You are here:

# Advanced Math/Amount of Time, Wire Length

Question
Wire (plain) .02 inches in diameter is wound on a spool 5.5 inches in length and .75 inches in diameter, turning at 25 revolutions per second. Determine amount of time (seconds) to wind the first layer and length of first layer.

How would the total time and for 1000 feet of plain wire wound on the spool be calculated?
The problem did not ask for total time and capacity for the spool- I was just wondering.  Thanks.

5.5 in × 1 wire/(0.02 in) = 275 wires
The first layer is comprised of 275 windings.

275 windings × 1 sec/(25 windings) = 11 sec
It takes 11 seconds to wind the first layer.

circumference of spool = 0.75π inches
275 revolutions × 0.75π in/revolution = 206.25 in
The length of the first layer is 206.25 inches.
:::::
Each subsequent layer uses a longer length of wire. The number of layers and time depend on how the wire is laid on. If you maintain 275 windings per layer, each layer adds 0.04 in to the diameter.

The wires can be laid on more compactly, with 273 windings for the even-numbered layers. The diameter will increase more slowly.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Quick, courteous response !!

Volunteer

#### Janet Yang

##### Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

##### Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.