Tension Ratio in a Uniformly Distributed Rope System

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Homework Help Overview

The discussion revolves around a physics problem involving a rope with uniform mass distribution attached to a spaceship, with a mass at the end of the rope. The objective is to find the ratio of tensions at two points along the rope, T_A and T_B, while considering the system's acceleration and the absence of gravity.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between the tensions at different points in the rope, with some suggesting to write expressions for T_A and T_B. There is discussion about the mass of the rope and its implications on the tension calculations.

Discussion Status

Participants are actively engaging with the problem, questioning assumptions about the mass distribution and the setup. Some have attempted to derive expressions for the tensions, while others are reflecting on their understanding and the implications of their calculations. There is no explicit consensus, but several lines of reasoning are being explored.

Contextual Notes

Participants note the importance of the mass of the rope in their calculations, and there are indications of confusion regarding the setup, particularly about the points of attachment and the distribution of mass. The absence of gravity is a key constraint in the problem.

Poetria
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Homework Statement


[/B]
A rope with uniform mass distribution is attached to a spaceship. At the end of this rope, there is a mass, m. The length of the rope - l.
Point A - where the rope is attached to a spaceship
Point B - in the middle of the rope.
The whole system moves with the same acceleration. I understand there is no gravity.

I am supposed to find a ratio T_A/T_B.

Tension - T

2. The attempt at a solution

I thought it would be simple: point B is in the middle of the rope and so the ratio is:
1 over 1/2.
 
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How about writing expressions for T_A and T_B? (What's the mass of the rope?)
 
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Doc Al said:
How about writing expressions for T_A and T_B? (What's the mass of the rope?)

I thought:

T_A= M/L*a
T_B=M/L*(L-1/2L)*a
 
Poetria said:
I thought:

T_A= M/L*a
T_B=M/L*(L-1/2L)*a
I'd say: T_A = (mass of rope + m)*a
and so on...
 
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Poetria said:

Homework Statement


[/B]
I thought it would be simple: point B is in the middle of the rope and so the ratio is:
1 over 1/2.
By that rationale, the tension at point C where the rope is attached to the spaceship would be zero.
 
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Chestermiller said:
By that rationale, the tension at point C where the rope is attached to the spaceship would be zero.

Do you mean point A?
 
Chestermiller said:
By that rationale, the tension at point C where the rope is attached to the spaceship would be zero.
You mean, attached to the mass, yes?
 
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haruspex said:
You mean, attached to the mass, yes?

Yes, I think so. I would be logical.

I already tried the method with (m of rope + m) but I couldn't get a numerical answer. I have to think what is wrong with it.
 
haruspex said:
You mean, attached to the mass, yes?
Oh yes. You're right. I misread the question.
 
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  • #10
Poetria said:
Yes, I think so. I would be logical.

I already tried the method with (m of rope + m) but I couldn't get a numerical answer. I have to think what is wrong with it.
Have you tried drawing a free body diagram of the mass plus the portion of the rope outboard of some point along the rope?
 
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  • #11
Poetria said:
I already tried the method with (m of rope + m) but I couldn't get a numerical answer. I have to think what is wrong with it.
What's the mass of the rope? All you've mentioned is its length L.
 
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  • #12
Thanks, guys, I got it right. I didn't notice that there are no two different masses.
I mean the mass of the rope = the mass of an object attached.
 

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