Relate inclined plane's angle of incline to FBD's weight COM

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Discussion Overview

The discussion revolves around the relationship between the angle of incline, θ, of an inclined plane and the angles used to determine the components of gravitational force in free body diagrams (FBDs). Participants are seeking a clear and simple way to communicate this relationship, particularly for educational purposes.

Discussion Character

  • Exploratory, Conceptual clarification, Homework-related

Main Points Raised

  • One participant requests a proof demonstrating that the angle of incline, θ, is equal to the angle used to find the components of gravitational force.
  • Another participant suggests that extending lines can reveal similar triangles, which may help illustrate the relationship.
  • A participant expresses a desire for a straightforward relationship that can be easily communicated to students, mentioning the use of physical models in their teaching.
  • There is a reference to the parallel line theorem, with a request for clarification on its relevance to the relationship being discussed.
  • One participant expresses gratitude for the assistance received, indicating a positive reception to the contributions made.

Areas of Agreement / Disagreement

Participants generally agree on the existence of a relationship between the angles but have not reached a consensus on the best way to prove or communicate it. Multiple approaches and requests for clarification remain unresolved.

Contextual Notes

Participants have not provided explicit mathematical steps or definitions, and there is an emphasis on finding a proof that is accessible for educational purposes.

Who May Find This Useful

Educators and students interested in understanding the geometric relationships involved in inclined planes and gravitational force components may find this discussion beneficial.

Tyrannosaurus_
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Please show me the relationship that proves how an inclined plane's angle of incline, θ, is equal to the angle used to find the components of gravity force.

I know that the angles are the same, but I'd like a way to show it.

Thanks!
 

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Thanks for the reply! I do appreciate your help, and support.
I understand similar triangles.

I am looking for a relationship that is simple to communicate with students. Currently, I use a physical model with a weighted string, & some cardboard arrows to show the x & y axis.

All help & discussion is appreciated.
I would appreciate it a little more if you could find, or show me the relationship explicitly; instead of, implying the relationship is there, & I'm too stupid to figure it out. I'd like the proof. I expect parallel line theorem is used. Is this true? Can someone show this to me, please.

Thank you!
 
Elegant & Exact.
A sincere Thank You!
 

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