Statics: Dimensionless Unit Vector

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Discussion Overview

The discussion revolves around the concept of dimensionless unit vectors in the context of statics, particularly focusing on the calculation and interpretation of unit vectors derived from force vectors. Participants explore the definitions and properties of unit vectors, including their magnitudes and directions.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes their attempt to calculate a unit vector by subtracting vector components and expresses confusion about the results provided in an online book.
  • Another participant points out that if each component of a vector had a magnitude of 1, it would not be a unit vector, suggesting a misunderstanding of unit vectors' properties.
  • Some participants note that the vector subtraction results in a vector with units (lbs), raising questions about the instruction to find a dimensionless unit vector.
  • There is a suggestion that dividing by the magnitude, which also has units, can yield a dimensionless direction vector, indicating a potential resolution to the confusion.

Areas of Agreement / Disagreement

Participants express confusion and differing interpretations regarding the definition and calculation of dimensionless unit vectors. There is no clear consensus on the interpretation of the instructions or the calculations involved.

Contextual Notes

Participants highlight the importance of understanding the units involved in vector calculations and the implications for defining unit vectors. There are unresolved aspects regarding the definitions and the specific calculations presented.

Who May Find This Useful

This discussion may be useful for students and individuals studying statics, vector analysis, and the properties of unit vectors in physics and engineering contexts.

belvol16
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Homework Statement


Equation.PNG

Question.PNG

Homework Equations


Unit Vector.PNG

The Attempt at a Solution


So I began by subtracting.
(205-160)=55 i
(495+128)=623 j
Both of these vectors are in the positive direction. So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and j.
The online book lists the answers as R hat = 0.0720 i + 0.997 j . I guess I'm not sure how the book got these answers. I thought unit vectors always had a magnitude of 1 and their purpose was to determine the direction of the vector.
Thank You!
 
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belvol16 said:
So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and j.
If each component had a magnitude of 1 then the vector would not be a unit vector!

belvol16 said:
The online book lists the answers as R hat = 0.0720 i + 0.997 j . I guess I'm not sure how the book got these answers. I thought unit vectors always had a magnitude of 1 and their purpose was to determine the direction of the vector.
The unit vector does have a magnitude of 1. Given those components, find the magnitude of the full vector. What do you get?
 
Minor point, but ##\vec{B} - \vec{A}## has units of lbs, and so would a unit vector in this direction. I'm puzzled by the instruction to "find a dimensionless unit vector" in this direction.
 
Mark44 said:
Minor point, but ##\vec{B} - \vec{A}## has units of lbs, and so would a unit vector in this direction. I'm puzzled by the instruction to "find a dimensionless unit vector" in this direction.
If you divide by the magnitude (also in lbs) you can get a dimensionless direction vector.
 
Doc Al said:
If you divide by the magnitude (also in lbs) you can get a dimensionless direction vector.
OK, that makes sense. Objection withdrawn...
 

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