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Two masses are connected by a string which passes over a pulley accelerating upward at a rate as shown. If $a_1$ and $a_2$ are the accelerations of bodies 1 and 2 respectively, find the value of $A$ (in terms of $a_1$ and $a_2$).

Figure

My attempt:

For the body 1:- $$T-m_1g-m_1A=m_1a_1$$

For the body 2:- $$T-m_2g-m_2A=-m_2a_2$$

Subtracting the two equations we get:- $$m_1g-m_2g+m_1A-m_2A=m_1a_1+m_2a_2$$

$$(m_1-m_2)A=m_1a_1+m_2a_2+m_2g-m_1g$$

I am not sure about this but assuming the numbers on the blocks are in fact the masses we can substitute $m_1=1kg$ and $m_2=2kg$. But even then there is still the $g$ variable I am not able to eliminate and by adding the initial equations a new tension $T$ variable shows up, what should I do?

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closed as off-topic by John Rennie, user81619, user36790, Kyle Kanos, Qmechanic Nov 7 '15 at 12:45

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I don't think your question asks you to eliminate $g$, however you can apply conservation of string to further reduce the equation, $a_1=-a_2$

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Considering effective gravity as it is an accelerating system, $$ g_{eff}=g+A $$ Now, $$ T-m_1(g+A)=m_1a_1\\ m_2(g+A)-T=m_2a_2 $$ Applying string constraint, $$ |T|.|a_1|-|T|.|a_2|=0 \\ |a_1|=|a_2| $$ Now you have got enough equations to finish of the problem!

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