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Thursday, July 26, 2012

Unit 5 - Problem 1 ==> Keeping Time


Given:

  • l_e = \mbox{length of pendulum on earth} 
  • m = \mbox{mass of pendulum}
  • g_e = \mbox{acceleration of gravity on the earth} 
  • g_m = \mbox{acceleration of gravity on the moon} 

Rationale:

  • T_{period-earth} = 2 \pi \sqrt\frac{l_e}{g_e}
  • T_{period-moon} = 2 \pi \sqrt\frac{l_m}{g_m}
  • T_{period-earth} = T_{period-moon}
  • 2 \pi \sqrt\frac{l_e}{g_e} = 2 \pi \sqrt\frac{l_m}{g_m}
  • \frac{l_e}{g_e} = \frac{l_m}{g_m}
  • l_m = l_e \frac{g_m}{g_e}

Calculate: Length of pendulum on moon

  • l_m = l_e \frac{1.6}{9.8} = 0.163265  l_e = 0.16  l_e

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