Accelerating motion with a pulley

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Discussion Overview

The discussion revolves around the dynamics of two bodies connected by a rope over a pulley, specifically focusing on the relationship between their motions, forces, and accelerations. It explores theoretical assumptions, the implications of these assumptions, and the application of free body diagrams (FBDs) in understanding the system.

Discussion Character

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

Main Points Raised

  • Some participants propose that the relationship between the two bodies involves tension and weight, questioning if tensionA equals weightB.
  • Others emphasize the need for assumptions such as the inextensibility of the rope, and the masslessness of the pulley and rope, while acknowledging these assumptions are not strictly true.
  • One participant challenges the idea that tension can equal weight, suggesting that if tension equals weight, body B would not fall.
  • Another participant notes that the same force in the rope implies different accelerations if the masses are different, raising questions about the implications of inextensibility.
  • Several participants recommend drawing free body diagrams (FBDs) to clarify the forces acting on each body and the resulting accelerations.
  • A participant expresses confusion regarding whether the tension is the same as the weight or if the accelerations are the same, indicating a lack of clarity in the analysis.

Areas of Agreement / Disagreement

Participants generally agree on the importance of using free body diagrams to analyze the problem, but there remains disagreement regarding the relationships between tension, weight, and acceleration, as well as the validity of the assumptions made in the analysis.

Contextual Notes

Limitations include the assumptions about the masslessness of the pulley and rope, and the inextensibility of the rope, which may not hold in practical scenarios. The discussion also reflects unresolved mathematical steps related to the forces and accelerations of the two bodies.

Who May Find This Useful

This discussion may be useful for students and educators in physics, particularly those exploring dynamics, pulley systems, and the application of free body diagrams in problem-solving.

House
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Let's suppose we have a body A with mass M that can move on a horizontal frictionless ground. Now we connect that with another body B, mass m, with the help of a rope. The body B can move vertically and the rope is curved with a pulley. Now we set the body B free to move.
What's the relationship of the motion of the two bodies? Is there a same force (tensionA = weightB or a same acceleration?
 
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The usual approach to this sort of problem involves three assumptions:
1) the rope is inextensible (it does not stretch)
2) the pulley is massless
3) the rope is massless
None of these is ever strictly true, but they significantly simplify the problem. Are you willing to live with these assumptions, or if not, what do you wish to assume instead about these two matter?
 
House said:
tensionA = weightB
If the tension would be equal to the weight of B, then B wouldn't start falling.
 
Dr.D said:
The usual approach to this sort of problem involves three assumptions:
1) the rope is inextensible (it does not stretch)
2) the pulley is massless
3) the rope is massless
None of these is ever strictly true, but they significantly simplify the problem. Are you willing to live with these assumptions, or if not, what do you wish to assume instead about these two matter?

Absolutely, I just forgot to mention them.
 
You need to draw FBDs for each body, and do not assume that T = Wb. Also, look at the kinematic constraint imposed by the inextensible cord.
 
Okay, so a professor of mine told me that the rope carries the same force from B to A. But same force means different acceleretion if the masses are different. If this is true how can different parts of the rope have different acceleretions if the rope is inextensible?
 
House said:
Okay, so a professor of mine told me that the rope carries the same force from B to A. But same force means different acceleretion if the masses are different. If this is true how can different parts of the rope have different acceleretions if the rope is inextensible?
The same net force means the same acceleration. What forces act on object A? What forces act on object B?
 
I repeat, you need to draw the FBDs for the two blocks. When you do, if done correctly, it will all become clear to you.
 
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  • #10
So, according to the FBDs we have a force for each object, but again I can't decide if the tension is the same as the weight or the accelerations are the same. I'm completely stuck here.
 
  • #11
Update: Problem solved. Thanks a lot for your time, much appreciated.
 

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