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Astronauts on the first trip to Mars take along a pendulumthat has a period on earth of 1.50 s. The period on Mars turns out to be 2.45 s.What is the free-fall acceleration onMars?

Respuesta :

skyluke89

Answer:

3.68 m/s^2

Explanation:

The period of a pendulum is:

[tex]T=2 \pi \sqrt{\frac{L}{g}}[/tex]

where L is the length of the pendulum and g is the gravitational acceleration.

On Earth, T = 1.50 s and g = 9.8 m/s^2, so we can solve the formula for L to find the length of the pendulum:

[tex]L=g(\frac{T}{2 \pi})^2=(9.8 m/s^2)(\frac{1.50 s}{2\pi})^2=0.56 m[/tex]

The length of the pendulum remains the same on Mars, and since on Mars the period of the pendulum is T = 2.45 s, we can now solve the equation again for g, the gravitational acceleration on Mars:

[tex]g=(\frac{2\pi}{T})^2 L=(\frac{2\pi}{2.45 s})^2 (0.56 m)=3.68 m/s^2[/tex]

onyebuchinnaji

The free-fall acceleration on the Mars is 3.68 m/s².

Equivalent length of the  pendulum

The length of the pendulum on mars is calculated as follows;

[tex]T = 2\pi \sqrt{\frac{L}{g} } \\\\L = \frac{T^2 g}{4\pi^2} \\\\L = \frac{(1.5)^2 \times 9.8}{4\pi ^2} \\\\L = 0.56 \ m[/tex]

Free- fall acceleration

The free-fall acceleration on the Mars is calculated as follows;

[tex]g = \frac{L4\pi ^2}{T^2} \\\\g = \frac{0.56 \times 4\pi ^2}{(2.45)^2} \\\\g = 3.68 \ m/s^2[/tex]

Learn more about acceleration of free-fall here: https://brainly.com/question/24677281

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