Application of Theory in Inclined Planes

AI Thread Summary
The discussion focuses on the application of forces on inclined planes, specifically how to calculate net forces when tensions are equal but gravitational forces differ. It questions whether the coordinate system can be consistently applied to each mass, leading to equations like Fnet = T - Fg1 for the first mass and similar for others. Additionally, it explores the implications of using a rotated coordinate system for an object moving between two inclined planes, particularly regarding the signs of the gravitational components. The poster is seeking clarification on these concepts due to difficulties in obtaining correct answers. Understanding these principles is crucial for accurately analyzing forces in inclined plane scenarios.
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Say I have to consider a situation like this:

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Say there are tensions (all the same) on each one and forces of gravity (different) on each one. Would the coordinate system there apply to each one in reference to their forces?

In other words for the first mass, would Fnet = T - Fg1? For the second, Fnet = T - Fg2? For the third, Fnet = T - Fg3? I tried this and I did not get the right answer

Say I have to consider another situation - two inclined planes and an objected from from the first to the second:

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Would the rotated coordinate system there apply to each force on an object that moves on these planes? In other words, would the Fgx on the left be + and the Fgx on the right be - according to that system?
 
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