Engineering Analysis

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Problem Statement: If you use a 400 ft extension cord for the power sander, will that 400 foot extension cord be enough to power the Ryobi power sander.

Diagram: [1]

Assumptions:

  • For the sander to run it needs 120 volts
  • The sander will not be able to run with 60 volts supplied from the cord
  • The current for the sander to run is 1.2 A
  • The radius of the extension cord is 1.5 mm
  • The extension cord is made out of copper
  • The temperature is 20 degrees Celsius
  • The resistivity is 1.62 x 10-8
  • The cord is made out of copper

Governing Equations:

  • R = V/i
  • R = (resistivity) * (L/A)
  • A = π*r^2

Solution:

R = V/i R = 60/1.2 = 50 ohms R = (resistivity) * (L/A) A = 3.14 * .00152 50 = (1.62 x 10-8) *(L/7.07x10-6) L = 71,590 ft

400ft < 71,590ft So the 400 ft extension cord would be enough to power the Ryobi power sander.


Discussion:

The 400 foot extension cord would be able to deliver enough power to the power sander. The 400 foot extension cord won’t be enough because it would take 71,590 feet of extension cord until the power sander wouldn’t be able to have enough power to run. This is true only under the assumption that the power sander would not work at 60 volts. However any higher voltage that the sander would not work at would mean the length of the cord would be less than 71,590 ft.