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

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SUMMARY

The mass of the hanging block (m2) in a system with a block on a smooth incline (m1 = 7.9 kg at a 40-degree angle) can be determined using the equilibrium condition. In this scenario, the tension in the rope equals the weight of m2, while the tension also equals the component of the gravitational force acting on m1 along the incline. The equation governing this relationship is T = m2 * g, where T is the tension and g is the acceleration due to gravity. By resolving the forces acting on m1, the mass m2 can be calculated to maintain equilibrium.

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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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