Constraint relation in a pulley spring system

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Homework Help Overview

The discussion revolves around establishing a relationship between the displacements of a block of mass m and a pulley of mass M in a pulley-spring system. Participants are exploring how to apply constraints in this context, particularly focusing on kinematic relationships and the implications of tension in the strings.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the importance of starting with kinematics rather than dynamics in pulley problems. Questions arise regarding the relationship between the movement of the pulley and the block, as well as the implications of tension being equal in both strings.

Discussion Status

The discussion is ongoing, with participants questioning the assumptions about tension and the rotation of the pulley. Some guidance has been offered regarding the need to establish kinematic relationships based on the constant length of the rope, but no consensus has been reached on how to proceed further.

Contextual Notes

There is uncertainty regarding the fixed nature of the pulley and how that affects the tension in the strings. Participants are grappling with the implications of the pulley not being massless and the need for a net torque for rotation.

Shivang kohlii
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Homework Statement


1546603482077-1365890843.jpg

How to apply constraints in the system to get a relationship between the displacements of block of mass m and pulley of mass M.?

Homework Equations


T.a= 0

The Attempt at a Solution


Assuming tension in both strings to be T .
-T × a1 ( for the block) + 2T × a2 ( for the strings attached to sides of pulley) + for the string attached from the centre = 0

I can't understand how to proceed
 

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The place to start on a pulley problem is this the kinematics, not the dynamics. If the center of the pulley moves downward a distance y, and the string is of constant length, how much does the mass move downward relative to the center of the pulley? Relative to the table?
 
Shivang kohlii said:
Assuming tension in both strings to be T .
If that were true, why would the pulley rotate?
 
haruspex said:
If that were true, why would the pulley rotate?
Why should it rotate ? It's fixed to a table so the tension in both strings should be same
 
Chestermiller said:
The place to start on a pulley problem is this the kinematics, not the dynamics. If the center of the pulley moves downward a distance y, and the string is of constant length, how much does the mass move downward relative to the center of the pulley? Relative to the table?
That's the issue .. I don't know how to establish a relation..
 
Shivang kohlii said:
Why should it rotate ? It's fixed to a table so the tension in both strings should be same
The pulley doesn't know what the string is attached to. This is not a massless pulley. If the pulley has accelerating rotation, some net torque must cause it. Where is that coming from?
 
Shivang kohlii said:
That's the issue .. I don't know how to establish a relation..
Establishing the kinematic relation is a math problem. The length of the rope is constant. This is the constraint you need to use.
 

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