# Newton's second Law of Acceleration, Inertia and Momentum, Freefall

1. May 1, 2013

### jeffrey c mc.

Okay, we have one-thousand pounds; at sea level, and a feather. We elevate them to a thousand meters and support them on a platform. All of which is in a vacuum. We remove the platform, they both hit the earth; the limiting surface; at the same time. Newton's second law suggests that this is due to the inertia of the the heavier object. Due to its' inertia it is slower out of the gate. Also a discussion of force and mass needs to be elucidated. Yet, momentum, is a hyperbolic function that is calculated by mass, distance moved, and rate of change, actually it's mass times velocity; but since the acceleration of gravity is inversely tied into the square of the distance traveled (or the distance between the two gravitating bodies) [sic ie. free-fall], one would think that in free-fall, a discussion of how far the object has traveled would be interesting to know, in the grand scheme of it, I dare say.

Any thoughts would be appreciated. The 'one' in the fifth sentence, that is; is myself of course, no implication that others may, or might think this, need apply.

Jeffrey

2. May 2, 2013

### Simon Bridge

I'm thinking that there is no question in there.
The observation about momentum is not inconsistent with the previous observations about force so it does not deserve the "yet".... yet - so what?

I wonder why you left off the mass-dependence of Newtonian gravity - perhaps this is the mass-force discussion that should be elucidated from you?

3. May 2, 2013

### jeffrey c mc.

Simon, thank you for the response. Yes, I haven't posed the question sufficiently, or correctly. Your statements are valid. I also see that I need to be even more succinct in my language from your discussion on my use of 'yet.' I observe that the language of science is even more exact then what I am apt to but it to, as I say. My observations are built around the idea that gravity is an accelerative force and tied in with mass. Both the mass of the gravitating object, and the falling object. So, while both objects are in free-all. Both objects are gaining a net increase in force--which is slaved to their mass--the closer they get to the gravitating object, they are approaching. So, from the independent viewpoint, they are not receiving a net-force increase, but, from an internal aspect, the larger mass is receiving a net force increase, the closer it gets to the gravitating body. Therein lies the crux of the conundrum--my conundrum--why is it they hit the limiting surface at the same time, in a vacuum.

http://www.physicsclassroom.com/Class/newtlaws/U2L3e.cfm

So the lesson seems to suggest that only the gravitation of the gravitating body--the earth sic-- applies; which suggests to me, that it--aka the gravitating body--is a rather singular thing, then I wonder why my original statement of the problem was rejected through moderation, by Dale-spam?

Once again thank you for the opportunity to sharpen my language skills--or lack of same, heh--and to realize that knowledge is a discourse between competing minds, and does not happen in a vacuum, or so they say. Although some might retort that my mind is a vacuum, which could have two different meanings, similar to Schrodinger's Cat musings, only better. Heh!

4. May 2, 2013

### DrewD

The force on the falling body is $F_g=mg$ where $m$ is the mass of the object and $g$ is a coefficient that depends on the mass of the earth (and the distribution of mass). The force then depends on the Earth and the mass of the body. The reason that both objects fall toward Earth in the same amount of time is because mass not only (partially) defines the force of gravity but also defines the resistance to acceleration (inertia). If only the earth mattered, then lighter objects would hit first since the force on both the heavy and the light object would be the same, but the heavier object would have more inertia.

I bet that the reason that a Mod rejected your other post is because it was totally incoherent and you misused almost every word that you used. Singular and singularity have a few very specific meanings in mathematics and in no way add to your question/rambling. If you want to ask questions and you don't understand the subject, you should stick to simple words, few words, and, well, ask a question.

From your OP, it seems to me that you have very little understanding of force and momentum. If you are using other sources to study, it would be best to ask straight forward simple questions about the specific thing that you read rather than saying weird things like "momentum, is a hyperbolic function".

5. May 2, 2013

### Bandersnatch

This is the false assumption in your reasoning that produces the expectation of different times of impact.
The reason why it is wrong has been explained above in DrewD's, perhaps a tad too grumpy, post.

If it's still unclear, consider the thought experiment wherein you divide the thousand pound mass into a multitude of tiny masses, each equal to, say that of a feather.
According to your reasoning, this 1000-pound mass should now fall slower, because nothing's stopping you from treating each individual feather-bit of the original mass as a separate falling body with lower inertia.
This produces a paradox where the same body can fall at different speeds depending only on your mathematical considerations, so it's an indication of a faulty reasoning.

To restate DrewD's explanation again, all masses equidistant from the central body accelerate at the same rate in its gravitational field, thanks to the force of gravity scaling with mass of the body being attracted.

6. May 2, 2013

### DrewD

Fair enough; I hadn't finished my coffee. Sorry to be rude, Jeffrey, but I do think that simple language works well.

7. May 2, 2013

### jeffrey c mc.

Thank you all for your discussion. I am not a physics student, yet I have received basic training in Aviation maintenance which covered theories of thermodynamics, gases, and heat; fluid dynamics, hydraulics, and flow movement, combined with gases, viz carburetors; gas dynamics, once again, carburetors, viz venturi effects, aerodynamics, airfoils; basic electricity; weights and balance, force; and how to sew a fabric covering together on old aircraft; added that just for whimsey, heh!. I incurred this in an Aviation maintenance course in the military, and a two year applied, Airframe and Power-plant course; unfortunately this was thirty years ago, and I may be a little out of touch with my demonstrable knowledge of same. And yes, your remarks are well stated, my use of terms is not coherent with those that have had a classical training in scientific knowledge; I will try to get up to speed with the terms I attempt to use to either ask questions or state my understanding of scientific principals; and I will either not use a term if I am un-clear about how it is used in the appropriate context, or follow the advice of Drew and ask, or relate my thoughts in a more general fashion.

With that said, I will also use the primer of the link to try to see if I can follow the discussion and suggestions Drew gave in his response. I'll be back if I can think of some clever way to confuse myself more. Heh.

Jeffrey

P.S. There was a discussion on the site I provided the link for about the idea Drew was discussing but I need to explore it further before I can relate much about it. Something about the ratio of the acceleration of gravity, which is the principle behind Drew's discussion.

P.S.S I only used hyperbolic because someone else used it on me, they got all hyper-colic on my a**.

Actually I was describing something as having an increased peak force as the evolution progressed; a graph sloping upward at an increasing rate at constant intervals; so to say. Or, a marked increase at each regular interval; one half of a bell curve; the acceleration of gravity. As gravity is inversely proportional to the square of the distance separating the two objects. What, 9.8 meters per second, per second. Something along those lines, I do assert.

More to follow

Jeffrey

8. May 2, 2013

### jeffrey c mc.

If Newton's second law were applied to their falling motion, and if a free-body diagram were constructed, then it would be seen that the 1000-kg baby elephant would experiences a greater force of gravity. This greater force of gravity would have a direct affect upon the elephant's acceleration; thus, based on force alone, it might be thought that the 1000-kg baby elephant would accelerate faster. But acceleration depends upon two factors: force and mass. The 1000-kg baby elephant obviously has more mass (or inertia). This increased mass has an inverse affect upon the elephant's acceleration. And thus, the direct affect of greater force on the 1000-kg elephant is offset by the inverse affect of the greater mass of the 1000-kg elephant; and so each object accelerates at the same rate - approximately 10 m/s/s. The ratio of force to mass (Fnet/m) is the same for the elephant and the mouse under situations involving free fall. [http://www.physicsclassroom.com/Class/newtlaws/U2L3e.cfm] [Broken]

This is what I was reviewing when I came out with the, 'It's slower out of the gate' metaphor. Slower out of the gate means it takes--due to its' inertia-- longer to get moving. It would seem I have been following your objections before you made them. Using colorful colloquial speech rather then using terms I 'do not understand.' Here's another conundrum derived from your remarks. If the force is distributed throughout both falling bodies, then, the smaller body has the greatest concentration of force as it is smaller. They both are equal in that they hit the same limiting surface at the same time--in a vacuum; therefore, the gravitating force is diffused over a larger mass in the large body.

This ratio (Fnet/m) is sometimes called the gravitational field strength and is expressed as 9.8 N/kg (for a location upon Earth's surface). The gravitational field strength is a property of the location within Earth's gravitational field and not a property of the baby elephant nor the mouse. All objects placed upon Earth's surface will experience this amount of force (9.8 N) upon every 1 kilogram of mass within the object. Being a property of the location within Earth's gravitational field and not a property of the free falling object itself, all objects on Earth's surface will experience this amount of force per mass. As such, all objects free fall at the same rate regardless of their mass. Because the 9.8 N/kg gravitational field at Earth's surface causes a 9.8 m/s/s acceleration of any object placed there, we often call this ratio the acceleration of gravity. (Gravitational forces will be discussed in greater detail in a later unit of The Physics Classroom tutorial.) [same as first cite]

So, that's all well and good, except we are not talking about objects resting on the Earths surface---{Because the 9.8 N/kg gravitational field at Earth's surface causes a 9.8 m/s/s acceleration of any object placed there, we often call this ratio the acceleration of gravity.}[from cite]---we're talking about objects falling, which by definition are not resting on the surface of the Earth. So objects are accelerating when placed on the surface of the earth, they assert.

So, I hope I've demonstrated that I can read at least.

In all my replies I have made in this forum I have been consistent in humbling myself, and deferring to others; due to the fact that I do realize my classical training in the subject is abject and wanting; and I do realize that my basic knowledge of the proper terms and the usage of same; is also wanting. Yet I do not need to be reminded of it constantly; especially after I have acknowledged that in a previous reply, in the same thread.

And again; [So the lesson seems to suggest that only the gravitation of the gravitating body--the earth sic-- applies; which suggests to me, that it--aka the gravitating body--is a rather singular thing, then I wonder why my original statement of the problem was rejected through moderation, by Dale-spam? ] (from third thread #3) This use of 'singular' is out of context in this thread, and OP. It makes a reference to an earlier started thread by myself, which quickly went into moderation and was removed as it was deemed not appropriate. Therefore, when I reviewed the discussion at the link I provided in my reply to Simon, I found it to say just about what I expressed in the post that was removed, so I began this thread. Only using ideas and concepts garnered from the aforementioned site link. I do hope no one wishes to claim that site is not a valid reference site. If we are to descend to that level of discourse that would leave me free to cast dispersions on this site also, I suppose.

Once again I do realize my reasoning skills may not be sufficient, and if you wish to point them out with demonstrations include, I won't cry foul, yet I may state my thoughts about the content, as I did with the above cite(s) pulled from another site{hopefully a site that all can consider to be a valid ref site); if I feel the only point being made is that I lack the superior reasoning, that others are endowed with, by the virtue of having a classical training in the fields of interest.

Last edited by a moderator: May 6, 2017
9. May 3, 2013

### Simon Bridge

And that is a misleading analogy - which should become apparent when you try to quantify the speed out of the gate. How much slower is the bigger mass out of the gate?

In fact, both masses have the same acceleration - neither is any more prompt from the gate that the other.
I can kind-of see what you mean but on balance - give up the metaphor: you'll get further.

You keep making a distinction between the two bodies in question, calling one the "gravitating body" and the other something else. You should realize that both bodies are gravitating.

In many examples, an approximation may be made where one body is much much more massive than the other, and greater in extent, so that, from the point of view of an observer on or close to the surface of the big body, small bodies fall towards "the ground" with a constant acceleration.

Note "colorful colloqual speech" is not useful for finding out about technical subjects - as your training and practice in aviation maintenance should have lead you to discover. Fuel burns, the ground is hard, and so on - pilots and engineers who mess about with those description on the job get into trouble. How would you feel towards a pilot who lapsed into poetic language in a report?

I'm still not sure that you have articulated your problem though.
Mostly you seem to be puzzled by some stuff you have read.

I suspect you will be best served by phrasing your puzzlement as a series of questions.
What is it that you don't understand about gravity?

10. May 3, 2013

### jeffrey c mc.

[And that is a misleading analogy - which should become apparent when you try to quantify the speed out of the gate. How much slower is the bigger mass out of the gate.]

Inertia is an inverse function(affect) of mass in acceleration. Acceleration is dependent on Force, and Mass; so says Newton.

{And thus, the direct affect of greater force on the 1000-kg elephant is offset by the inverse affect of the greater mass of the 1000-kg elephant; and so each object accelerates at the same rate - approximately 10 m/s/s. The ratio of force to mass (Fnet/m) is the same for the elephant and the mouse under situations involving free fall.} Not my content, it's from independent reference source, sic

[You keep making a distinction between the two bodies in question, calling one the "gravitating body" and the other something else. You should realize that both bodies are gravitating.]

Yes that's a correct statement, because gravitating is a word that means being under the influence of gravity. My postulate is that the Earth, which is by all means a gravitating body, has a singular nature, then objects that are subject to the Earths gravity field. All things (objects) are subject to gravity, to be sure; though with the demonstration of two falling objects--in a vacuum--one could suppose that they--the falling objects--do not share the same nature, as the Earth, and the Earth's Gravity field.

[n many examples, an approximation may be made where one body is much much more massive than the other, and greater in extent, so that, from the point of view of an observer on or close to the surface of the big body, small bodies fall towards "the ground" with a constant acceleration.]

Every object in a Gravity field falls at a constant rate of acceleration. 9.8 meters per second, per second, to be succinct

[I'm still not sure that you have articulated your problem though.
Mostly you seem to be puzzled by some stuff you have read.]

The force of gravity is inversely proportionate to the product of; Mass, and the square of the distance between two objects in question. Acceleration is proportionate to the product of the; Mass, and Force applied. Unless I've learned my lesson incorrectly.

Therefore, even while the Acceleration of Gravity is a constant; the altitude of an object, and it's mass, has a direct bearing on; the initial force as it rests on a platform; the net force 'increase' as it gets closer to the object it is falling towards; and, as Acceleration is tied into force and Mass; an object that has a larger Mass should receive a higher 'net force' increase--the closer it gets to the center of an object it is falling towards--then an object with a dramatic decrease in it's mass; as set against the larger object. Yet, in free-fall, in a vacuum, they arrive at the limiting surface--the same limiting surface--together. And yes, this puzzles me! And yes, I'm still working with the ideas and concepts I received from the source material.

Contrary to the impression I am likely to be seen as projecting, I am here to learn, and do welcome discourse and debate; but, just as I have to learn the proper use of terms that are applicable to the fields in question; I would ask that others be a little patient with me; and make the attempt to work around my 'world-view' and the way I express it.

citations
[brackets] are cites from Simon's discussion. {fancy brackets} are full citations--meaning no exclusion of content from bracket to bracket--from independent source. Paragraphs that start with no diacritical marks comprise my thoughts.

11. May 3, 2013

### Bandersnatch

You're still missing the point we(and the source you're citing) are trying to convey.

Yes, more massive objects have higher inertia - they require higher force to accelerate in the exact same way as less massive objects. If you supply twice as high a force to twice as massive a body, it'll have the exactly same acceleration, at all times.
The force of gravity scales with mass, so it will always provide exactly enough extra force to move any object(equidistant from the source) at the same rate.

Take a look at the equations:

Newton's 2nd Law of Motion is expressed by:

$F=ma$
$a=\frac{F}{m}$

Where F in newtons is the force needed to accelerate the mass m in kilograms with a metres per second squared.

Integrating acceleration over time nets you all the remaining kinematic equations(velocity and position), so all you need for two bodies to move in an identical fashion is for the acceleration to be identical. With identical acceleration they'll have identical instantenous velocites and positions.

If you have two masses m and 2m, and you need both to move in exactly the same way(equal a), then you need forces F and 2F respectively.

Now, the force of gravity is given by:

$F_g=G\frac{Mm}{R^2}$

Where Fg is the force between the two bodies of masses M and m(M>m, by convention), separated by R metres. G is a constant.

Substitute Fg to the equation of motion to find out that:

$F=F_g$
$ma=G\frac{Mm}{R^2}$

and the result is:

$a=G\frac{M}{R^2}$

Which tells you that how the body moves in the gravitational field of mass M is independent of the object's mass. Whether you have a body of mass m(a feather) and gazzilion*m(an obese hippo), matters not, since their mass is absent from the equation of motion as shown above. As long as the two bodies begin their movement at the same distance R, and gravity is the only force acting, then they will always move in the same way.

12. May 3, 2013

### jeffrey c mc.

Thank you Bandersnatch. I believe I understand my thinking error now. One; I was placing to much emphasis on Newtons second law of acceleration; which, is a general statement, as compared to the force of gravity, and acceleration of same. Which could be considered a specific, or special, phenomena. Where as I could be the one applying the force in the general nature to an object. Gravity is the supplier of the force in the specific, concerning objects in free-fall. I do understand that gravity, as a force is thought of as a constant, and is accelerative; ad is defined by Mass, and the inverse of the square of the distance between the center of two objects. Which provides the accelerative nature of gravity. So, when we have two objects on a platform, at an elevation, the masses of both can only be considered as potential. When the support is removed, both begin descent at appx the same time; the mass becomes kinetic. Yet the energy can only be realized if and when an obstruction is met. So, while they are in free-fall, the force of gravity acts on both equally. And even though the moment of inertia in the larger mass is greater, that energy only becomes manifest when it impedes on, or strikes a limiting surface, or something that can, and may cause a change in the force vector. Such as atmospheric drag.

So, I'm happy to retort my perplexity has lessened on this thread, and thank everyone who had the patience to continue remarking on my musings.

Jeffrey

13. May 4, 2013

### Buckleymanor

Actualy is there not three bodies gravitating.The more massive one by far does not seem to move never mind it having the same acceleration as the others.Is the acceleration of small objects
mearly dependent on size with relation to the largest object.If one of them was scaled up to be more massive like say the size of the moon would it still have the same acceleration.
Things like kilo weights, elephant's and feathers are all insignificant in size in comparison to the Earth, so you would expect them to move with the same speed towards it and are common with our everyday experiance.When things are scaled up don't they get stranger.

14. May 4, 2013

### Jupiter6

We've all been through the same line of thought at some point, whether we admit it or not.

One thing I'll point out is stop referring to gravity as a; "force", "g-force", "force of gravity" etc. It is not a force. When you stop referring to it as such, you'll make the mental connection more concrete and recognize what the f, m, and a in a real-life system are more easily.

Another biggie is understanding momentum and how energy relates to it (integral). Some "scientific" people seem to have a really hard time grasping the concept.

15. May 5, 2013

### Simon Bridge

Your language has become less poetic so it's easier to parse - well done.
Lets see if I can spot the questions in all that ...
(Don't forget the question mark at the end of questions - they clue-in English speakers as to your intent.)
The acceleration due to gravity depends only on the relative positions of the gravitating objects and the mass of the other one. It does not matter what the size or the mass actually is.

If our two masses are $m$ and $M$ for the smaller and the larger mass, you have already realized that Newton's laws tell you (for the small mass):
$$\begin{array}{rrclr} & F & = & ma &\text{(1)}\\ \Rightarrow & \frac{GMm}{r^2} & = & ma &\text{(2)}\\ \Rightarrow & \frac{GM}{r^2} & = & a & \text{(3)}\end{array}$$ ​
... it does not matter how big $m$ actually is, the fact it appears on both sides of the equation means it cancels itself out.
If we were to scale m up to 1000000x the initial amount, then it would scale the same 1000000x on both sides of the equation in step (2) and still cancel out to have no effect on the acceleration (3).

What you or I may intuitively expect to be the case is not important. What is important is what is actually the case.

How do you mean?
Generally you cannot just scale up a bunch of dimensions and expect things to stay the same - no.
But there is nothing weird about that.

There are situations where Newtonian gravitation (what you have been struggling to understand above) does not apply - this is because it is, itself, a kind of approximation due to the investigative tools available to Newton and people of his ilk. A more complete picture of gravitation is provided by General Relativity ... this is why Jupiter6 is suggesting you stop talking of gravity as a "force": it can help with the transition to GR when you are finally ready for it. I think it's six of one and half-a-dozen of the other myself; but I'm pretty sure that your use of language is a major obstacle to your understanding here.

Last edited: May 5, 2013
16. May 5, 2013

### TurtleMeister

He may be referring to the fact that if the mass of either body is increased, the time interval decreases (be it the period or the time to impact). This is often a source of confusion for folks learning Newtonian gravity because it seems to contradict the universality of free fall. The key to understanding why this is not a contradiction to the UFF is in understanding the frame of reference.

17. May 5, 2013

### Simon Bridge

Sure... or it could be a reference to black holes, or something else.
But lets let OP tell us what OP means.

18. May 6, 2013

### Buckleymanor

I agree, so if we were to make mass 1 the size of the Moon, mass 2 a feather and mass 3 the Earth.
Then release mass 1 and 2 together slightly apart a thousand metres above the Earth.
Mass 1 and 2 won't hit the ground of the Earth together?
Even if the feather was released at the lowest possible levell point of the Moons circumference.

19. May 6, 2013

### Simon Bridge

3-body problem has no analytic solution.

Lets rewrite the thought experiment so the math is tractable.

Let there be two masses A and B with masses M and m respectively so that M>>m.
Let them fall under the uniform gravity approximation for objects close to the Earth - so the force of Newtonian gravity is Mg for mass A and mg for mass B.
Let mass A and B have equal, small, spherical volumes so that we don't have to worry about disparate sizes.
Now do the math - neglecting air resistance etc.