Simple Tension Problem

1. The problem statement, all variables and given/known data[/b]
A block with mass M = 5kg sits at rest on a frictionless incline. The mass is connected to the wall by a string with linear density μ = 5.0 g/m. The incline is fristionless, with angle Θ = 30°. Let the positive x-direction point up along the incline, and let the origin (x=0) be at the end of the string attached to the mass. HERE IS A DIAGRAM OF WHAT THE PROBLEM LOOKS LIKE:

Draw a free body diagram of the block. What is the normal force on the block?

2. Relevant equations

This is probably where I’m lacking. I’m not sure if there is an equation that will give me a way of solving for T or not, but other than that there are no real equations necessary.

3. The attempt at a solution

I’m having no real problems with the free body diagram. It’s simple enough. The issue I’m having is that I don’t know how to calculate the Normal force on the block due to the incline. I calculate that:

N[itex]\ast[/itex]sin(60) + T[itex]\ast[/itex]sin(30) = mg
N = [itex]\frac{(mg – 1/2T)}{sin(60)}[/itex]
N = [itex]\frac{(2mg – T)}{\sqrt{3}}[/itex]

But now the only way I can see myself solving for N is with the value of T, which I can’t seem to figure out. Am I just missing a valuable equation?

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