What's the Trick to Solving Incline Plane Problems?

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To solve incline plane problems, one approach involves assuming acceleration downwards and to the right, leading to the equation where net forces promoting acceleration are balanced against opposing forces. Free body diagrams and tension can also be utilized for clarity, but some argue that simpler methods can yield correct answers without them. The key is understanding that tension is an internal force, allowing for a focus on external forces acting on the entire system. While implicit assumptions about acceleration can simplify the process, clear reasoning should be communicated on tests to avoid appearing as if guessing. Ultimately, both methods can lead to accurate solutions if understood correctly.
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How i solve this problem would be, i assume acceleration to go right and downwards. WHich would give me the equation. The forces promotes the acceleration - the forces which opposes the acceleration = F_net

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However, U could solve this with free body diagrams, and Tension. How come I can just do like this and get the right answer? LIke how do i "motivate" on the test, without doing free body diagram and equation systems! Has it something to do with TEnsion = internal force and we look at the forces on the whole system external? Or how would u write on a test, just to motivate that u don't just guess the numbers!?

2. Do i get the correct answer? :p
 
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That is correct, and I don't think it needs further motivation.
You have the implicit assumption that both accelerations are the same in magnitude, but that is easy to see.
 

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