(Vector statics) Effect of a pulley on free body diagram?

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Discussion Overview

The discussion revolves around the effect of a pulley on the free body diagram of a beam subjected to a load. Participants explore the implications of introducing a pulley system in terms of axial loads, tension forces, and equilibrium conditions, focusing on both theoretical and practical aspects of statics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a scenario involving a 1-m bar fixed to a wall with a 100 N weight, questioning how the free body diagram changes with the addition of a pulley.
  • Another participant mentions axial load in the beam under compression but does not elaborate on its implications.
  • There is a request for clarification on the magnitude of the axial force in the beam and the reasoning behind it, emphasizing the use of free body diagrams and equilibrium equations.
  • A participant explains that the tension in a rope through an ideal pulley is equal on both sides, suggesting that the force exerted by the wall on the rope must equal the tension, affecting the forces acting on the beam.
  • It is proposed that drawing a free body diagram of the pulley can help identify the direction of tension forces, leading to the conclusion that the beam experiences the same horizontal and vertical forces, but with an additional axial force that remains unspecified.

Areas of Agreement / Disagreement

Participants express differing views on the specifics of the axial force and its calculation, indicating that the discussion remains unresolved regarding the exact magnitude and implications of the forces involved.

Contextual Notes

Participants have not reached a consensus on the magnitude of the axial force in the beam, and there are unresolved aspects regarding the assumptions made in the free body diagrams and equilibrium equations.

dmk90
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For example, a 1-m bar fixed to a wall holding a weight of 100 N, like this:

f88b0724bf.jpg


How will the free body diagram of the second case different from the first?
 
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Axial load In beam (compression).
 
PhanthomJay said:
Axial load In beam (compression).
Can you explain what the magnitude of that force would be, and why?
 
dmk90 said:
Can you explain what the magnitude of that force would be, and why?
As always, use free body diagrams and the equilibrium equations. The tension in a rope passing through an ideal pulley is the same on both sides of the pulley. So the force of the wall on the rope must have a magnitude of T, acting left. By summing external forces of the system in the x direction = 0, the horizontal force of the wall on the beam must also be T, acting right, since that it is the only place where another external force can exist. The shear and moment values in the beam are the same as in the first case.

Alternatively, you can draw a free body diagram of the pulley to identify the direction of the tension forces down and left, then a free body diagram of the beam without the pulley must show the same horizontal and vertical forces acting on it down and left. This gives the same result for beam forces and moments, but now their is an additional axial force in the beam, equal to _??__ N.
 

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