer is not shown on the marble 1 scale, and the reason is because of that they both have the same number, so they overlapped each other.  And as well as the fourth one.
• From the graph we can see that from all six marbles, only two of them have the closest or same sized when measuring with string and micrometer, this shows that most of the marbles have different size.
• Marble 5 has the biggest difference. 1.72 (*10-2m) with ruler and 1.62 (*10-2m) with micrometer, the difference between it 0.11(*10-2m).

As you can see on this graph, I converted the micrometer’s unit into cm, to be able to graph it fairly and to see the differences.

Differences between measuring with String and Micrometer

 Marbles

Conclusion

Also the marbles that we have used in the physics room are used for a long time, because many of them were chipped or has crack on them, which I think it might affect the measurement because the surface is damaged. This shows that, if I could redo my experiment, I would buy a new marble, so the surface of the marbles is all the same. In addition, rather than complaining about this, I think I could have used 3 different kinds of ruler to measure the strings, as well as I could have look at the brand new marbles to see how the new ones are different from the used ones.

For some of the improvements on my lab if I could do it again, will be that I would use more devices to measure the size of marbles if there are other available equipments. And for the further investigation, I would try measure handmade marbles (if I can find it), and compare it with the machine made marbles, to see whether handmade marbles are all in the same size of is it the same as machine marbles, that all the sizes are different.

And the most important thing was that, I think if I could do it again, I would change the uncertainty for the micrometer, because if the uncertainty for ruler is ±0.05 and it wouldn’t be the same for the micrometer, it should have been smaller than that, so I think I might have made a mistake in the lap, but at the end I still got the result that I was expected.

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