# Newton's 2nd law for an object in free fall

• I
• user079622
user079622
From inertial frame, object in free fall has just one force mg.

So Fnet=non zero, but acceleration =0, isnt this in "fight" with Newton 2law?

Is object accelerating or not ?

Can I say, yes object is accelerating but object dont "experience" acceleration?

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Motore
This seems very confused.

A free falling object of mass ##m## is subject to a gravitational force of magnitude ##mg##, so it accelerates with acceleration ##g##. This is perfectly consistent with Newton's second law.

vanhees71
Ibix said:
This seems very confused.

A free falling object of mass ##m## is subject to a gravitational force of magnitude ##mg##, so it accelerates with acceleration ##g##. This is perfectly consistent with Newton's second law.
Ok but, water are not leaking from holes , when bucket of water is in free fall, that mean his acceleration is zero.

PeroK
user079622 said:
Ok but, water are not leaking from holes , when bucket of water is in free fall, that mean his acceleration is zero.
No it doesn't. It means the water and the bucket have equal accelerations.

pines-demon, PeroK, Vanadium 50 and 1 other person
Ibix said:
No it doesn't. It means the water and the bucket have equal accelerations.
Yes that make sense. So accelerometer housing and test mass has same accelerations, that is why he read zero?

So "real" acceleration(accelerometer) is not valid in inertial frame for free fall, because Fnet=non zero and he read zero?

user079622 said:
So accelerometer housing and test mass has same accelerations, that is why he read zero?
Yes.
user079622 said:
So "real" acceleration(accelerometer) is not valid in inertial frame for free fall?
In Newtonian physics an accelerometer of the "mass on a spring" type will not give you your acceleration with respect to an inertial frame, true. You have to find an object moving inertially (e.g. the surface of the Earth) and measure your rate of change of velocity with respect to that.

If you could find a material that was not affected by gravity (analogous to uncharged bodies being unaffected by electric fields) you could make your accelerometer mass out of that, and then you could detect gravitational acceleration with a mass on a spring. That no such material has ever been found is a step on the road to general relativity, which predicts that no such material will ever be found.

cianfa72 and Dale
Ibix said:
Yes.

In Newtonian physics an accelerometer of the "mass on a spring" type will not give you your acceleration with respect to an inertial frame, true. You have to find an object moving inertially (e.g. the surface of the Earth) and measure your rate of change of velocity with respect to that.

If you could find a material that was not affected by gravity (analogous to uncharged bodies being unaffected by electric fields) you could make your accelerometer mass out of that, and then you could detect gravitational acceleration with a mass on a spring. That no such material has ever been found is a step on the road to general relativity, which predicts that no such material will ever be found.
Dont understand. You are talking only for free fall?

For car in turn accelerometer will show mv^2/r, that corespond to result from inertial frame.

When using Newtonian physics you take the surface of the earth as inertial and calculate the velocity/time of the free falling object and you find out that it has acceleration of g (althgough the accelerometer on the object reads 0).
When using general relativity the object in free fall has no acceleration (his accelerometer reads 0) and in some sense it is the earth surface that is closing on the object with the acceleration of 1g, because the earth surface is not inertial.

cianfa72 and Dale
Motore said:
When using Newtonian physics you take the surface of the earth as inertial and calculate the velocity/time of the free falling object and you find out that it has acceleration of g (althgough the accelerometer on the object reads 0).
When using general relativity the object in free fall has no acceleration (his accelerometer reads 0) and in some sense it is the earth surface that is closing on the object with the acceleration of 1g, because the earth surface is not inertial.
moving inertially means move const speed or at rest?

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user079622 said:
Is object accelerating or not ?
The object has no proper acceleration. In some reference frames it has coordinate acceleration.

It is important to distinguish between proper acceleration and coordinate acceleration.

user079622
user079622 said:
For car in turn accelerometer will show mv^2/r, that corespond to result from inertial frame.
No, it'll show acceleration ##v^2/r## in the horizontal direction and ##g## in the vertical direction. It's just a mass on a spring - it won't stop measuring the weight of the mass just because you're calling it an accelerometer!

Many accelerometers are designed to only show acceleration in one dimension (for example, a spring mounted in a tube so it can only extend in the direction of the axis of the tube). These can be set up horizontally so they ignore the vertical plane where they go wrong, but that just means you have to be careful not to tilt your sensors if you want correct results.

Note there's no ##m## in any of my expressions. You keep mixing up force and acceleration. It probably doesn't matter all that much in this particular context, but sloppiness like that will bite you eventually.

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Ibix said:
No, it'll show acceleration ##v^2/r## in the horizontal direction and ##g## in the vertical direction. I
Yes I forgot that he meassure just a not Fc.
But v^2/r you will get if you calculate from inertial frame as well

user079622 said:
Yes I forgot that he meassure just a not Fc.
But v^2/r you will get if you calculate from inertial frame as well
Yes. In a Newtonian inertial frame your acceleration when moving in a horizontal circle on the surface of the Earth is ##v^2/r## in the radially inward direction. In deep space (or in free fall generally) moving in a circle your acceleration in a Newtonian inertial frame is ##v^2/r## radially inwards. They are the same, and in both cases there is no acceleration perpendicular to the plane of the circle.

A "mass on a spring" accelerometer will read differently in the two cases, however, because it will tell you that there is also a vertical acceleration when you are on the surface of the planet. This is because there is zero net force in the vertical direction, but this design of accelerometer cannot detect the gravitational force and only detects the normal reaction from the floor.

In Newtonian terms, this kind of accelerometer does not function correctly in a gravitational field when measuring accelerations that are not perfectly horizontal. If you know which direction is vertical you can always correct the readings with a little bit of vector addition, of course.

Note that I've edited the second paragraph in my previous post, which was written in a way that might have been confusing.

user079622
Ibix said:
If you could find a material that was not affected by gravity (analogous to uncharged bodies being unaffected by electric fields) you could make your accelerometer mass out of that, and then you could detect gravitational acceleration with a mass on a spring. That no such material has ever been found is a step on the road to general relativity, which predicts that no such material will ever be found.
You mean that in free-fall the accelerometer housing would "accelerate" w.r.t. the mass not affected by gravity compressing the spring attached between it and the accelerometer housing.

Yes.

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