What is the mass of the hanging block in this system in equilibrium?

AI Thread Summary
To determine the mass of the hanging block (m2) in a system with a block on a 40-degree incline (mass m1 = 7.9 kg), the equilibrium condition must be established. The tension in the rope, which keeps the system in equilibrium, is equal to the weight of m2. Since the blocks are not accelerating, the forces acting on both blocks must balance out. A free body diagram is essential to break down the forces into components for accurate calculations. Ultimately, the equilibrium condition for m1 must also be considered to find the relationship between m1 and m2.
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Homework Statement


T
here are 2 blocks connected by a string, as shown in the first image attached. The smooth inclined surface makes an angle of 40 degrees with the horizontal, and the block on the incline has a mass m1 = 7.9kg. What is the mass of the hanging block m2 that will cause the system to be in equilibrium.


Homework Equations



\sumF = ma
then find the components...

The Attempt at a Solution



I know that I have to set up a free body diagram then break everything up into components. I also know that objects in equilibrium do not accelerate. But I can't figure out how to find the one mass. What equation would I use or what would I set things equal to?
 

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Since the bodies are in equilibrium, they don't accelerate. Which means that the rope is keeping them still.
The tension in the rope is thus equal to the weight of m2. This is the equilibrium condition for m2.
Now try to right the condition up for m1. (i.e. the tension in the rope is equal to ...).
 
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