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Efficiency Lab

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Introduction

Anthony Leung

Block E

Bow and Arrow Lab – Efficiencyimage00.png

Research Question: How does efficiency with which the bow transfers energy to the arrow depend on the mass of the arrow?

Hypothesis: Efficiency will increase as the mass of the arrow increases, as Eff= Eout/ Ein.

Variables:        Independent – the mass of the arrow. In this procedure, this variable was calculated by weighing with an electronic balance to ascertain and acquire the margin of error. A series of different massed arrows were used to determine the change in efficiency of the energy transfer from the bow and to increase the level of precision.

        Dependent – efficiency with which the bow transfers energy. The dependent variable is the resultant, or the value that we are attempting to measure. As the equipment to measure this is out of our reach, we can only to calculate this value.

        Controlled – the height of the bow. The height of the bow is kept at a constant height in order to maintain the precision of the procedure. If

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Middle

8

6.88

9

Note: The percentage error is an approximate value and is present due to human and equipment errors. The equipment used will always contain a certain degree of uncertainty and lack the precision present in technology beyond the reach of high school students

Displacement of Bowstring

Arrow

Displacement (cm) ± 0.05

1

9.0

2

9.0

3

9.0

4

9.0

6

9.0

8

10.0

9

10.0

Note: There is a certain degree of uncertainty involved in these measurements due to error in human sight and error in the metre stick. It is impossible to have the bowstring exactly at a certain measurement, so the uncertainty is present.

Displacement of Arrow

Arrow

Displacement (m) ± 0.1

1

0.87

2

0.48, 0.50, 0.58

3

0.64

4

0.76

6

0.30, 0.50

8

0.65

9

0.32, 0.38, 0.78, 0.2

Distance from floor to rail: 3.0 m

Distance from floor to bow: 0.70 m

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Conclusion

Limitations: The range of uncertainty for this procedure is very large, due to error in human sight, and error in measuring tools such as the measuring tape and the metre stick. For one, we do not know exactly the distance the bowstring is pulled back each time. The distance 9.0cm is a rough estimate, as we lacked the time to properly measure. Another limitation is the recorder at the top of the railing. As we can only roughly estimate the maximum height of the launch, there is a huge variance.

Improvement: Perhaps a more realistic method to perform this procedure is to attach some sort of string to the arrow. When launched into the air, the arrow will go up, bringing the string with it. During the peak moment, where there is a very brief pause, we will place a mark on the string (from the floor) and then measure afterwards. Therefore, the limitation of human sight can be lessened. However, the string must be long enough and be light enough as to not corrupt the precision of the experiment. Of course, there will be a degree of error involved, but significantly reduced and smaller than the present one.

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