[alancalverd]

If we use a falling weight/pulley to accelerate a mass on a dynamics trolley then, eliminating friction, and weighing the trolley (gravitational mass) we can calculate the inertial mass from the force applied and the motion of the trolley. The 2 mass values should be the same.
Have I missed something here?

It was a very near miss ("force" becomes a bit tautologous as we define force from F = ma) but the idea is sound.

Start by dropping a mass m, and measure g. (For student demonstrations you may assume g = 9.81 ms^-2)

Now arrange a trolley with mass m pulled by a falling mass of 2 m. If m_i  = m_g than the system should accelerate at 2g/3. (students may assume weightless strings and frictionless pulleys, as usual)

That's the easy bit. For $64,000, explain why  m_i  = m_g !

[Colin2B]

It was a very near miss ("force" becomes a bit tautologous as we define force from F = ma) but the idea is sound.

Yes, I did hesitate thinking more of circular arguments and definitions. Not easy with many of these fundamental properties.

I’m sure it can be shown with a pendulum period vs length, but you have to make small angle approximations and leave m_i/m_g in there.
There ought to be a way using centrifugal force of a lateral mass to lift a vertical mass. One fictitious force lifts another?

That's the easy bit. For $64,000, explain why  m_i  = m_g !

What do you mean? I left you the easy bit 

[hamdani yusuf (OP)]

just like the rotation of the planets in the Solar System prevented the Solar System from collapsing into the Sun.

The correct term is revolution of planets, instead of rotation.

[hamdani yusuf (OP)]

Lots of interesting stuff in here.
https://www.britannica.com/science/gravity-physics/Gravitational-fields-and-the-theory-of-general-relativity#ref210883

Here is a statement found in the article.

The Eötvös experiments therefore show that the ratio of gravitational and inertial mass is the same for different substances.

It seems that the experiments had somehow excluded the effects of other kind of forces such as electric and magnetic forces, which is not easy for high precision measurement. You need to block cosmic rays, for instance.
If the result shows that the ratio is different for different substances, we can still claim the mass equality by introducing a new type of force, which is not considered as gravity.

[evan_au]

Physicists set  ...  2 = 1   if they want to

Maybe - but they don't do it without qualification. For example:
- 2 pints = 1 quart (ie the units have to be the same)
- sin(2π) = sin(1π)  (ie you have to state the function that is being applied)
- 2 = 1 in modulo 1 (ie you have to identify the number system or algebraic symmetry operating in the system)

[jeffreyH]

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

[gem]

Hi all,
So Jeffery

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

If what you state is correct, how do my bathroom scales work ?

[jeffreyH]

Hi all,
So Jeffery

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

If what you state is correct, how do my bathroom scales work ?

Your bathroom scales work by preventing gravity from moving an object. The tension in a spring will do it. The tension propagates through the spring until it overcomes gravity. Gravity does not propagate through objects, otherwise you would be able to measure your acceleration during free fall.

Look at the slinky drop video in slow motion and see the tension acting against gravity. It is not gravity propagating through the slinky but the release of tension.

This is why the two Fs in the equation about are not the same. Also why I believe you will never be able to properly measure a difference between m_i and m_g.

[gem]

Hi all,
So Jeffery I believe your last post contradicts your previous post.

Hi all,
So Jeffery

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

If what you state is correct, how do my bathroom scales work ?

Your bathroom scales work by preventing gravity from moving an object. The tension in a spring will do it. The tension propagates through the spring until it overcomes gravity. Gravity does not propagate through objects, otherwise you would be able to measure your acceleration during free fall.

Look at the slinky drop video in slow motion and see the tension acting against gravity. It is not gravity propagating through the slinky but the release of tension.

This is why the two Fs in the equation about are not the same. Also why I believe you will never be able to properly measure a difference between m_i and m_g.

As a spring scale follows Hooke’s Law

https://en.m.wikipedia.org/wiki/Hooke's_law

Which measures Force 🤔

[alancalverd]

Gravity does not propagate through objects,

So my head is weightless if I stand up?

One of the odd things about gravity is that it does indeed propagate through objects, and rather than being attenuated as happens with other forces, it is enhanced.

[jeffreyH]

Static fields do not propagate.

https://en.m.wikipedia.org/wiki/Speed_of_gravity
The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field are, because of relativistic considerations, the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continue to "point" in the direction of the charge, at all distances from the charge.

The consequence of this is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.

In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.

[jeffreyH]

Hi all,
So Jeffery I believe your last post contradicts your previous post.

Hi all,
So Jeffery

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

If what you state is correct, how do my bathroom scales work ?

Your bathroom scales work by preventing gravity from moving an object. The tension in a spring will do it. The tension propagates through the spring until it overcomes gravity. Gravity does not propagate through objects, otherwise you would be able to measure your acceleration during free fall.

Look at the slinky drop video in slow motion and see the tension acting against gravity. It is not gravity propagating through the slinky but the release of tension.

This is why the two Fs in the equation about are not the same. Also why I believe you will never be able to properly measure a difference between m_i and m_g.

As a spring scale follows Hooke’s Law

https://en.m.wikipedia.org/wiki/Hooke's_law

Which measures Force 🤔

And the force propagates through the spring. Gravity does that only indirectly. It pulls the weight which changes the stress on the spring. If you were put in place of the weight you would feel the acceleration as the stress on the spring slowed you down. You would not feel this acceleration in free fall. It's force Jim, but not as we know it.

[alancalverd]

To quote your Wikipedia reference

In classical theories of gravitation, the changes in a gravitational field propagate.....[at].... the speed of light .

Now a gravitational field is only associated with a mass. So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c, and if we introduce another lump of material between a gravitational source and a detector, the change in net gravitational field at the detector will propagate at c.

The anomalous property of gravity is that we can't interpose anything that will reduce the detected field at a distant point.

[gem]

Hi all,
mmm Jeffery I think you surpass yourself you manage to contradict yourself in one statement:

And the force propagates through the spring. Gravity does that only indirectly. It pulls the weight which changes the stress on the spring. If you were put in place of the weight you would feel the acceleration as the stress on the spring slowed you down. You would not feel this acceleration in free fall. It's force Jim, but not as we know it.

Do you know what weight is ?    

[hamdani yusuf (OP)]

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation. So F ≠ mg.

How do we feel forces?
What should be added to make the second equation balanced?

[Eternal Student]

Hi all.

So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c,

   and also,

The speed of physical changes in a gravitational or electromagnetic field

   Seems like we're talking about the "speed of gravity".  This could be a whole new thread for discussion on its own.
It's complicated and depends on whether you're using Newtonian gravity or General Relativity.  I'm not an expert on this but I would advise caution and extreme skepticism about the Wikipedia articles that have previously been cited.
   For example, creating mass/energy ex nihilo isn't something that can be tested in reality.  It can't even be considered on a theoretical level using Einstein's Field Equations from GR.  There's less that would stop you considering the possibility with Newtonian gravity  (ignoring the violation of some conservation of energy) but it is generally agreed that Newtonian gravity assumes instantaneous action at a distance.  So if you add (or remove) a mass then instantly the whole universe knows about it, the transmission of that new gravitational force occurred at inifinte speed.
    There were several attempts to impose a finite "speed of gravity" in Newtonian physics but this results in unstable orbits for massive bodies in our solar system unless the speed is incrediably high (far above the speed of light).

[Colin2B]

So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c,

...... it is generally agreed that Newtonian gravity assumes instantaneous action at a distance.  So if you add (or remove) a mass then instantly the whole universe knows about it, the transmission of that new gravitational force occurred at inifinte speed.

It is generally agreed that Newton was wrong. The assumption in GR is that information does not travel faster than light and a number of papers that explain why Wiki is correct.
You might want to follow the link in this post https://www.thenakedscientists.com/forum/index.php?topic=82133.msg636147#msg636147

[Origin]

While you can state F = ma this is not the same as saying F = mg. No force is felt in the second equation.

I feel a 185 lb force on my feet when I stand, which is due to F=mg so I have to disagree.

[alancalverd]

For example, creating mass/energy ex nihilo isn't something that can be tested in reality. 

My colleagues do it every day, converting the mass of an electron-positron pair into the energy of two photons. My clients do it on a larger scale, called nuclear power generation. Admittedly most of the useful applications are the other way around, annihilating mass rather than creating it, but the fact remains, and we now have sufficient evidence from the detection of gravity waves that gravity propagates at c. 

[Eternal Student]

You might want to follow the link in this post

  Thanks for the suggestion,  I will check it out.

My colleagues do it every day, converting the mass of an electron-positron pair into the energy of two photons.

    I was thinking someone would say something like that.  Energy and mass are both used in the stress-energy tensor for GR.  It's fine to convert one to the other.  The problem is only when you create one from nothing (or remove one and leave nothing).  It might seem that I have been quite unkind to you, Alancalverd, but that was not my intention.

    I mentioned that I am not an expert concerning the speed of gravity and I'm not, I'm certainly not.  I only started learning about General Relativity a couple of years ago by reading a book to pass the time.  Not having any lecturing staff to talk to, I made a post in another forum asking what would happen after an instantaneous removal of the sun and how long it would take before the earth's orbit was altered (i.e. "what is the speed of propagation for gravity").  There were some very unkind replies at first and then I seem to recall I was taken outside and slapped for an hour (ok, maybe my memory is a little distorted but I do know it felt like I was being slapped).  The fact that such ideas are frequently used as examples to show the difference in transmission speed for Newtonian gravity vs. GR was not considered an excuse for my ignorance.  I was told that only popular media and trashy science videos ever discuss such an absurd thing and it was never done in any peer reviewed literature.  One of the more note worthy replies I received was something like "No one but no one should ever suggest the stress-energy tensor can be that discontinuous and still be allowed to live". The thread was closed down immediately and if there had been an "idiot of the week" board then my picture would have been pinned to it.
   I can assure you, Alancalverd, that I get things wrong quite often.