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

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SUMMARY

The relationship between an inclined plane's angle of incline, θ, and the components of gravitational force can be demonstrated using the properties of similar triangles. Specifically, when analyzing the forces acting on an object on an inclined plane, the angles formed by the gravitational force and the inclined surface are equal due to the parallel line theorem. This relationship can be visually represented using a physical model with a weighted string and cardboard arrows to illustrate the x and y axes, making it easier for students to understand the concept.

PREREQUISITES
  • Understanding of basic trigonometry and angles
  • Familiarity with the concept of similar triangles
  • Knowledge of gravitational force components
  • Experience with physical modeling techniques in teaching
NEXT STEPS
  • Research the parallel line theorem and its applications in geometry
  • Explore the concept of gravitational force components on inclined planes
  • Learn how to create effective physical models for teaching physics concepts
  • Investigate methods for teaching similar triangles in a classroom setting
USEFUL FOR

Physics educators, students learning about inclined planes, and anyone interested in teaching the principles of force decomposition in a clear and engaging manner.

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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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