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

[jaded18]

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.

 

[learningphysics]

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

 

[m2003]

Your approach is correct. As m_1 goes to infinity, the mass of the system is dominated by m_1 and the acceleration of the system approaches 0. This means that the tension in the rope, which is equal to the force pulling on m_2, is equal to the weight of m_2, which is m_2*g. So your answer of m_2*g is correct. This is a special case of the Atwood machine, known as the "unbalanced Atwood machine" where one mass is much larger than the other and the larger mass essentially becomes the fixed point in the system.