A very difficult problem(hooke's law)

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Homework Help Overview

The problem involves a mass held by three extensible strings with different spring constants (k1, k2, k3) and a specified length (l) for the middle string. The objective is to find the tension in the three strings, but the information provided appears to be insufficient for a complete solution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of the given length of the middle string and question whether the lengths of all strings are the same. There are attempts to relate the tensions to the mass and gravitational force using Hooke's law, but concerns about missing information arise.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some suggest that the lack of mass information makes it impossible to determine the tensions, while others propose using geometric relationships to analyze the setup further. Hints are being shared, but no consensus has been reached regarding the approach to take.

Contextual Notes

There is a noted absence of information regarding the mass and the natural lengths of the strings, which participants identify as critical for solving the problem. The constraints of the problem and the potential for multiple interpretations are acknowledged.

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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
 
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Please post the full problem exactly as given.

Show what you've done so far and where you are stuck.
 
that's all the information given.

I just don't know how the use the l
 
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.
 
i think the answer is in terms of l,k1,k2,k3 and theta
 
think or know?
 
know
 
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?
 
how can you know they having the same length and all do it by x cm.
 
  • #10
I agree. length can't be the same...

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

Use pythag for lenghts.
 
  • #11
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.
 
  • #12
however, the natural length is not given. they might not be the same
 
  • #13
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?
 
  • #14
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?
 

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