Tuesday, July 17, 2012

Unit 4 - Problem 10 ==> Generalized Equations


Given:

  • Acceleration of gravity  = 9.8 m/s/s
  • Mass of the object = 1 kilogram
  • Height over ground = 50 meters
  • G = 6.674 x 10^-11
  • Radius of the earth = 6400 kilometers = 6,400,000 meters
  • Mass of the earth = 5.97 x 10^24 kilograms

Calculate: Gravitational potential energy using mgh

  • $$ E_{potential} = m * g * h = 1 * 9.8 * 6400009 = 62720088.2  $$

Calculate: Potential energy using (G*M1*M2)/r

  • $$ E_{potential} = G_{earth} * M_{object} * M_{earth} $$ 
  • $$ E_{potential} = \left(\frac{6.674^{-11} * 1 * 5.97^{24}}{6400009}\right) $$
  • $$ E_{potential} = 6.225581870275496 * 10^-6 * 10^{-11} * 10^{24} $$
  • $$ E_{potential} = 6.225581870275496 * 10^7 $$
  • $$ E_{potential} = 62255818.70275496 $$

Calculate: Difference & % difference in two calculations

  • $$ E_{mgh} - E_{GM1M2/r} = difference$$
  • $$ 62720088.2 - 62255818.70275496 = 464269.4972450435 $$
  • $$ \left(\frac{difference}{E_{GM1M2/r}}\right) * 100 = percent_{difference}$$
  • $$ \frac{464269.4972450435}{62255818.70275496} * 100 = 0.745744746305133$$

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