| Both sides previous revision Previous revision Next revision | Previous revisionLast revisionBoth sides next revision |
| 183_notes:localg [2021/02/15 02:43] – [The Gravitational Acceleration] stumptyl | 183_notes:localg [2023/01/17 19:07] – [The Gravitational Acceleration] hallstein |
|---|
| 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 $\dfrac{m}{s}$.** |
| |
| {{183_notes:week2_m2m.png?150}} | {{ 183_notes:week2_m2m.png?350}} |
| |
| Mathematically, we represent this force like this: | Mathematically, we represent this force like this: |
| 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, |
| |
| $$\vec{g} = \langle 0, -g, 0\rangle \approx \langle 0, -9.81, 0\rangle \dfrac{m}{s}$$ | $$\vec{g} = \langle 0, -g, 0\rangle \approx \langle 0, -9.81, 0\rangle \dfrac{m}{s^2}$$ |
| |
| We also accept some variation in $\vec{g}$ from [[http://en.wikipedia.org/wiki/Gravity_anomaly|place to place]]. | We also accept some variation in $\vec{g}$ from [[http://en.wikipedia.org/wiki/Gravity_anomaly|place to place]]. |