# Q & A: Length of a tangle of wire

Q:
Can you suggest a way to use Archimedes’ principle to find the length of a tangled bundle of wire iwthout undoing the tangle?
- Kelly (age 17)
New Jersey
A:
Hi Kelly,

I'm sure you can also figure this one out! There are several ways I can think of, some involving putting the wire in a fluid, which appears to be what you are asking about.

1) Submerge your bundle of wire in water (or other appropriate fluid -- if the wire is made up of sodium, water is not recommended -- it will explode. Try oil in this case). Use a graduated cylinder or other container which measures the fluid level accurately. Note the change in fluid level -- the change in volume is the volume of the wire. Divde the volume of the wire by its cross-sectional area, and voila, you have the length. To be careful about: make sure you shake off *all* of the air bubbles which will invariably accompany your tangle of wire into the water.

2) Archimedes principle speaks about the buoyant force on objects submerged in a fluid. You could weigh the bundle of wire when it is dry, tie a thread to a bit of the bundle and dip it all into water (or other fluid, and shake off the bubbles!). Measure the force is needed on the thread to hold up the wire (preferably with the same scale, and make sure you hold the scale the same way as when measuring the dry wire). The difference in these weights is the weight of the water displaced, and water has a mass of 1 gram per cubic centimeter. This lets you compute the volume of the wire again (without having to measure a water level, which can be tricky). You still need to know the cross-sectional area of the wire to get the length once you have the volume.

3) Best of all, but no credit to poor Mr. Archimedes: just weigh the dry wire and look up or measure the weight per unit length of the wire and divide.

4) Also no Archimedes: you could measure the resistance of the wire and divide by the resistance per unit length. Some things to be careful about here -- the wire has to be insulated, so that the places where it touches itself in the tangles do not create short circuits. Contact resistance also can be a problem.

5) Also no Archimedes: Get an electronic pulse generator and an oscilloscope. Pulses travel at about 1 foot per nanosecond through most wires; use the scope to measure the propatation time of short pulses in the wire. Again warning: short circuits mess this up.

Tom

(published on 10/22/2007)