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

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SUMMARY

The tension in an Atwood machine with one mass infinitely large (m_1) and the other mass finite (m_2) approaches the value of m_2 times the gravitational constant (g). In this scenario, the acceleration of the infinitely large mass (m_1) is zero, while the finite mass (m_2) accelerates upwards at g. Therefore, the tension in the rope is effectively equal to the weight of the finite mass, confirming that the tension approaches m_2 * g as m_1 increases without bound.

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  • Understanding of Newton's laws of motion
  • Basic knowledge of gravitational force and tension in ropes
  • Familiarity with the concept of massless and frictionless pulleys
  • Ability to analyze forces in a system of connected objects
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  • Study the dynamics of Atwood machines with varying mass ratios
  • Learn about the implications of infinite mass in mechanical systems
  • Explore tension calculations in non-ideal pulley systems
  • Investigate the effects of friction on tension in real-world applications
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Physics students, educators, and anyone interested in classical mechanics, particularly those studying systems involving pulleys and forces.

jaded18
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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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What is the tension in a regular atwood machine with masses m1 and m2?
 

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