Constraint relation in a pulley spring system

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SUMMARY

The discussion focuses on establishing the relationship between the displacements of a block of mass m and a pulley of mass M in a pulley spring system. Key equations include the tension equations and the constraint that the length of the rope remains constant. Participants emphasize the importance of starting with kinematics rather than dynamics to derive the necessary relationships. The conversation highlights the need to account for the pulley’s rotation and the effects of tension in both strings.

PREREQUISITES
  • Understanding of kinematics in mechanical systems
  • Knowledge of tension forces in pulley systems
  • Familiarity with torque and rotational dynamics
  • Basic principles of constraints in mechanical systems
NEXT STEPS
  • Study the kinematic relationships in pulley systems
  • Learn about torque and its effects on pulley rotation
  • Explore the concept of constraints in mechanical systems
  • Review tension force calculations in multi-string pulley setups
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Students studying physics, mechanical engineers, and anyone interested in understanding the dynamics of pulley systems and constraints in mechanical motion.

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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