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183_notes:localg [2021/02/15 02:31] – [The Gravitational Acceleration] stumptyl | 183_notes:localg [2021/02/15 02:44] – [The Gravitational Acceleration] stumptyl |
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Countless experiments near the surface of the Earth have shown that the force that the Earth exerts on a system with mass is the product of the system's mass ($m$) and the local gravitational acceleration ($\vec{g}$).where we have defined "up" as positive $y$-direction and the magnitude of the gravitational acceleration ($g$) is equal to **9.81 $\dfrac{m}{s}$.** | Countless experiments near the surface of the Earth have shown that the force that the Earth exerts on a system with mass is the product of the system's mass ($m$) and the local gravitational acceleration ($\vec{g}$).where we have defined "up" as positive $y$-direction and the magnitude of the gravitational acceleration ($g$) is equal to **9.81 $\dfrac{m}{s}$.** |
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\\ | {{ 183_notes:week2_m2m.png?350}} |
Mathematically, we represent this force like this: | Mathematically, we represent this force like this: |
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$$\vec{F}_{Earth} = m\vec{g}$$ | $$\vec{F}_{Earth} = m\vec{g}$$ |
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{{183_notes:week2_earth.png | |
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where the local gravitational acceleration is directed towards the center of the Earth. In your typical "flat-Earth" models,((By "flat-Earth", I mean [[http://en.wikipedia.org/wiki/Geographical_distance#Flat-surface_formulae|the distance over which the Earth is curved is much larger than any distance the system will travel]] not that [[https://en.wikipedia.org/wiki/Modern_flat_Earth_societies|the Earth is truly flat as some might think]].)) you will say the gravitational acceleration points "downward", which we typically consider to be the negative $y$-direction. In this case, | where the local gravitational acceleration is directed towards the center of the Earth. In your typical "flat-Earth" models,((By "flat-Earth", I mean [[http://en.wikipedia.org/wiki/Geographical_distance#Flat-surface_formulae|the distance over which the Earth is curved is much larger than any distance the system will travel]] not that [[https://en.wikipedia.org/wiki/Modern_flat_Earth_societies|the Earth is truly flat as some might think]].)) you will say the gravitational acceleration points "downward", which we typically consider to be the negative $y$-direction. In this case, |
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