Two blocks connected with a fragile rope

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Discussion Overview

The discussion revolves around the mechanics of two blocks connected by a fragile rope, specifically examining how the maximum force applied to the blocks affects the tension in the rope and whether this depends on which block is being pulled. The scope includes theoretical considerations and practical implications of force application.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the maximum force applied to the blocks may depend on which block is being pulled.
  • Others argue that the method of force application (slow vs. quick) significantly influences the tension in the rope.
  • A participant mentions that without a diagram, it is challenging to provide a definitive answer, highlighting the importance of context such as friction and the orientation of the blocks.
  • One participant suggests that the tension in the rope will vary depending on the side from which the force is applied, even under stationary conditions.
  • Another participant calculates the maximum acceleration for each block based on the tension limit of the rope and discusses the implications of pulling each block directly.

Areas of Agreement / Disagreement

Participants express differing views on whether the choice of block affects the maximum force that can be applied without breaking the rope. There is no consensus on the conditions under which the tension varies or the implications of different force application methods.

Contextual Notes

Limitations include the lack of clarity on the presence of friction, the specific orientation of the blocks, and the nature of the force application (slow vs. fast). These factors remain unresolved and are critical to understanding the scenario.

ChessEnthusiast
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Let's say that we have two blocks - 2 kg and 1 kg.
They are connected with a rope that can stand the maximal tension of 20 N.

Does the maximal force we can apply to the block so that the rope does not break apart depend on the choice of the block?
 
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A diagram could help here. Does this involve a pulley? It's impossible to suggest and answer at the moment.
 
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There is no pulley. We simply pull one of the block so that it increases the tension.
 
ChessEnthusiast said:
There is no pulley. We simply pull one of the block so that it increases the tension.
A diagram would still help. Horizontal or vertical? Fast or slow application of force? Friction? Stationary or accelerating?

The answer is probably yes, but I can think of scenarios where it could be no.
 
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Are the blocks floating in space or is there some friction involved. Without a diagram neither of us can help you.
 
I have drawn a diagram.
 

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If the force applied is very slow then it makes no difference. If the force is applied in a very quick jerk then it makes a big difference.
 
The tension in the rope will depend on which side you apply the force. Even for the stationary case (or very slow application of force). Actually the fast application of force is the one that may break the rope in both cases.
 
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ChessEnthusiast said:
I have drawn a diagram.
That's more useful. Thanks
Yes, it's all to do with F=ma.
I am assuming that the applied force is ramped up slowly enough to avoid any stretching of the rope and no jerking.
For a start, the block at the end that's pulled will make no difference to the tension in the rope; we are just concerned with the 'other' block.
If the rope will stand 20N then the maximum acceleration it can give to the 10kg block will be 20/10 = 2m/s2. It can only give the 20kg block 20/20 = 1m/s2
To accelerate both blocks, the Force needed will be total mass X acceleration so the force when pulling the 20kg block directly can be as high as 30X2 = 60N and for pulling the 10kg block directly the force can be no more than 30N.
Any other practical details would need to be added in and the calculation would be much more complicated.
 
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