VECTOR ADDITION
Skylur Jameson
26 February 2009
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Experiment # 3
Purpose:
The purpose of this experiment was to study vectors and vector addition in
Cartesian and Polar coordinates.
Equipment: Ruler, protractor, and small map of Italy
Discussion:
The journey across the country of Italy will allow us to visit eight of the country’s
finest cities so prepare your camera, video recorder, and binoculars for an
experience unlike any other. The tour will begin in the major city of Milan
(Milano) then take us to Venice (Venezia) and promptly next to Florence
(Firenze). From Florence we shall sightsee to the historical city of Rome (Roma)
from the comfort of a train. Next, we will continue on to Naples (Napoli), Bari,
Messina, and Palermo by way of our luxurious bus. Last but not least, we will
conclude the tour will a scenic trip through the Mediterranean by way of boat to
our tour guide’s (Professor Di Cecca) home town of Gaeta.
Procedure:
The scale we’ll be using is located on the small map and should be in metric units.
1. Measure the vector displacement from city to city which will give the
magnitude and direction of each of the 8 vectors. Mark the x-axis and yaxis for each point by using the top or bottom of the paper to help create a
base line for the two axes.
2. Add the eight vector displacements together by way of the component
method to help solve for the resultant vector displacement.
3. Measure the resultant vector on the map to get a measured displacement
for the direct route from beginning to end.
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4. Compare the calculated resultant vector displacement to the measured
resultant vector displacement to get the percent error.
Observations: The pencil at times made it difficult to line up from the center of one city to the
exact center of another city. Thickness of the lead or size of pen affected vector
placement. Map was photocopied slanted compared to top of page. Axes could
have been not precise. Lines had to be extended out to be able to read protractor.
Lines between measurements were approximated. Mathematically equations
done on excel. Clear rulers were more precise than normal rulers because were
flat on paper. Highlighting cities was easier to find small mark to measure to.
Some protractors were difficult to read.
Conclusion:
In conclusion, my resultant vector measured 569 kilometers in distance, had a
reference angle of 55o, and had a polar angle of 305 o. Upon comparing my
measured displacement of 569 km and my calculated displacement of 569.23
km, I found that my percent error was 4.06%. Furthermore, I found that my
percent error for the polar angle was 0.0%. The experiment overall was a very
helpful tool in aiding my understanding of how to add vectors, calculate their
displacements, and use the program Microsoft excel. The one thing that I would
change about the lab would be that I would try to make it less congested
because often at times it was hard to locate the center dot for each city since
Italy is a relatively small country with many towns in comparison to say
America.
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