Question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cmcm. She finds that the pendulum makes 110 complete swings in a time of 145 ss.

Answer 1

Hi there!

First, let's find the period of the pendulum. This can be found by solving for the amount of time it takes for the pendulum to make ONE complete swing.

$T = \frac{\text{Total time}}{\text{Number of complete swings} }\\\\T = \frac{145}{110} = 1.318 s$

Now, let's use the equation for the period of a simple pendulum:
$T = 2\pi \sqrt{\frac{L}{g}}$

T = Period (1.318 s)
L = length of string (0.55 m)

g = acceleration due to gravity on planet (? m/s²)

Let's solve for 'g' doing some quick rearranging of the equation:
$T^2 = 4 \pi^2 (\frac{L}{g})\\\\g = \frac{4\pi^2 L}{T^2}$

Solving for 'g' by plugging in values:
$g = \frac{4\pi^2 (0.55)}{(1.318)^2}\\ \\= \boxed{12.496 \frac{m}{s^2}}$