A very difficult problem(hooke's law)

[DarkNess_wtc]

a mass is held by 3 extensible strings with spring constant k1,k2 and k3 respectively.
Now, the string in the middle is having a length of l
that's all the info. given
find the tension of the 3 strings

please help!

http://imageshack.us/photo/my-images/821/helptd.jpg

http://imageshack.us/photo/my-images/821/helptd.jpg

 

[Doc Al]

Please post the full problem exactly as given.

Show what you've done so far and where you are stuck.

 

[DarkNess_wtc]

that's all the information given.

I just don't know how the use the l

 

[ja_tech]

To be honest I don't think it's possible, seeing as though it's asking for the tension... This would require a quantity for mass which is not given.

If anything the answer would be in terms of K2.

 

[DarkNess_wtc]

i think the answer is in terms of l,k1,k2,k3 and theta

 

[ja_tech]

think or know?

 

[DarkNess_wtc]

know

 

[jane32260]

Well, if the string in the middle is having a length of l, there's high probability that all 3 strings are having the same lenght. So, when they extend, they all do it by x cm.
Now, the sum of the three tensions equals the weight of the object held by the three strings: T1+T2+T3=m*g, where m is the mass and g is the gravitational constant. But according to hooke's law, T1=k1*x, T2=k2*x and T3=k3*x.
Then, it becomes: k1*x+k2*x+k3*x=m*g<=>x*(k1+k2+k3)=m*g<=> x=(m*g)/(k1+k2+k3).
Once you found out x, you can find the three tensions.
Did I explain it well enough?

 

[DarkNess_wtc]

how can you know they having the same length and all do it by x cm.

 

[ja_tech]

I agree. length can't be the same...

I know the answer but will just give hints for now...

Use pythag for lenghts.

 

[jane32260]

The problem gives the length of the middle string, right?
Why didn't it give the length of any other? Because then there would be a chance that the mass didn't stay perfectly horizontal.
But you're right about the x cm. I can't be sure of that.

 

[DarkNess_wtc]

however, the natural length is not given. they might not be the same

 

[jane32260]

Yes, you're right.
I can't figure it out, though. How can I use pythag, when all I've got is the length of the middle string?

 

[Doc Al]

As far as I can see, there is not enough information to solve this problem. After all, you can disconnect the middle spring and still have the others support it; alternatively, you can have the middle spring support as much of the weight as you like.

Where did you get this problem?