/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 Magnet wire is to be coated with... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 53

Magnet wire is to be coated with varnish for insulation by drawing it through a circular die of \(1.0 \mathrm{mm}\) diameter. The wire diameter is \(0.9 \mathrm{mm}\) and it is centered in the die. The varnish \((\mu=20\) centipoise) completely fills the space between the wire and the die for a length of \(50 \mathrm{mm}\) The wire is drawn through the die at a speed of \(50 \mathrm{m} / \mathrm{s}\) Determine the force required to pull the wire.

Short Answer

Expert verified
Use the steps above to calculate the force. Remember to convert units where needed before entering values into the formula.

Step by step solution

01

Calculate the Area

First, calculate the area of the annular space where the varnish resides. The radius of this space is given by half the difference of the die and wire diameters in meters. Area \( A = \pi (r_d^2 - r_w^2) \) where \( r_d \) is the radius of the die and \( r_w \) is the radius of the wire. Remember to convert diameters to radius by dividing by 2 and millimeters to meters by multiplying by \( 10^{-3} \).
02

Convert Viscosity

Next, convert the viscosity of the varnish from centipoise to pascal seconds. 1 Centipoise equals \( 0.001 \) Pascal seconds, so multiply the viscosity \( \mu \) by \( 0.001 \).
03

Apply Force Formula

Now, put values into the formula \( F = \mu \times A \times v/ l \). Plug in your calculated area from step one, your converted viscosity from step two, the drawing speed in meters per second, and the length where the varnish fills in meters and then simplify.

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