Competitive exam Question: Work done to shorten string

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Homework Help Overview

The problem involves calculating the work done in shortening a string attached to a rotating particle. The context includes concepts from mechanics, specifically angular momentum and rotational motion.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between the radius of rotation and velocity, questioning whether angular momentum is conserved and how it affects the work done. There are attempts to derive expressions for work done based on force and velocity.

Discussion Status

There is ongoing exploration of the problem, with some participants agreeing on certain aspects while others express uncertainty about the correctness of their approaches. Guidance has been offered regarding the integration of force and the need to express variables in terms of constants.

Contextual Notes

Participants are navigating assumptions about the conservation of angular momentum and the behavior of velocity as the radius changes. There is a recognition of the need for verification of the proposed solutions.

adeelrizvi
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Q) A particle of mass 'm' attached to a string rotates with velocity Vo when the length of the string is Ro. How much work is done in shortening the string to R?

One way I thought about doing this was:
W= {(m*r*w^2) * r}dr and integrate this from R to Ro
But I am not sure if that is correct. So if someone can help me with this question I will really appreciate it.
Thanks in advance!
 
Last edited:
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Sounds good.
What happens to the velocity as r decreases?
I suppose angular momentum will be conserved.
 
You think my solution is correct? Can someone else also please confirm this.

v=rw, w is constant. r decreases so v decreases as well. Correct me if I am wrong.

Angular momentum I believe is conserved.
 
v=rw, w is constant.
I don't think w is constant. The constant is k = mrv so v = k/(mr)
and w = v/r = k/(mr^2).

r decreases so v decreases as well.
v increases as r decreases.
 
I guess you are right. I was taking the wrong assumption. If angular momentum is conserved then velocity increases if radius decreases.
Now when you have corrected me I think my solution to the problem was not correct either. Can you please verify that for me as well?
Thanks
 
I haven't seen a solution yet. I just agreed that integrating Force*dr would be the way to do it. And you have to be careful to express v or w in terms of k and r because v and w are not a constants.
 
Solution:

dW= F.dr
dW= {(m*v^2)/r}dr (v=k/mr)
dW= {(k^2/m)*(1*r^3)}dr
Integrate this with limits Ro to R

W = [(k^2)/(2m)]*[(1/Ro^2) - (1/R^2)] <----Answer

Please check and let me know if this seems correct to you?
Thanks
 
That is precisely what I got!
Of course I am not infallible! I'm just a retired high school teacher missing the good feeling of helping my students.
 
I really appreciate your help. I hope we are correct but it will be good to know if someone else here can verify our solution.
 

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