What Happens to Percent Error as the Number of Vectors Increases?

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SUMMARY

The discussion centers on the relationship between the number of vectors added and the percent error in graphical or force table methods. It was established that as the number of vectors increases, the percent error also tends to increase. The calculations provided included a percent error of 5.88% for two vectors (A and B) and 6.03% for three vectors (A, B, and C). The correct formula for percent error is defined as % error = 100 × (Experimental - Theoretical) / Theoretical, emphasizing the importance of distinguishing between experimental and theoretical values.

PREREQUISITES
  • Understanding of vector addition and its implications in physics.
  • Familiarity with the concept of percent error and its calculation.
  • Basic knowledge of experimental versus theoretical values in scientific experiments.
  • Proficiency in using graphical methods for data representation.
NEXT STEPS
  • Research the impact of increasing sample sizes on statistical error margins.
  • Learn about the principles of vector addition in physics.
  • Explore advanced error analysis techniques in experimental physics.
  • Investigate graphical methods for data representation and their accuracy.
USEFUL FOR

This discussion is beneficial for physics students, educators, and researchers involved in experimental design and data analysis, particularly those focusing on vector analysis and error measurement in experiments.

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Homework Statement



What will happen to the percent error of graphical or force table method as the number of vectors to be added increases? Give proof.

3 vectors
A = 400 g
B = 450 g
C = 427 g


Homework Equations





The Attempt at a Solution



First, I computed for the percent error of 2 vectors. I used vectors A & B:

% error = [(400 - 425)/425] x 100 = 5.88%

Then, I computed for the percent error of 3 vectors:

% error = [(400 - 425.67)/425.67] x100 = 6.03%

I concluded that as the number of vectors to be added increases, the percent error also increases. I'm not really sure about my answer.
 
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I am not sure what you are doing, you seemed to have taken an average of two or three numbers and then compared the first with the average? This is not correct. The percent error is the
((experimental value determined from the graph or force table - theoretical value determined from calculations)/theoretical value)) times 100 , or,

% error = 100(Experimental - Theoretical)/Theoretical.

The theoretical value is always the same. What about the experimental value as you increase the number of vectors in a given experiment?
 

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