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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).

enter image description here

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).

Car acceleration (gravity ignored)

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?

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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.)

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  • $\begingroup$ In the bottom image, why does my body want to accelerate to the right? Is it due to inertia? $\endgroup$ – neeh Dec 3 '19 at 22:25
  • $\begingroup$ @neeh: Your body want to remain at its current velocity due to inertia. In the reference frame of the accelerating car your body wants to accelerate to the right. $\endgroup$ – James Dec 3 '19 at 23:30
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Well, this question has a couple of different levels of explanation. As a matter of fact, I believe Einstein wondered the same thing so you are in good company. The resolution was that you feel the same effect whether you are in a gravity field (standing on the earth) or in an accelerating frame of reference (the car). The is the beginning of the General Theory of Relativity, but in both cases the force you experience is proportional to your mass ("inertia"). With gravity it is F=mg, and with the accelerating reference frame, it is F=ma. I hope this helps.

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  • $\begingroup$ Thanks, I can calculate the forces but what I don't understand is related to the behaviour of these forces. Specifically : 1) why the resulting force is pointing in the same direction for the gravity but in opposite direction for the car and 2) why "accepting" the acceleration results in an apparent force in the car but nothing with the gravity (freefall). It seems like gravity ignores inertia? $\endgroup$ – neeh Dec 2 '19 at 9:54

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