(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two springs are hung in a "v" shape, and a 500g mass is attached to the point of the v.

One spring is observed to stretch 9mm, the other 23mm.

Students are NOT permitted to measure any angles, before or after the weight is attached.

Is it possible to calculate the spring constants of the two springs?

2. Relevant equations

F = -kx (Hooke's law)

F = k1*x1*sin(θ) + k2*x2*sin(∅) (Vertical component of force if the two springs' angles were known.)

3. The attempt at a solution

The problem doesn't seem solvable to me. If the angle of the springs from horizontal is very small, then the stretching will be the equivalent of many times the weight that is actually applied. At 30 degrees from vertical, EACH spring stretches as much as it would if it had a 500g weight pulling on it vertically. At smaller angles, each stretches further yet.

For example, at 10 degrees for both springs:

F = k1*x1*sin(θ) + k2*x2*sin(∅)

0.5*9.8 N = (k1)*0.009m*.173 + (k2)*0.023m*.173

... the ".173" (sin(10)) means that each stretches about 3x what it would with the entire weight hanging vertically on that spring alone.

If the angle of the springs from vertical is very small, then each will more or less carry a share of the weight, and both will stretch less than they would if they carried the weight alone.

Note that this is an "engineering" class rather than a physics class, so I don't think that the answer has to be rigorous or exact. But as far as I can tell, you could make various assumptions (each spring carries about half of the weight, each spring carries a share in inverse proportion to the amount stretched, both angles about 45 degrees, both angles about 60 degrees, one 45 and the other 60 degrees, etc.) that yield wildly different results.

Is there something obvious that I'm missing, or is this more likely a "make guesses for the things you weren't allowed to measure" sort of problem?

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# Weird 2-spring problem with VERY limited data

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