Find depression in wire with hanging mass

[bodensee9]

Hello: I have the following:

Homework Statement

A wire of unstretched length l is extended by a distance (1/1000)l when a mass M is hung from its bottom end. If this same wire is connected between points A and B that are at a distance l from each other on the same horizontal level, and the mass M is hung from the midpoint of the wire, find the depression y of the midpoint.

Homework Equations

2Tsin(theta) = mg
sin(theta) = y/(the stretched length of l/2).

The Attempt at a Solution

Not sure where to go from there. Would it be safe to say that each half of the wire is stretched by l/2000? Thanks.

 

[tiny-tim]

Hello bodensee9!

(have a theta: θ )

Would it be safe to say that each half of the wire is stretched by l/2000? Thanks.

How did you get that?

Use Pythagoras, and an approximation.

 

[mmmboh]

I need help with this problem too. 2Tsintheta=mg, and tantheta=2y/l, for small angles tan theta=sin theta, so if we could use that approximation then sin theta=2y/l,...I can also use Pythagoras to find the hypotenuse and then find the real sin theta and equate them to find y, I don't think that's a proper answer though...I'm not sure where the L/1000 comes in...

This isn't homework, I know the answer already is L/20, just don't know how to get that..

 

[tiny-tim]

...I'm not sure where the L/1000 comes in...

L/2 = adjacent, (1 + 1/1000)L/2 = hypotenuse.