Question

A pendulum has a period of 1.69 s on earth. what is its period on mars, where the acceleration of gravity is about 0.37 that on earth?

Answer 1

The formula for the period of the pendulum is
$T=2 \pi \sqrt{ \frac{L}{g} }=$
where L is the pendulum's length and g the gravitational acceleration.

Labeling with E the Earth and with M Mars, we can write the period of the pendulum on Earth as
$T_E = 2 \pi \sqrt{ \frac{L}{g_E} }$
and the period of the pendulum on Mars as
$T_M = 2 \pi \sqrt{ \frac{L}{g_M} }$

if we calculate the ratio, we get
$\frac{T_M}{T_E}= \sqrt{ \frac{g_E}{g_M} }$
but we know that the gravitational acceleration on Mars is 0.37 times the gravitational acceleration on Earth:
$g_M = 0.37 g_E$
Substituting into the formula, we find
$\frac{T_M}{T_E}= \sqrt{ \frac{1}{0.37} }=1.64$
And so, the period of the pendulum on Mars is
$T_M = 1.64 T_E = 1.64 (1.67 s)=2.78 s$

Answer 2

The period of pendulum on Mars is about 2.78 s

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Further explanation

Let's recall Elastic Potential Energy and Period of Simple Pendulum formula as follows:

$\boxed{E_p = \frac{1}{2}k x^2}$

where:

Ep = elastic potential energy ( J )

k = spring constant ( N/m )

x = spring extension ( compression ) ( m )

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$\boxed{T = 2\pi \sqrt{ \frac{L}{g} }}$

where:

T = period of simple pendulum ( s )

L = length of pendulum ( m )

g = gravitational acceleration ( m/s² )

Let us now tackle the problem!

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Given:

Period of Pendulum on Earth = T_E = 1.69 s

Acceleration of gravity on Earth = g_E = g

Acceleration of gravity on Mars = g_M = 0.37 g

Asked:

Period of Pendulum on Mars = T_M = ?

Solution:

$T_E : T_M = 2\pi \sqrt{ \frac{L}{g_E} }} : 2\pi \sqrt{ \frac{L}{g_M} }}$

$T_E : T_M = \sqrt{g_M} : \sqrt{g_E}$

$1.69 : T_M = \sqrt{0.37g} : \sqrt{g}$

$1.69 : T_M = \sqrt{0.37}$

$T_M = 1.69 \div \sqrt{0.37}$

$\boxed {T_M \approx 2.78 \texttt{ s}}$

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Learn more

• Kinetic Energy : https://brainly.com/question/692781

• Acceleration : https://brainly.com/question/2283922

• The Speed of Car : https://brainly.com/question/568302
• Young Modulus : https://brainly.com/question/9202964
• Simple Harmonic Motion : https://brainly.com/question/12069840

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Answer details

Grade: High School

Subject: Physics

Chapter: Elasticity