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Infinite Atwood (pulley) system - what's wrong with this?

Each block has mass \(m\). We are finding acceleration of topmost block.

Assume the tension \(T\) acting on topmost block and acceleration \(a\) in upward direction.

Then tension on second block is \(\frac{T}{2}\). If we see the block w.r.t the pulley that it is connected to, then apply psuedo force $ma$ in upward direction (as the pulley it is connected to is moving in downward with $a$), then the system observed is same as the above, I.e acceleration will be same.

Hence \[T-mg=ma\\ \frac{T}{2}+ma\text{ (psuedo force) }-mg=ma \]

We obtain \(a=g\) but the answer should be ...(this is a question on brilliant and I can't share answer)

Please help pinpoint the error.

Note by Megh Parikh
2 years, 9 months ago

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Why do you think it is the same system? Pratik Shastri · 2 years, 8 months ago

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Why is the acceleration of the 2nd pulley wrt 2nd block \(a\)? Pratik Shastri · 2 years, 8 months ago

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@jatin yadav. @Anish Puthuraya @David Mattingly. Please help. Megh Parikh · 2 years, 9 months ago

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All the blocks will be relative to each other as all the blocks are not stable, and thus the acceleration of each block will be different and you took them as same. just find the relation between the accelerations of different blocks and find a sequence and similarly you will find that acceleration of topmost block is g/2. ,try by taking a suitable observable position. Ronak Pawar · 2 years, 9 months ago

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@Ronak Pawar You misunderstood me.

I am seeing block2 wrt pulley2. Then pulley2 is at rest and it also has a system similar to pulley one. The acceleration of block2 is \(a\) wrt pulley2 Megh Parikh · 2 years, 9 months ago

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@Megh Parikh See the mistake which you did while solving this senario....

https://brilliant.org/community-problem/infinite-atwood-machine/ Ronak Pawar · 2 years, 9 months ago

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@Ronak Pawar Are you able to access solutions. I am waiting long but the solutions are just not coming on mobile. Will have to try on computer. Thanks anyway

There is also another such question which i am resharing so that you may answer it. Megh Parikh · 2 years, 9 months ago

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@Megh Parikh Its the same problem which u asked..here only you have to assume that g=9.8 m/ss in place of 10m/ss Ronak Pawar · 2 years, 8 months ago

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@Ronak Pawar No see my comment in that question on your solution.

I have no problem with 10 & 9.8 Megh Parikh · 2 years, 8 months ago

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