Question

Astronauts on the first trip to Mars take along a simple pendulum that has a period on earth of 1.80 s . The period on Mars turns out to be 2.94 s . How long is the pendulum?What is the Martian acceleration due to gravity?

Answer 1

Answer:

l = 0.8 m

gMars = 3.65 m/s2

Explanation:

The period of a pendulum depends on the length of it and the acceleration of gravity according to this equation:

$T = 2 \pi \sqrt{\frac{l}{g}}$

If the pendulum has a period of 1.8s on Earth, the length must be:

$l = g * (\frac{T}{2\pi})^2 = 9.81 * (\frac{1.8}{2\pi})^2 = 0.8 m$

If it has a period of 2.94 s on Mars, the gravity must be:

$g = \frac{l}{(\frac{T}{2\pi})^2} = \frac{4 \pi^2 l}{T^2} = \frac{4 \pi^2 * 0.8}{2.94^2} = 3.65 \frac{m}{s^2}$