Why does 2T-(M+m)g=(M+m)a not work here?

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    Pulley pulley problem
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Discussion Overview

The discussion revolves around the mechanics of a man pulling on a rope to accelerate himself and a platform, specifically questioning the force required for this acceleration and the implications of tension in the rope. The scope includes conceptual understanding and mathematical reasoning related to forces and acceleration in a system involving multiple masses.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions why the force P required to achieve acceleration a is not calculated as (m+M)(a+g)/2, suggesting instead it should be (m+M)(a+g).
  • Another participant notes that when the man pulls the rope, an equal and opposite force is exerted on the platform.
  • A participant raises a point about the platform having an equal and opposite normal force, seeking clarification on its role in the system.
  • One participant asserts that a greater force is necessary to accelerate the combined mass of the man and platform, providing a mathematical expression: 2P=(m+M)(g+a)+P.
  • Another participant questions whether the tension in the rope on the opposite side contributes equally to the force, implying it could double the total upward force.
  • A participant agrees that the tension is crucial for the man to lift himself, indicating that this is why the left side of the equation is represented as 2P.

Areas of Agreement / Disagreement

Participants express differing views on the calculation of the force required and the role of tension and normal forces, indicating that multiple competing perspectives remain without a consensus on the correct approach.

Contextual Notes

Participants do not fully resolve the implications of the normal force or the contributions of tension, leaving some assumptions and mathematical steps unclear.

physicstime
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Can someone explain why the force P with which the man must pull on the rope to achieve an acceleration a m/s2 IS NOT (m+M)(a+g)/2 and is instead (m+M)(a+g). M+m is the combined mass of man and platform.

Why does 2T-(M+m)g=(M+m)a not work here?
 

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when he pulls the rope, an equal and opposite force is exerted on the platform.
 
Thanks for the response. But doesn't the platform have an equal and opposite normal force?
 
Exactly why greater force is required to accelerate the mass of the man + platform.

2P=(m+M)(g+a)+P
 
but doesn't the tension of the rope on the other side contribute just as much as the man therefore doubling the total force upwards?
 
Yes, and that is the only reason he can lift himself. This is why the left is 2P.
 

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