What's the Trick to Solving Incline Plane Problems?

[Optikspik]

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

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

 

[mfb]

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.