(Eli5)How come A=G in physics(acceleration=gravity)


I know that we cannot feel velocity we feel acceleration in a car. But why tho?

In: Physics

Acceleration only equals gravity when in a free fall.

Humans cannot really feel acceleration or velocity. We can feel a change in acceleration called jerk. We can feel this for a number of reasons, one of which is that your organs move.

The theories that made Einstein famous (Special and General Relativity) both deal with the fact that there is no experiment you can do to determine if you are being accelerated or you are in a gravitational field; they are exactly identical in all scenarios. [PBS Space Time](https://www.youtube.com/c/pbsspacetime/videos) on youtube did a good series of videos about this recently, but to *way* oversimplify, the universe doesn’t care if you’re on an accelerating rocket in space or on the surface of a planet; the results of any experiment are always the same.

As for why we feel acceleration but not velocity, imagine this scenario: You and I are both astronauts in space, and there is nothing else around us to measure our position by. The distance between us is shrinking. Who’s moving? Are you coming towards me while I’m still, is it the other way around, or are we both moving towards a common center point? Answer: it doesn’t matter. Physics literally does not care which of us is “doing” the moving, and any of those three possibilities are all equally and simultaneously true.

Because you can’t really say who’s doing the moving, you can’t ever build a machine or grow an organ that can detect absolute movement, because as far as it’s concerned the entire universe might be moving around it while it’s stationary. Thus, you can’t feel constant velocity.

You can, however, feel forces quite easily, since applied forces and momentum work together to cause objects to bend or lag behind (imagine moving only one end of a spring and watching what happens to the other). Since acceleration is nothing but the result of a force applied over a period of time, you can quite easily measure acceleration too. But to circle back around, you can’t ever tell if that acceleration was due to gravity or it was due to an outside force.

you can feel it whenever gravity is pulling you down, for example when you are falling or your weight pushing against a chair.
the body is used to having a constant force of 1G pulling it down, so you don’t notice it as much as the much higher sideways acceleration force when accelerating a car for example.

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.