What is the equation I'm looking for? I have 50# monofilament. What's the force? The length's vary.

Question

The length of each monofilament is variable (depending on the force exerted at the 0.028" diameter flat tip. How do I calculate the force exerted if I know the diameter and the length of the line?

I thought of Hooke's Law, but the application is more for the use as disposable von Frey filaments or Semmes-Weinstein filaments at force delivery that can elicit pain thresholds, not sensation.

I was thinking of the monofilament as a linear spring...but I'm not sure...

I can't find anything about von Frey or Semmes-Weinstein filaments and the derivation of how they know how much force is delivered before the hair bends.

This is why I asked Y! Answers.

I thought of Hooke's Law, but the application is more for the use as disposable von Frey filaments or Semmes-Weinstein filaments at force delivery that can elicit pain thresholds, not sensation.

I was thinking of the monofilament as a linear spring...but I'm not sure...

I can't find anything about von Frey or Semmes-Weinstein filaments and the derivation of how they know how much force is delivered before the hair bends.

Answer 1

The easiest thing to do is apply Hooke's law, F=kx. Where x is the extra length due to stretching.

If you hang on various weights, you can solve for k, which will let you find an unknown weight hung on the line by how far the line stretches.

Keep in mind this is only valid for stretched lengths << total length.

I see your angle, if you make the assumption that the volume of the line is conserved. Then from V=L(pi)r^2

dV = 0 = (pi)r^2dL + 2L(pi)rdr or dL/L = (-2/r)dr so that

Lf/L0 = (rf/r0)^(-2)

This relates the original L0 and final Lf lengths to the original and final radii, but it does not tell you the force applied to do so.