G forces when falling - proper acceleration question

[zanick]

The question comes from a thought experiment of a rocket approaching the Earth accelerating at a constant rate of 1g from say from a hypothetical "earth like planet" near by. . we would be standing on the floor of the upright rocket as it lifts off, if we are standing on a scale, our weight, if we weighed 100kgf before lift off, we would be 200kgf . thrust would be , let's say 20,000kgf and the entire rocket had a weight of 10,000kgf. (to achieve 1g acceleration of the rocket against the 1g of the planet)
the G meter on board... is saying 9.81, or 1g while standing the scale before lift off... after lift off, it reads, 2g for a while and then after thrust is reduced, it reads 1g again.
As it leaves the gravitational pull of the "planet", it pulls back the thrust to keep the acceleration at 1g. (I.e. 10,000kgf thrust).
we are still able to stand on the floor of the rocket because it is still accelerating at 1g
Now, we approach the earth... we throttle back the rockets as to keep the 1g acceleration constant, due to the gravitational attraction until we are close to the Earth where the rocket now has 1g of acceleration as we travel down to the surface of the earth.. (ignore air resistance... say there is no atmosphere)

My question is we all know when the thrust is removed as the rocket nears the Earth , it will be in free fall... however, it will be accelerating. what will the G meter read? just before we crash into the earth??

the real question is why the g meter will read 0 gs in the vomit comet for example , even though you have an acceleration of 9.81m^2.

I hope someone can answer this question!

thanks

 

[Dale]

Summary: why does an accelerometer measure 9.81m^2 when standing on a scale not moving? why does it measure 0 when free falling, or in the vomit comet?

the real question is why the g meter will read 0 gs in the vomit comet for example , even though you have an acceleration of 9.81m^2.

The 1 g acceleration is a coordinate acceleration, not a proper acceleration. Accelerometers measure proper acceleration, which is what you think of as physical acceleration. Coordinate acceleration is not physical since it can be changed simply by changing your coordinate system.

 

[Nugatory]

The word “acceleration” is used to describe two different things, and not all authors are always careful about making the distinction between them.

One is “coordinate acceleration”, which is the second derivative of position with respect to time. Clearly it will depend on how you define position: if you take positions relative to someone standing on the surface of the earth, then a nearby falling object will have a coordinate acceleration of 9.8 m/sec^2; but if you take positions relative to another object in free fall, the coordinate acceleration will be zero. (And before you object that someone standing on the surface of the Earth is more “not moving” than an object in free fall, consider that the Earth is rotating and moving around the sun, and then think about what someone watching through a telescope from Mars and moving at several kilometers per second relative to the Earth would think of that claim).

The other is “proper acceleration”, which is what an accelerometer measures. Take a box, put a weight in it, suspend the weight with six springs connected to each of the six sides. If you apply a force to the box to accelerate it, the springs on one side will stretch and the ones on the other side will relax, thereby measuring the acceleration. That’s proper acceleration, and it is completely unrelated to how we define position - either the springs stretch or they don’t.

 

[zanick]

ok, so we are talking "proper acceleration"... because I'm interested in what it will read when we are in free fall. because we are accelerating at 9.81mpsps, will it read this? also, is this independent of a frame of reference in that if you had someone falling next to you , you would not look like you are accelerating or even moving ..

when talking of inertial frames of reference , we have to agree that some are good enough, for consideration in being called. "inertial frames of reference" , right? i mean, if you are on the side of a merry go round and you consider the merrygoround and all riders as in the inertial frame of reference, then the observer would be the inertial...but is he really, when the Earth is spinning? and spinning around the sun.. and spinning around the galaxy? at some point , isn't it good enough if the spin or acceleration is small in respect to the frames being considered?

back to the accelerator and my example on the first post... maybe one of the reasons the person falling in the spacecraft seems to be floating due to the 1g acceleration (yes, change in velocity with respect to time) is because the "gravity" is effecting ALL the mass in the rocket as well as the rocket itself.

 

[Ibix]

I'm interested in what it will read when we are in free fall. because we are accelerating at 9.81mpsps, will it read this?

No. In free fall you are not undergoing proper acceleration so a spring accelerometer of the kind @Nugatory described will read zero.

also, is this independent of a frame of reference in that if you had someone falling next to you , you would not look like you are accelerating or even moving ..

You seem to have answered your own question here. If you can make it go away by changing frame it can't be frame independent.

when talking of inertial frames of reference , we have to agree that some are good enough, for consideration in being called. "inertial frames of reference" , right?

This just depends on the accuracy of your measurement and the type of experiment you are doing. Modern artillery needs to take into account the rotation of the Earth because of the ranges of the shells, and of course meteorology depends heavily on it. In principle one could see such effects on a thrown ball in a lab, but you'd need extremely precise measurements, so typically you treat the lab as inertial and let the non-inertial effects be lost in the rounding.

maybe one of the reasons the person falling in the spacecraft seems to be floating due to the 1g acceleration (yes, change in velocity with respect to time) is because the "gravity" is effecting ALL the mass in the rocket as well as the rocket itself.

That's the Newtonian explanation, yes. Everything accelerates the same way so you cannot detect the acceleration. Contrast with a charged object in an electric field, which can detect its acceleration by comparing itself to an uncharged body.

 

[Nugatory]

ok, so we are talking "proper acceleration"... because I'm interested in what it will read when we are in free fall. because we are accelerating at 9.81mpsps, will it read this?

In free fall your proper acceleration is zero; the springs in the ideal accelerometer of post #3 aren’t stretched. If you were in a windowless box do you couldn’t look out to see the surface of the Earth rushing towards you, you would have no way of knowing whether you were falling towards the Earth or floating in interstellar space lightyears away from the nearest gravitating body.

also, is this independent of a frame of reference in that if you had someone falling next to you , you would not look like you are accelerating or even moving?

Yes, proper acceleration is frame-independent. Either the springs in the accelerometer are stretched or they aren’t, but they won’t be stretched in one frame but not another.

when talking of inertial frames of reference , we have to agree that some are good enough, for consideration in being called. "inertial frames of reference" , right? i mean, if you are on the side of a merry go round and you consider the merrygoround and all riders as in the inertial frame of reference, then the observer would be the inertial...but is he really, when the Earth is spinning? and spinning around the sun.. and spinning around the galaxy? at some point , isn't it good enough if the spin or acceleration is small in respect to the frames being considered?

Yes. In an inertial frame an object that has zero coordinate acceleration (this is frame-dependent) has zero proper acceleration. A frame that is inertial for all practical purposes (no noticeable proper or coordinate acceleration) may turn out not to be inertial if we’re using more sensitive accelerometers and position-measuring devices.

back to the accelerator and my example on the first post... maybe one of the reasons the person falling in the spacecraft seems to be floating due to the 1g acceleration (yes, change in velocity with respect to time) is because the "gravity" is effecting ALL the mass in the rocket as well as the rocket itself.

Yes, and that’s why an object in free fall has no proper acceleration. Gravity is unique in that it doesn’t produce proper acceleration and this makes it possible to reformulate the laws of physics in such a way that gravity is not considered a force - Google for “Einstein’s elevator”.

 

[A.T.]

...because I'm interested in what it will read when we are in free fall...

There are apps that record and display the proper acceleration of your phone. Have you tried one?

 

[zanick]

I know what it will read, so it was a more a question of why ... I also was curious why the gmeter would read 9.8m^2 when standing on a scale... obviously we are not moving or accelerating, so you would think it could read 0 when standing and 9.8m^2 when falling . (kind of analogous to a absolute pressure gauge)

so, i guess the real answer her is gravity is the pseudo force and something falling to the Earth is experiencing it, right up until it crashes into Earth where it will then experience a proper acceleration. (decel). similar to centrifugal force that could move you off a merry-go-round, and you wouldn't feel anything, even though from the non inertial reference frame, you would be accelerating to the edge and off the merry- go- round... or be stopped by cable or wall on the merry go round keeping it from leaving the frame. (centripital force).

 

[A.T.]

so, i guess the real answer her is gravity is the pseudo force and something falling to the Earth is experiencing it, right up until it crashes into Earth where it will then experience a proper acceleration. (decel).

Yes, the contact force from the ground causes proper acceleration, that the accelerometer can pick up. Gravity does not.

 

[Ibix]

I know what it will read, so it was a more a question of why

The Newtonian answer is that it's easier to regard the accelerometer as measuring the force needed to keep the ball at rest with respect to the box it's inside. In free fall all the components feel the same force of gravity and no normal force from the ground, so no extra force is needed from the springs to keep the ball stationary. Sitting on the ground, however, the box feels a normal force from the ground, and to keep the ball stationary with respect to the box requires a force from the springs.

The relativistic answer is that in free fall everything is moving inertially so of course the springs don't stretch. Sitting on the ground, the box is accelerating upwards so the springs need to provide a force to make the ball accelerate upwards at the same rate.

Note that the relativistic explanation is about half the length of the Newtonian one...

 

[jbriggs444]

obviously we are not moving or accelerating

General rule when searching for errors in an argument: look for the word "obviously" or "clearly".

 

[Nugatory]

obviously we are not moving or accelerating,

If we make the essentially arbitrary choice to consider the surface of the Earth to be at rest then we are not moving in the sense that our coordinate velocity and our coordinate acceleration are both zero - but only because we are making that arbitrary choice. (And the frame in which the surface of the Earth is at rest is not inertial because we have zero coordinate acceleration in that frame but non-zero proper acceleration).

However, someone on Mars watching through a telescope and choosing to make the equally reasonable choice to consider the Martian soil under their feet to be at rest will not find it obvious, or even correct, that “we are not moving”. Closer to home, someone freefalling towards the surface of the Earth will also find it neither obvious nor correct to say that “we are not moving or accelerating”. Relative to them we have non-zero coordinate acceleration - and who’s to say they’re wrong? Their accelerometer reads zero and ours reads 9.8 so it seems obvious that we’re the one that’s accelerating.

If you haven’t tried googling for “Einstein’s elevator” yet, now is the time to do so.

What’s going on here is that the force of the spring scale is accelerating us upwards, pushing us off our natural zero proper acceleration freefall path. If the surface of the Earth was more permeable so that it couldn’t push on us we would fall through it towards the center of the earth... and if it weren’t for friction we’d be in free fall with zero proper acceleration.