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I'm looking at this article from Scientific American: https://www.scientificamerican.com/article/star-wars-science-light-speed/#:~:text=Normal%20humans%20can%20withstand%20no,heavier%20blood%20to%20the%20brain.

The third paragraph states that: "When undergoing an acceleration of 9 g's, your body feels nine times heavier than usual, blood rushes to the feet, and the heart can't pump hard enough to bring this heavier blood to the brain."

Can I just clarify some points:

  1. What is meant by "feels" here? Does this relate to the equivalence principle in general relativity (https://en.wikipedia.org/wiki/Equivalence_principle)? In other words, is it correct that the person is actually nine times heavier in their (non-inertial) reference frame?
  2. Is it correct that a person undergoing a horizontal acceleration of, for example, 2 g's on Earth becomes twice as heavy in their reference frame, and therefore now has a weight that is double their weight when at rest on Earth (or roughly double, since Earth is not technically an inertial reference frame)? In other words, can acceleration in any direction (not just vertically) make someone heavier?
  3. If (1) and (2) are true, then how does an inertial observer (person 1) explain seeing someone (person 2) pass out due to high g-force (unable to pump heavier blood to the brain as required)? (i.e. does person 1 still see person 2 as having the same weight as when they (person 2) are at rest?)
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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – Buzz
    Commented Mar 31, 2023 at 22:51

3 Answers 3

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Just to clarify, if I am in a car on Earth that is accelerating forwards at a rate of 2𝑔 , I won't feel twice as heavy?

You will feel more than twice as heavy. Here's what it looks like from the point of view of somebody standing by the side of the road:

enter image description here

The car is accelerating you horizontally (to the left, in this picture) at two gees, while at the same time, gravity is giving you an upward acceleration of one gee.

Acceleration is a vector quantity, and the total acceleration that you feel is the vector sum of the two accelerations. From your point of view, it will feel the same as if your car was stationary on the surface of a planet with 2.24 times Earth gravity, and your seat in the car was tipped backward:

enter image description here

The third paragraph states that:...blood rushes to the feet,...

Your blood will "rush" in the opposite direction of the acceleration. So, in this case, the blood will rush to your butt.

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    $\begingroup$ @Thomas, I suppose it depends on what problem you are trying to solve. If you were an automotive engineer designing the seat for the car in your example, then you had better make sure that the seat won't collapse when bearing 2.24 times its own weight plus the 2.24 times the weight of the person sitting in it when it's tipped back at that angle. On the other hand, if you are drawing pictures trying to explain where the shell fired from a gun will land, then you might trust that the "weight" felt by the shell as it accelerates down the barrel is somebody else's problem. $\endgroup$ Commented Mar 27, 2023 at 18:08
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    $\begingroup$ If I wanted to calculate the frictional force, for example, on the accelerating person, I'm guessing that I would have to use the new value for their weight? @SolomonSlow $\endgroup$
    – Thomas
    Commented Mar 27, 2023 at 18:53
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    $\begingroup$ Wouldn't the gravity force component be directed downward? $\endgroup$ Commented Mar 28, 2023 at 8:21
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    $\begingroup$ @LorenzoDonatisupportUkraine, Do you mean, as opposed to the upward arrow that I drew? Gravity wants us to fall toward the center of the Earth, but the force that we feel when we stand on the ground is the contact force between our feet and the ground. It's the force of the ground pushing up on us from beneath, preventing us from falling. $\endgroup$ Commented Mar 28, 2023 at 11:54
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    $\begingroup$ Einstein said that a person in a closed box cannot tell whether the box is standing on the ground or, standing in a rocket accelerating at one gee through space. The person feels the same acceleration in either case, and in the case of the rocket it should be clear that the acceleration vector points from the "floor" toward the person's head. $\endgroup$ Commented Mar 28, 2023 at 12:04
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What is meant by "feels" here? Does this relate to the equivalence principle in general relativity

Yes, exactly.

From point of the physics laws happening in own reference frame- we can't distinguish are we traveling at $9g$ with a space-ship or are we standing on the planet which gravity force on your body is $F_g=m(9g)$. These situations in general relativity is basically identical.

In other words, can acceleration in any direction (not just vertically) make someone heavier?

Also, yes.

Equivalence principle doesn't talk about the "special directions" where this principle would be valid only for. Instead, equivalence principle is direction-change invariant. Look it in this way,- it doesn't matter to what wall or place you'll be pushed against by a spaceship accelerating at $9g$,- whatever direction it will accelerate,- you will feel same $9g$ on your body.

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A body has a reluctance to accelerate and a measure of the reluctance is the mass of the body.

What you feel are the forces or lack of them that are applied to your body.

When you stand on the Earth you body has an upward force exerted on it due to the ground pushing up and in this case the magnitude of the force on you due to the ground is equal to the weight of your body $m$ where $m$ is your has and $g$ is the gravitational field strength of the Earth.
In terms of Newton's second law $F=ma\Rightarrow \text{force up - force down}= ma\Rightarrow mg-mg = ma \Rightarrow a=0$, thus your acceleration $a$ is zero.

On the Moon where $g$ is smaller you would feel lighter because the upward force due to the Moon on your feet would be smaller.

If you were in free-fall above the Earth's atmosphere you would feel weightless as there is no upward force acting on you in opposition to the downward gravitational force.

Now consider an upward acceleration equal to $9g$.
Remember that your body is reluctant to accelerate and so when an upward force is applied to your body, the rest of your body needs an upward force to make it accelerate upwards.
To do this you body including the body fluids are compressed which causes the blood to rush to your feet, ie the containing blood vessels at your feet are dilated and your interprets this dilation and the forces associated with it as extra blood in the lower body.

Now let's see how the heart reacts to this acceleration.
Consider a mass of blood $b$ undergoing an upward acceleration of $9g$.
$F=ma \Rightarrow$
$\text{force exerted on the blood by the pumping action of the heart - weight of blood} = m\times 9g$

$\text{force exerted on the blood by the pumping action of the heart} = b\times 9g + bg = 10bg$.

With no acceleration the required force due to the heart would be $bg$.
So if the acceleration is too large the heart cannot exert enough force (pressure) to make the blood circulate.

I believe that jumping into a non-inertial frame of reference does not necessarily explain things better.

For example why do you feel that there is on outward (centrifugal) force acting on you when you go around a corner when standing in a bus?
If the bus did not exert a force on you, no friction and you not hanging on to anything) you would $feel$ no force but you would see the bus turning the corner but you moving outwards relative to the bus (in a straight line).

Now whilst holding on to the bus as it turns the corner the bus exerts an inward force on you (to make you undergo a centripetal acceleration) and you feel this inward force acting on you and interpret the situation as though there is also an outward force (centrifugal) force acting on you (trying to fling you outwards) as you have no acceleration relative to the bus.

The reason for introducing pseudo/fictitious forces in non-inertial frame of reference is to enable the use of Newton's second law, $F=ma$.

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