Tension Ratio in a Uniformly Distributed Rope System

[Poetria]

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.

 

[Doc Al]

How about writing expressions for T_A and T_B? (What's the mass of the rope?)

 

[Poetria]

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

 

[Doc Al]

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...

 

[Chestermiller]

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.

 

[Poetria]

By that rationale, the tension at point C where the rope is attached to the spaceship would be zero.

Do you mean point A?

 

[haruspex]

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?

 

[Poetria]

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.

 

[Chestermiller]

You mean, attached to the mass, yes?

Oh yes. You're right. I misread the question.

 

[Chestermiller]

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?

 

[Doc Al]

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.

 

[Poetria]

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.