Two masses connected by strings on an incline

[David Mordigal]

This is a problem from my physics homework. I copied the diagram below as best I could from the text. It's not the best rendering but you'll get the idea.

1. Homework Statement
Two blocks are at rest on a frictionless incline, as shown in the figure.

Part A. What is the tension in the string number 1 if m₁ = 9.0kg and m₂ = 3.9kg?
Part B. What is the tension in the string number 2 if m₁ = 9.0kg and m₂ = 3.9kg?

The answer to Part A is: T₁ = 30.2 N, which I don't understand.

Homework Equations

So far, I know the following:
F = ma
F_x = ma_x
F_y = ma_y
w = w_y = mg = 9.0kg * 9.8 m/s² = 88.2 N

The Attempt at a Solution

I tried splitting the tension of string 1 into its vector x and y components, but that wasn't getting me to the right answer. I am not quite sure where to start or how they got that answer, 30.2 N (part A). Any guidance would be much appreciated.

T_y = mg = 88.2 N
T = T_y/sin(20) = 257.9 N

 

[Satvik Pandey]

Hi David welcome to PF.
I suggest you to choose your co-ordinate axis as shown in figure.
After drawing free body diagrams of m₁ can you find T₁?

 

[Simon Bridge]

It does work to have the axes so gravity points in the -y direction ... but, as Satvik suggests, the maths is way easier if you point the x-axis along the slope. The reason you are having trouble is probably because you have not included all the forces on each mass ...

The first step is always to draw a free body diagram - make it a habit.
Please tell us what forces you put on it and where they point.