# Chapter 19 - Think and Solve: 41

$1.6 \frac{m}{s^{2}}$.

#### Work Step by Step

Some internet research about pendulums, or referring to Footnote 2 on page 358, shows that the period $T = 2 \pi \sqrt{\frac{L}{g}}$. The astronaut observes that the period T for one complete swing is $\frac{75 s}{15 swings} = 5.0 s$. Use the relation $T = 2 \pi \sqrt{\frac{L}{g}}$ and solve for g. $$g = 4 \pi ^{2} \frac{L}{T^{2}} = 4 \pi ^{2} \frac{1.0 \; m}{(5 s)^{2}} = 1.6 \frac{m}{s^{2}}$$

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