Solving Acceleration Problem: Find a3 Differently

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SUMMARY

The discussion centers on the challenge of calculating the acceleration of a system involving two masses, m1 and m2, connected by a pulley. The key issue identified is the incorrect assumption that m1 and m2 can be treated as a single mass when applying Newton's 2nd law. This approach leads to confusion, as the calculated acceleration represents the center of mass rather than the actual acceleration of the pulley system. Properly distinguishing between the two masses is essential for accurate results.

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varunKanpur
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I am thinking of finding a3 through another way in this solved question

attachment.php?attachmentid=72787&stc=1&d=1410005214.jpg

attachment.php?attachmentid=72783&stc=1&d=1410005022.jpg


I am thinking of considering m2 and m1 as one mass but answer in not matching. I couldn't find what I am doing wrong.
attachment.php?attachmentid=72782&stc=1&d=1410005022.jpg


Thanx in advance .
 

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varunKanpur said:
I am thinking of considering m2 and m1 as one mass but answer in not matching. I couldn't find what I am doing wrong.
The problem with treating m1 and m2 as a single system is that the acceleration you'll find (using Newton's 2nd law) will be the acceleration of their center of mass. That acceleration is not the same as the acceleration of the pulley.

If m1 and m2 were fixed together, instead of in relative motion, then you'd be fine. (Obviously, that is not the case here.)
 

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