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Rational Exponents — Part 1

Source: Stacked Coins - AtnoYdur/iStock/Getty Images

Structural Analysis

Fatigue Resistance

\(F_{sr}=\left( \dfrac{\gamma}{nN} \right)^{\frac{1}{3}}\) where

  • \(\gamma =\) fatigue life constant
  • \(n=\) number of stress range cycles
  • \(N=\) number of passages of the moving load

Steel bridge.

Source: Steel Bridge - SonerCdem/iStock/Getty Images

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Lesson Goals

  • Define the principal \(n\)th root of a number.
  • Explore rational exponents of the form \(\dfrac{1}{n}\).

Try This

A person's body surface area (\(BSA\)) is used to help doctor's determine dosages of certain medications.

A commonly used formula to calculate someone's \(BSA\) in square metres is given by

\[BSA = \left(\frac{W\times H}{3600} \right)^\frac{1}{2}\]

The weight in kilograms is given by \(W\), and the height in centimetres is given by \(H\).

Try to calculate your own body's surface area.

The surface area of a 3D modelled human mannequin.

Source: 3D Surface Area of a Human - Photitos2016/iStock/Getty Images