What is the tension in an Atwood machine when one mass is infinitely large?

AI Thread Summary
In an Atwood machine with one mass infinitely large, the tension in the rope approaches the weight of the finite mass, m_2, multiplied by the gravitational constant, g. As m_1 becomes infinitely large, its acceleration approaches zero, while m_2 accelerates upward at g. This results in the tension being equal to m_2 times g, confirming that the initial assumption was partially correct. The discussion highlights the relationship between mass, tension, and acceleration in this specific scenario. Understanding these dynamics is crucial for analyzing the behavior of Atwood machines under extreme conditions.
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An Atwood machine consists of two blocks (of masses m_1 and m_2) tied together with a massless rope that passes over a fixed, perfect (massless and frictionless) pulley.
For all parts of this problem, take upward to be the positive direction and take the gravitational constant, g, to be positive.

Now here's the problem: suppose m_1 goes to infinity while while m_2 remains finite. What value does the the magnitude of the tension approach??

I think it's m_2 times g, but I think that's not entirely correct. I tried to find the acceleration of m1 and concluded it was 0, and then thought that acceleration of m2 was g (positive, because it's going up) so that tension is just the sum of two forces... which is how i arrived at my partially correct answer m_2 times g.
 
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