I know that we cannot feel velocity we feel acceleration in a car. But why tho?
In: Physics
Note: I’m not dipping into general or special relativity here as I wouldn’t give an accurate enough account of either and would over complicate this as well.
1) Acceleration experienced by an object subjected to force is equal to the size of the force divided by the mass of the object a = F / m.
2) Force of gravitational attraction experienced between two objects is equal to the product (multiplication) of the masses of the two objects, multiplied by a number we call the gravitational constant and then divided by the distance between the objects squared. F = GMm / r^2.
3) using point 2, the force attracting you to the centre of the Earth is equal to the mass of you multiplied by the mass of Earth, multiplied by the gravitational constant divided by the square of Earth’s radius. This force attracting you to Earth’s centre is called your weight.
4) repeat step 3 for me. The only difference is my mass is being multiplied and divided by the other terms (Earth mass, gravitational constant, Earth radius squared). The other terms in this case are roughly equal to 9.8 if using SI units. So you can find the size of the force attracting someone to Earth by multiplying their mass by roughly 9.8. We call this number “g” and it means (Eli 5 terms) how strong gravity is at Earth’s surface.
5) point 4 means this force (weight) is given by the product of your mass and “g”. F = mg
6) from point 1, acceleration at Earth’s surface experienced by any object (when no other forces e.g. air resistance are in play) is given by the force it experiences due to gravity (weight) divided by its’ mass: a = F/m.
7) as point 5 tells us that F = mg then the equation from points 1 & 6 can be represented again with substitution of F for mg: a = mg / m.
The mass of the object at the top and bottom of the fraction cancels giving us a = g.
So acceleration experienced due to gravity = gravitational field strength.
Edit: re the feeling acceleration not velocity, you feel the force, rearranging the equation in point 1: Force = mass x acceleration.
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