Addition of Perpendicular Vectors in two ways

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SUMMARY

The discussion centers on the addition of perpendicular vectors, specifically a force vector of 100N at a 45-degree angle to the x-axis. The components calculated trigonometrically yield 70N for both the x and y directions. However, the user mistakenly adds these components arithmetically, resulting in 140N, rather than recognizing that the correct resultant vector is the hypotenuse of the right triangle formed, which remains 100N. The key takeaway is the importance of vector addition principles, particularly when dealing with perpendicular components.

PREREQUISITES
  • Understanding of vector components and their representation
  • Basic trigonometry, specifically sine and cosine functions
  • Knowledge of vector addition methods, including the Head-to-Tail method
  • Familiarity with the concept of resultant vectors in physics
NEXT STEPS
  • Study vector addition techniques in physics, focusing on graphical methods
  • Learn about the Pythagorean theorem as it applies to vector components
  • Explore the implications of vector directionality in force analysis
  • Review trigonometric identities and their applications in physics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics or vector analysis, particularly those seeking to deepen their understanding of vector addition and force resolution.

Raabi Anony
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I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis.
When I find their Components trigonometrically, I get 70N each; as
Fx = 100xCos(45) = 70N
Fy = 100xSin(45) = 70N

Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N.

Why is there discrepancy or where am I making a mistake?
Please help.
 
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Raabi Anony said:
Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N.
You are just adding them together arithmetically. Aren't they vectors in different directions (90 degrees)? What's the hypotenuse of that right angled triangle?
 
The hypotenuse of that right angled triangle is 100N.
 
Raabi Anony said:
The hypotenuse of that right angled triangle is 100N.
So the two components add together to produce the original force. The other two components will cancel because they are at 90 degrees to the original force. Your mistake was in not reconstituting the original force correctly.
Is there still a problem? I think we've solved your query.
 
Thanks for your time. Let me re-phrase my question and come back.
 

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