I'm trying to simulate the perception of weight by a human in a system but I'm struggling to treat gravitational acceleration and other accelerations in the same way.
As I understand, when I stand on the Earth's ground I can feel an acceleration of $9.81\,m.s^{-2}$ pointing downwards : the gravity.
Because of the Earth's ground my body is experiencing an acceleration of $1\,g$ pointing downwards.
If we remove the Earth's ground, I am freefalling and I feel weightless (0g).
When I am seating in a car accelerating forward from 0 to 100 km/h in 1 second, I get an acceleration of $27.78\,m.s^{-2}$ and I can feel a "force" of approx. $2.8\,g$ dragging me backwards (if we ignore the Earth's gravity).
Firstly, I don't understand why I experience those $2.8\,g$. Unlike with the gravity, I'm not resisting this acceleration, I am taking it otherwise I would not be moving in the Earth's referential. Does this is has something to do with inertia? Like: my body struggles to stay in the car?
Secondly, why is the force I am feeling during the car acceleration pointing in the opposite direction of the car's actual acceleration while in the case of the gravity, I can clearly feel this force pulling me in the same direction as the gravity?
I guess what confuses me is that, in the case of gravity, I have to "pull" $1\,g$ to resist the acceleration, while in the case of the car, I have to "pull" $2.8\,g$ to stay in the acceleration.
Maybe it's because the gravity is applied to my body while the car acceleration is applied to the car, not my body. The force I'm feeling in the car could be an apparent force that results from my body's intertia?
Best Answer
In the top image, your body want to accelerate downward relative to the ground. The ground prevents your acceleration through the force on your feet which you feel.
In the bottom image, your body wants to accelerate to the right at 27.8 $m/s^2$ relative to the car. The seat back prevents your acceleration through the force on your back which you feel.
As discussed by another answer, the effect of an accelerating reference frame is identical to a gravitational field. In other words, the forces you experience in the accelerating car are the same forces you would experience in a stationary car standing on its back end on a planet with a 2.8g surface gravity. (Except in the accelerating car there is also a 1g downward acceleration due to gravity as you mentioned.)