We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The period of pendulum on Mars is about 2.78 s
[tex]\texttt{ }[/tex]
Further explanation
Let's recall Elastic Potential Energy and Period of Simple Pendulum formula as follows:
[tex]\boxed{E_p = \frac{1}{2}k x^2}[/tex]
where:
Ep = elastic potential energy ( J )
k = spring constant ( N/m )
x = spring extension ( compression ) ( m )
[tex]\texttt{ }[/tex]
[tex]\boxed{T = 2\pi \sqrt{ \frac{L}{g} }}[/tex]
where:
T = period of simple pendulum ( s )
L = length of pendulum ( m )
g = gravitational acceleration ( m/s² )
Let us now tackle the problem!
[tex]\texttt{ }[/tex]
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:
[tex]T_E : T_M = 2\pi \sqrt{ \frac{L}{g_E} }} : 2\pi \sqrt{ \frac{L}{g_M} }}[/tex]
[tex]T_E : T_M = \sqrt{g_M} : \sqrt{g_E}[/tex]
[tex]1.69 : T_M = \sqrt{0.37g} : \sqrt{g}[/tex]
[tex]1.69 : T_M = \sqrt{0.37}[/tex]
[tex]T_M = 1.69 \div \sqrt{0.37}[/tex]
[tex]\boxed {T_M \approx 2.78 \texttt{ s}}[/tex]
[tex]\texttt{ }[/tex]
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
[tex]\texttt{ }[/tex]
Answer details
Grade: High School
Subject: Physics
Chapter: Elasticity
Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
The formula for the period of the pendulum is
[tex]T=2 \pi \sqrt{ \frac{L}{g} }= [/tex]
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
[tex]T_E = 2 \pi \sqrt{ \frac{L}{g_E} } [/tex]
and the period of the pendulum on Mars as
[tex]T_M = 2 \pi \sqrt{ \frac{L}{g_M} } [/tex]
if we calculate the ratio, we get
[tex] \frac{T_M}{T_E}= \sqrt{ \frac{g_E}{g_M} } [/tex]
but we know that the gravitational acceleration on Mars is 0.37 times the gravitational acceleration on Earth:
[tex]g_M = 0.37 g_E[/tex]
Substituting into the formula, we find
[tex] \frac{T_M}{T_E}= \sqrt{ \frac{1}{0.37} }=1.64 [/tex]
And so, the period of the pendulum on Mars is
[tex]T_M = 1.64 T_E = 1.64 (1.67 s)=2.78 s[/tex]
[tex]T=2 \pi \sqrt{ \frac{L}{g} }= [/tex]
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
[tex]T_E = 2 \pi \sqrt{ \frac{L}{g_E} } [/tex]
and the period of the pendulum on Mars as
[tex]T_M = 2 \pi \sqrt{ \frac{L}{g_M} } [/tex]
if we calculate the ratio, we get
[tex] \frac{T_M}{T_E}= \sqrt{ \frac{g_E}{g_M} } [/tex]
but we know that the gravitational acceleration on Mars is 0.37 times the gravitational acceleration on Earth:
[tex]g_M = 0.37 g_E[/tex]
Substituting into the formula, we find
[tex] \frac{T_M}{T_E}= \sqrt{ \frac{1}{0.37} }=1.64 [/tex]
And so, the period of the pendulum on Mars is
[tex]T_M = 1.64 T_E = 1.64 (1.67 s)=2.78 s[/tex]
