Respuesta :
The time period for the simple the simple pendulum on the earth is
[tex]T_{e} =2\pi \sqrt{\frac{l}{g_{e} } }[/tex]
The time period for the simple the simple pendulum on the mars is
[tex]T_{m} =2\pi \sqrt{\frac{l}{g_{m} } }[/tex]
Here, [tex]T_{e}[/tex] and [tex]T_{m}[/tex] are the time periods on the earth and mars respectively and [tex]g_{e}[/tex]and [tex]g_{m}[/tex] are the acceleration due to gravity on earth and mars respectively.
We can also write,
[tex]\frac{T_{e}}{T_{m}} =\frac{\sqrt{\frac{l}{g_{e}} } }{\sqrt{\frac{l}{g_{m}} } }[/tex]
or
[tex]\frac{T_{e}}{T_{m}} =\sqrt{\frac{g_{m}}{g_{e}} }[/tex]
Given [tex]T_{e} = 1.70 s[/tex] and [tex]g_{m} = 3.71 m/s^2[/tex]
Therefore,
[tex]\frac{1.70 s}{T_{m} } =\sqrt{\frac{3.71 m/s^2}{9.8 m/s^2} }[/tex]
or
[tex]T_{m}=\frac{1.70}{0.615} = 2.76 s[/tex].
Thus, the time period on the surface of mars is 2.76 sec.
The period of simple pendulum on the surface of Mars is about 2.76 s
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Further explanation
Simple Harmonic Motion is a motion where the magnitude of acceleration is directly proportional to the magnitude of the displacement but in the opposite direction.
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The pulled and then released spring is one of the examples of Simple Harmonic Motion. We can use the following formula to find the period of this spring.
[tex]T = 2 \pi\sqrt{\frac{m}{k}}[/tex]
T = Periode of Spring ( second )
m = Load Mass ( kg )
k = Spring Constant ( N / m )
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The pendulum which moves back and forth is also an example of Simple Harmonic Motion. We can use the following formula to find the period of this pendulum.
[tex]T = 2 \pi\sqrt{\frac{L}{g}}[/tex]
T = Periode of Pendulum ( second )
L = Length of Pendulum ( kg )
g = Gravitational Acceleration ( m/s² )
Let us now tackle the problem !
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Given:
Period of the pendulum on the Earth = T_e = 1.70 s
Gravitational Acceleration of the Earth = g_e = 9.8 m/s²
Gravitational Acceleration of the Mars = g_m = 3.71 m/s²
Unknown:
Period of the pendulum on the 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{\frac{1}{g_e}} : \sqrt{\frac{1}{g_m}}[/tex]
[tex]T_m = \sqrt{\frac{g_e}{g_m}} \times T_e[/tex]
[tex]T_m = \sqrt{\frac{9.8}{3.71}} \times 1.70[/tex]
[tex]T_m \approx 2.76 \texttt{ s}[/tex]
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Learn more
- Model for Simple Harmonic Motion : https://brainly.com/question/9221526
- Force of Simple Harmonic Motion : https://brainly.com/question/3323600
- Example of Simple Harmonic Motion : https://brainly.com/question/11892568
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Answer details
Grade: High School
Subject: Physics
Chapter: Simple Harmonic Motion
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Keywords: Simple , Harmonic , Motion , Pendulum , Spring , Period , Frequency
