What's wrong with my answer?

  • Thread starter mooncrater
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  • #1
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Homework Statement

The question says
A chain of mass per unit length k and length 1.5 m rest on a fixed smooth sphere of radius R= 2/π m
. Tension in the thread is asked.The question figure is attached.


Homework Equations


N/a


The Attempt at a Solution


IMG_20150217_145935.jpg
IMG_20150217_145935.jpg

I think that the tension has to balance two types of forces :
1) rightward force of part AC(touching)
2)downward force of part CB(hanging)
Finding first type of force:
Using Fbd(attached) of small part taken in touching part
Then Ncos(theta)=(dm)g
→ N=(dm)g/cos(th.).......(1)
Length of that part =R(d(th.))
mass of that small part =Rk(d(th.))
Using Fbd rightward force on the small part =Nsin(th.)=(dm)g(tan(th.))
=Rkgtan(th.)(d(th.))
Now if I want to integrate it , i would have to use limits from 0 to π/2
BUT tan (th.) is not integrable b/w 0 to π/2 . So whats wrong with my answer ?
 

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Answers and Replies

  • #2
BvU
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I'm missing something in your force balance for the little chunk of chain. I see an N and an mg and they clearly don't balance. What force could possibly complete the picture ?
 
  • #3
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I'm missing something in your force balance for the little chunk of chain. I see an N and an mg and they clearly don't balance. What force could possibly complete the picture ?
It could have been friction BUT the sphere is smooth so , what can be the force (you are talking about ) left out that balances the tension of the thread ?
 
  • #4
haruspex
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It could have been friction BUT the sphere is smooth so , what can be the force (you are talking about ) left out that balances the tension of the thread ?
But you don't have the tension in the chain in the equation. Indeed, that's what's missing. Remember, it will not be constant along the the chain.
 
  • #5
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You have to consider the tension on both sides of the element along the tangential direction!
 

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