Ropes/Pulleys with moving weights

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Homework Help Overview

The discussion revolves around a physics problem involving two blocks connected by an ideal pulley system, where the goal is to find the velocity of block B. The masses of the blocks are specified, and the scenario assumes ideal conditions for the pulleys and rope.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the tension in the rope, questioning the consistency of tension values derived from different equations. Some express confusion over the relationship between tension and weight, suggesting that tension should remain unknown to simplify the analysis. Others point out potential errors in the equations used, particularly regarding the treatment of acceleration terms.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some have offered insights into the equations and assumptions being made, while others are questioning the validity of the approaches taken. There is no explicit consensus yet on the correct method or solution.

Contextual Notes

Participants are working under the constraints of ideal conditions for the rope and pulleys, and there is a mention of static analysis, which may influence the interpretation of the problem. The presence of conflicting tension values suggests a need for clarification on the assumptions being made.

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Homework Statement


Find the velocity of block B (the one to the right) A has a mass of 3kg and B a mass of 5kg. Pulleys and rope are ideal.

Homework Equations


F=ma

The Attempt at a Solution


I used two different methods, got the same WRONG answer. The correct answer is Vb= -35.8m/s
Let me know if you can't see what the pictures say

IMG_2768.jpg

IMG_2769.jpg
 
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How is it consistent for T=49.1 N but 2T=29.43 N if it's the same rope? Tension doesn't vary across an ideal rope, because the rope is massless.

You can't say the tensions are equal to the weights. The objects will accelerate; but if the tension equals the weight, how would the objects accelerate?
I would leave the tension unknown and eliminate it, no reason to solve for it.
 
I used this method:

 
Ah, I didn't see that you wrote "static analysis" above that part.

In either eq 2 or eq 3, you have an extra factor of -1 on the acceleration term.

Edit:
Actually, it could be fixed by slightly altering any of your 3 equations; they just need to be consistent.
You said, -ab = 2aa which implies that you're letting ab and aa represent the magnitudes and direction (one of them is negative) of acceleration; but then you have an extra factor of -1 on a3 in eq.3, which implies that you're taking aa and ab to be just the magnitude
 
Last edited:

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