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

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