Peculiar Acceleration: Solving a Massless and Frictionless Pulley Problem

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Homework Help Overview

The problem involves a massless and frictionless pulley system with two masses and two pulleys. Participants are tasked with finding the accelerations of the masses and pulleys, while questioning the implications of their results.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to establish relationships between the accelerations of the masses and pulleys, noting a peculiar result where one pulley appears to accelerate downwards at a rate greater than g. Other participants question the validity of this result and explore the conditions under which such an acceleration could be possible.

Discussion Status

Participants are actively engaging with the reasoning presented, with some expressing agreement with the calculations while others seek clarification on the implications of the results. There is a productive exchange regarding the nature of the accelerations involved.

Contextual Notes

Assumptions about the massless and frictionless nature of the pulleys and strings are central to the discussion, and participants are examining the consequences of these assumptions on the calculated accelerations.

Vibhor
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Homework Statement



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All pulleys are massless and frictionless and string is massless . Find the acceleration of the two masses and the two pulleys .

Homework Equations

The Attempt at a Solution



I will call the left mass A and right mass B and left pulley P and right pulley R .

Acceleration of B is same as pulley R .

From the string constraint , the relationship between accelerations is ##a_P = a_A+2a_B##

Consider the forces on pulley P . Since it is massless , tension in the string has to be 0 .

Since tension is zero , accelerations of both A and B is ##g## downwards .

Acceleration of pulley P comes out to be ##3g## downwards .

The results look quite strange , especially the acceleration of left pulley .

How is left pulley P accelerating downwards with acceleration greater than g ?

Cam someone point out the mistake .

Many thanks
 

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Vibhor said:
How is left pulley P accelerating downwards with acceleration greater than g ?
I don't see why it should not. Even if it had mass, it would be possible to construct a pulley arrangement with other, larger masses that would make it drop faster than g.
 
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haruspex said:
I don't see why it should not. Even if it had mass, it would be possible to construct a pulley arrangement with other, larger masses that would make it drop faster than g.

OK. So the result that acceleration of pulley P is ##3g## downwards is correct ?
 
Vibhor said:
OK. So the result that acceleration of pulley P is ##3g## downwards is correct ?
Your reasoning all looks right to me.
 
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