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Monday, July 30, 2012

Unit 6 - Problem 6 ==> Battle of the Forces


Given:

  • K_{electrostatic-constant} = 8.99 * 10^9
  • G_{gravity-constant} = 6.67 * 10^-11
  • \mbox{Two bodies with same mass and charge of 1 coulomb each.}

Question:

  • \mbox{At what mass are the force of gravity and the electrostatic force equal?}

Rationale:

  • F_{gravity} = F{electrostatic-charge}
  • \frac{G * m^2}{r^2} = \frac{K * Q^2}{r^2}
  • m^2 = \frac{K * Q^2}{G}
  • m = \sqrt\frac{K * Q^2}{G}

Calculate

  • m = \sqrt\frac{(8.99 * 10^9)}{(6.67 * 10^-11)}
  • m = \sqrt{(1.347826 * 10^{20})}
  • m = 1.16 * 10^{10}

Comparison:

  • \mbox{mass of the earth} = 5.972 * 10^{24}\;\mbox{kg}
    • \frac{ 1.16 * 10^{10}}{5.972 * 10^{24}} = 0.19*10^{-14}
    • \mbox{Much smaller than the earth}
  • \mbox{mass of the earth's moon} = 0.07349 * 10^{24}
    • \frac{ 1.16 * 10^{10}}{0.7349 * 10^{24}} =15.7844604 * 10{-14}
    • \mbox{Much smaller than earth's moon}
  • \mbox{mass of a US Navy nuclear-powered aircraft carrier} = 196 * 10^6 \;\mbox{lbs}
    • \mbox{number of carriers} = \frac{1.16 * 10^{10}}{196 * 10^6} = 59.18367
    • \mbox{That's more carrier's than the US Navy has ever had.}

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