Calculating change in length for a projection

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Discussion Overview

The discussion revolves around calculating the change in length of a vector in a rectangular prism as it is tilted at a known angle, theta. Participants explore the mathematical justification for this change and seek to understand the implications of projecting a vector onto a plane.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant expresses a need to understand how the length of a vector changes with respect to the angle theta and specifically asks for the increase in length when theta becomes zero.
  • Another participant suggests that drawing an end view of the prism may provide an immediate visual solution to the problem.
  • A different participant emphasizes the need for mathematical backing to support the visual solution and mentions the necessity of calculating uncertainty based on the measurements.
  • There is a clarification regarding the perspective of the end view, indicating a need for a specific orientation in the drawing.
  • One participant questions the terminology related to the projection of a vector onto a plane and seeks guidance on relevant equations to use in this context.
  • Another participant reiterates the suggestion to draw a diagram, indicating that marking known lengths and desired distances may clarify the solution, and hints at the presence of a right angle in the geometry involved.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the terminology or the specific mathematical approach to take. Multiple viewpoints and suggestions for visual aids and diagrams are presented, indicating an unresolved discussion.

Contextual Notes

Participants express uncertainty regarding the appropriate terminology and mathematical methods to apply, highlighting a potential dependence on visual representations and the need for further clarification on the geometry involved.

Who May Find This Useful

Individuals interested in vector projections, geometry of prisms, and those seeking to understand the relationship between angles and lengths in physics contexts may find this discussion relevant.

Furious_George
I haven't touched a physics textbook in a while and need help with something fairly simple. I am staring straight down on a rectangular prism that is tilted on one axis to a known angle, theta. I have a measurement of a vector length in this orientation. I would like to know how much that length changes with respect to theta. What is the increase in length when theta becomes zero?

upload_2017-10-11_9-47-8.png
 

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Draw the end view and you should see the solution immediately .
 
Nidum said:
Draw the end view and you should see the solution immediately .
The image on the right is the end view. My issue is that I need to back this up mathematically - I need more justification beyond just a picture and I need to calculate an uncertainty later on based off of my numbers.
 
I think @Nidum means a view of one of the left or right hand ends (as we're looking at it).
 
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I'm also not sure what terminology I would google to find a solution. Am I projecting an vector onto a plane here? Or does that imply that I am not changing my length (which I am in this situation). What equations can I use to solve this?
 
Draw the diagram Nidum suggested. Mark on it the length you know and the distance you want to know. Hopefully the answer will be immediately obvious from high school maths (hint - there ought to be a right angle somewhere). If not, take a photo if your diagram (in good light!) and upload it and we can see where you've got to.
 
Tilted block with a hole.jpg
 
Last edited:

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