# What's wrong with my answer?

1. Feb 17, 2015

### mooncrater

1. The problem statement, all variables and given/known dataThe 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.

2. Relevant equations
N/a

3. The attempt at a solution

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 ?

#### Attached Files:

• ###### IMG_20150217_145912.jpg
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2. Feb 17, 2015

### BvU

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. Feb 20, 2015

### mooncrater

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. Feb 21, 2015

### haruspex

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. Feb 21, 2015

### nil1996

You have to consider the tension on both sides of the element along the tangential direction!