Why Are Polar Coordinates Essential in Solving the Ant and Rubber Band Problem?

[IamVector]

Homework Statement

An ant is moving along a rubber band at velocity
v = 1 cm/s. One end of the rubber band (the one from which

the ant started) is fixed to a wall, the other (initially at dis-
tance L = 1 m from the wall) is pulled at u = 1 m/s. Will the

ant reach the other end of the band? If yes then when will it
happen?

Relevant Equations

approach is : we can use the relative position on
the band which fraction k of the rubber is left behind starts with k = 0, and k = 1 corresponds to the ant reaching the end of the band .

why can't we use Cartesian coordinates and in which way to proceed?

 

[berkeman]

Please show the Relevant Equations and show your work on this, or your thread will be deleted. Thank you.

 

[IamVector]

Please show the Relevant Equations and show your work on this, or your thread will be deleted. Thank youl

ok

 

[haruspex]

why can't we use Cartesian coordinates

You can use whatever coordinates you like, but sometimes it is easier to use a frame of reference that is moving. Sometimes, even using a noninertial frame is easiest.

 

[IamVector]

You can use whatever coordinates you like, but sometimes it is easier to use a frame of reference that is moving. Sometimes, even using a noninertial frame is easiest.

the hint given is related to using Lagrangian coordinates but I don't have any idea what they are.

 

[haruspex]

the hint given is related to using Lagrangian coordinates but I don't have any idea what they are.

http://glossary.ametsoc.org/wiki/Lagrangian_coordinates
Imagine that the band starts out marked in some equal intervals. Of course, the gap between them grows as the band is stretched, so in these units the ant slows down.
How fast is the ant going, in these units, at time t?

 

[DaveE]

the hint given is related to using Lagrangian coordinates but I don't have any idea what they are.

You don't have ANY idea what they are? Have you searched google or Wikipedia?
If you ask a specific question you may get an answer here, but this sounds like giving up.
"Solve my problem for me" isn't likely to work here.
You've gotten some good hints here, work with those and ask about what confuses you.

 

[IamVector]

You don't have ANY idea what they are? Have you searched google or Wikipedia?
If you ask a specific question you may get an answer here, but this sounds like giving up.
"Solve my problem for me" isn't likely to work here.
You've gotten some good hints here, work with those and ask about what confuses you.

Hmm got the answer
Ant cover Vdt distance in dt time and final length of rubberband = L+ut
So dk = Vdt/(L+ut) on taking integrals and putting values t = e^100 - 1
[thread closed]

 

[haruspex]

Hmm got the answer
Ant cover Vdt distance in dt time and final length of rubberband = L+ut
So dk = Vdt/(L+ut) on taking integrals and putting values t = e^100 - 1
[thread closed]

Yes, that's good. To put it into a Lagrangian coordinates view you would say that speed of the ant in those coordinates is $\frac{L V}{L+ut}$, etc.

 

[epenguin]

Am I wrong to say you don't need any equations for this question?

 

[haruspex]

Am I wrong to say you don't need any equations for this question?

Not sure how you are going to arrive at time =$\frac Lu(e^{\frac uV}-1)$ without using equations.

 

[Cutter Ketch]

Not sure how you are going to arrive at time =$\frac Lu(e^{\frac uV}-1)$ without using equations.

I bet Galileo could do it. I think it involves an imaginary conversation where two rational people continually insult the village idiot while saying “therefore” a lot.

 

[IamVector]

I bet Galileo could do it. I think it involves an imaginary conversation where two rational people continually insult the village idiot while saying “therefore” a lot.

what does that even mean XD??

 

[Cutter Ketch]

what does that even mean XD??

Galileo (and most philosophers for many hundreds of years before him) used the Socratic method. His observations were published in the form of dialogues between a wise teacher and two students: one a neutral inquisitive person and the other a devil’s advocate always making counter arguments for the teacher to shred. He was tellingly named ‘Simplicio’. In these dialogues instead of equations the relations are spelled out using language, so, for example you will find quotes like this,

“ The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time intervals employed in traversing those distances.”

So I was jokingly saying Galileo would find a way to say it all with words and he would do so in the Socratic form.

 

[IamVector]

Galileo (and most philosophers for many hundreds of years before him) used the Socratic method. His observations were published in the form of dialogues between a wise teacher and two students: one a neutral inquisitive person and the other a devil’s advocate always making counter arguments for the teacher to shred. He was tellingly named ‘Simplicio’. In these dialogues instead of equations the relations are spelled out using language, so, for example you will find quotes like this,

“ The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time intervals employed in traversing those distances.”

So I was jokingly saying Galileo would find a way to say it all with words and he would do so in the Socratic form.

of course I knew you were joking but what was the need? I thought something triggered you XD

 

[epenguin]

Not sure how you are going to arrive at time =$\frac Lu(e^{\frac uV}-1)$ without using equations.

You are right, I had hastily misread the questio.

 

[IamVector]

You are right, I had hastily misread the questio.

Np