Derivate the forumla for the acceleration due to gravity

[JohnDubYa]

RE: "This argument about the terminology has dragged on this long probably because there hasnt been an actual students opinion..."

Actually, some of the posters in this thread are probably students.

RE: "well I am here to solve that problem, I am a high school student that took physics this past year. Acceleration due to gravity is most certainly the easiest way to get across to anyone, what g actually is."

Well, to YOU. But don't assume that everyone thinks like you.

As I said earlier, assigning g as the acceleration of objects that are not in free fall is a tremendous problem in introductory physics. Obviously there are a lot of confused students out there. I am suggesting that calling g the acceleration due to gravity is the primary cause of the confusion.

RE: "Its very clear, and obviously self explanatory. Saying anything else would confuse the crap out of a student."

If so, then how did you learn physics related to the electric field? After all, if the term "gravitational field" confuses the crap out of you, how could you possibly learn electromagnetism with its reference to the electric field? The two are directly analagous.

RE: "It might not seem that way to some, but it will because not every student that wants to know physics is necessarily a very bright one. Anyways, I, as a student agree that with everyone that prefers "acceleration due to gravity" instead of "universal constant".

I don't recall the term "universal constant" being offered in this thread. Where did you read that?

 

[JohnDubYa]

RE: "What would answer if the student asked me which way the book is accelerating? Upward, as the equivalence principle predicts and is confirmed by the freely falling observer."

And a student is going to wonder what allows you to examine the physics of a event in a non-inertial reference frame. And why you have chosen that particular reference frame, when special relativity assumes that there is no preferred reference frame.

RE: "And reading that again, yes that would confuse the heck out of most students."

Most students? I am not aware of any introductory physics student who would have any hope of understanding the topic with such a definition.

RE: "Even so, the fact that the book even IS accelerating isn't introduced till GR. So, leavi"ng some of the more complicated details until later in their studies, by calling g the "acceleration due to gravity" the students who do choose to go on to more complicated subjects won't have to completely switch around their thinking."

Actually, calling g the gravitational field shouldn't either.

 

[robphy]

What would answer if the student asked me which way the book is accelerating? Upward, as the equivalence principle predicts and is confirmed by the freely falling observer. And reading that again, yes that would confuse the heck out of most students. Even so, the fact that the book even IS accelerating isn't introduced till GR. So, leaving some of the more complicated details until later in their studies, by calling g the "acceleration due to gravity" the students who do choose to go on to more complicated subjects won't have to completely switch around their thinking.

In GR, the book at rest on a table on the Earth's surface is accelerating upward (as you say).
Why is it said to be "accelerating" in GR? It is because the book is not moving inertially. Its worldline is not geodesic. [In GR, acceleration is an invariant measure of worldline curvature.] By contrast, a freefalling book has a worldline which is geodesic. Indeed, a freefalling accelerometer will read zero.

Now, what agent is applying the force on the book (keeping it off a geodesic)?
It is the table pushing upward... the book's acceleration is "due to the table".
(Near the Earth's surface, the magnitude of this upward acceleration is 9.8 m/s^2.) [Note that, in GR, "forces" always refer to "non-gravitational forces".]

So, it seems to me, that invoking GR suggests that "acceleration due to gravity" is not meaningful. ("Freefall acceleration" would also not be meaningful.)

I know, like ArmoSkater I'm a student too who happened to be so taken in with physics in my first course, that I've been teaching myself relativity, quantum theory, etc. Earlier, I had been a little confused about why everything accelerates at g in the Earth's gravity, even if we view them as being at rest, but I didn't exactly lose sleep over it. And it made understanding the equivalence principle that much easier.

 

[ArmoSkater87]

JohnDubY: First of all, "universal constant" was mentioned earlier in the thread. Second...u say not everyone might think like I do, then why should everyone think like YOU?? I didnt necessarily mean to say that everyone should think of "acceleration due to gravity" like i do, i was simply offering my opinion on it as a student. I understand that you are too, i really don't have a problem with "free fall acceleration", it's not a bad way to explain g, but its more specific than nessasary. In my opinion, i think the student should get the bigger picture first. "Acceleration due to gravity" just seems very clear, g is an acceleration...cause by gravity. Seems pretty simple to any student taking physics. To a student the whole deal with "accelaration due to gravity" being inaccurate doesn't come to mind at all, since the problems they deal with uses g as an acceleration in some gravitational field. I'm just giving my view, no one has to agree with it. :D

 

[JohnDubYa]

I sure don't remember anyone offering "universal constant" as an acceptable term for g. *I* certainly didn't. But I agree that such a term is a terrible definition.

RE: "Second...u say not everyone might think like I do, then why should everyone think like YOU??"

I offer my opinion based on teaching well over 1000 students over the past few years, not on my own cognition. After all, *I* am not confused by the definition. But too many of my students have been.

RE: "I didnt necessarily mean to say that everyone should think of "acceleration due to gravity" like i do, i was simply offering my opinion on it as a student."

Okay, fair enough.

RE: "I understand that you are too, i really don't have a problem with "free fall acceleration", it's not a bad way to explain g, but its more specific than nessasary."

I think its specificity is exactly why it would work. By being very specific, it is less likely to be used in cases where it doesn't apply.

RE: "In my opinion, i think the student should get the bigger picture first. "Acceleration due to gravity" just seems very clear, g is an acceleration...cause by gravity. Seems pretty simple to any student taking physics."

Any student? That is a pretty big statement. Believe me, the number of students that will go home and screw it up is quite considerable (and unnecessary).

RE: "To a student the whole deal with "accelaration due to gravity" being inaccurate doesn't come to mind at all, since the problems they deal with uses g as an acceleration in some gravitational field. I'm just giving my view, no one has to agree with it. :D"

Let me give you an example of where things go wrong.

You ask a student to find the time it takes for a block to slide down a plane. You give them the mass of the block, the geometry of the plane, and the kinetic coefficient of friction.

The student is expected to use Newton's second law to find the acceleration along the plane, and then use that acceleration to find the time of motion.

But many students will say to themselves, "Gravity is pushing this block down the plane. The acceleration due to gravity is 9.8 m/s/s. Therefore, I will use g in my distance formula..."

And you can talk about the proper use of g until the cows come home, but as long as it is called the "acceleration due to gravity" they will use it in such situations. The term "free-fall acceleration" is much better, because at least it hints that there is a problem with using it since the block is obviously not in free fall. (I like gravitational field, but let's ignore that definition for the purpose of this discussion.)

 

[ArmoSkater87]

Okay, what you say if fair enough. I had no idea you were a teacher I though you were a student. I guess some students can be misled by it. To me it would be clear that the friction decreases the acceleration, but i guess not every student can realize that. But I think "acceleration due to gravity" sounds cooler. :D

 

[VantagePoint72]

Well, JohnDubya, you're the teacher, if you think it will make the concepts clearer to your students then go for it. While my preference will still be to refer to it as the acceleration due to gravity, what I call it won't have the slightest bearing on the people you teach anyway.

 

[JohnDubYa]

Well, I think this has been a great thread. I understand your points. If you ever get to teach, do a little experimentation and see if the term acceleration due to gravity is confusing to students.

And "gravitational fields" is definitely cooler than "acceleration due to gravity." Students think "wow, fields... man! Like, force fields, and electric fields, and Fields of the Nephilim, and ..."

 

[jcsd]

John, upon review you didn't call g a universal consant, Doc Al did, tongue firmrly in cheek. But you did call it the graviational field constant which is what I object to strongly as it's not a constant (the value of g varies measurably even on the Earth's surface); if somone was talking about "the graviational field constant" G rather than g would spring into my mind (infact seraching for this term returns very few results, some of which refer to g others of which refer to G, though I am suprised to see that it does seem some school curriculums do use this term for g). Freefall acceleration is a much more acceptable term and it's it's one that is often preferred.

 

[Doc Al]

John, upon review you didn't call g a universal consant, Doc Al did, tongue firmrly in cheek.

Where did I do that? What I actually said was:

I'll probably start calling g the "gravitional field strength/constant at the Earth's surface".

Yes, my tongue was somewhat in cheek, since most students would give a blank stare at such a statement, at least at the time when "g" is first introduced. But on further reflection, considering that most students learn kinematics before dynamics before gravitation, I would probably say:
In covering the kinematics of projectile motion:

the freefall acceleration due to gravity = g (downwards)​

(As krab pointed out, this is a crucial fact that must be taught.)

In covering dynamics (Newton's second law):

the "weight" of body is w = mg (downward) (here pointing out that "g" is a measure of the strength of the Earth's gravitational field--more to come)​

In covering Newton's law of gravity:

here we can explicitly derive that "g" is the gravitational field strength (Force per unit mass) at the Earth's surface​

So I would have to start calling "g" the magnitude of the freefall acceleration due to gravity, and then later add that it is a measure of the gravitational field strength at the Earth's surface. Which is what I do already. Oh well.

Even though we've beat this topic to death, it still has been instructive. If nothing else, it has made me more aware of how easy it is to confuse students with sloppy terminology.

 

[JohnDubYa]

Yes, I earlier dropped the term "constant" in my definition.

While students are learning kinematics, I don't give g a name. I tell them that near the surface of the Earth a body in freefall accelerates at 9.8 m/s/s, and we give that value the label g. Later, after discussing gravity, I define it in terms of the gravitational force and call it "the gravitational field."

Overall, a good discussion.

 

[robphy]

One last post...
Here are some comments on "acceleration due to gravity" by some physics teachers [from "The Physics Teacher"].

http://scitation.aip.org/dbt/dbt.jsp?KEY=PHTEAH&Volume=37&Issue=5
SURVEY OF HIGH-SCHOOL PHYSICS TEXTS: Quibbles, misunderstandings, and egregious mistakes
Physics Textbook Review Committee
The Physics Teacher--May 1999 Volume 37, Issue 5, pp. 297-308

7. The texts differentiate between mass and weight in various chapters. All of them refer to g as the “acceleration due to gravity.” This is surely confusing, if not misleading, to students who wonder why acceleration should have anything to do with the weight of an object sitting still on a pan balance. A more useful definition of g is that it is the gravitational field strength. The analogy with the electric field strength can be made early as well as late. Thus F_grav = mg is analogous to F_electric = qE. To two significant figures, g =9.8 N/kg; thus the weight of 1.0 kg is 9.8 N. Otherwise the weight of 1.0 kg is 9.8 kg m/s2, which of course is valid, but confusing for a student.

and

http://scitation.aip.org/dbt/dbt.jsp?KEY=PHTEAH&Volume=38&Issue=3
NOTES: g-whizz
John A. McClelland
The Physics Teacher--March 2000 Volume 38, Issue 3, p. 150

In the review of current textbooks¹, it is pointed out that g should be described as the strength of the gravitational field rather than as an acceleration. The distinction may benefit from a little elaboration.

A book of mass m rests on a table. What is its weight w? A typical textbook answer is that w = mg where g is “the acceleration due to gravity.”

Given that the book is in equilibrium² it has no acceleration due to gravity, nor has anything else in the figure, so the statement is self-contradictory. A worse case arises where a body is falling but is not in free fall. Its weight is still described as the “mass times the acceleration due to gravity,” but its acceleration is less than this—potentially very confusing.

Even if g is called the acceleration of a body in free fall, it is not at all obvious to a beginner that the product of a mass m kilogram and g m/s2 gives w Newton. It is more logical and much more transparent if g is introduced as the gravitational field at the surface of Earth in Newton/kilogram. This may or may not be related to GM/R² according to the level of the course. If the concept of a field is not required, g can be called the strength or intensity of gravity. The gravitational field (or the strength of gravity) at a point can be defined as the force in Newtons experienced by each kilogram of mass placed there. It is not hard to see that m kg x g N/kg gives w N. Because this is analogous to how we deal with forces on electric charges in an electric field it also makes pedagogical sense.

Applying Newton’s second law to a body at Earth’s surface shows that, when w = mg is the net force, the acceleration of the body, in m/s2 is numerically equal to the strength of the field in Newton/kilogram. This is free fall. In all other cases, the net force is different from w and the acceleration is different from the acceleration in free fall. In other words, the acceleration in free fall is both a consequence of the strength of the gravitational field and a special case.

Away from Earth’s surface, there really is no satisfactory way to arrive at the acceleration of a body in free fall except through the strength of the gravitational field there. For example, at the surface of the Moon, g=1.6 N/kg, so the acceleration of a body in free fall is 1.6 m/s2.

There are probably two reasons why it has become conventional to define g as an acceleration rather than as a field strength. One is that most introductory textbooks cover kinematics before dynamics and use examples of bodies taken to be falling freely, often including projectiles. Having introduced a value for the acceleration in free fall and attributed it to gravity, it then becomes “the acceleration due to gravity” in all that follows. The other is that it is possible to obtain a quite reasonable value for this acceleration experimentally. To be logically and pedagogically sound, we should quote g in Newton/kilogram, refer to “the acceleration in free fall,” and mothball the expression “acceleration due to gravity.”

References

1. Editorial comment, “Quibbles, misunderstandings and egregious mistakes,” Phys. Teach. 37, 297 (1999).

2. If the table is on a rotating Earth it is not in equilibrium.

 

[JohnDubYa]

RE: "This is surely confusing, if not misleading, to students who wonder why acceleration should have anything to do with the weight of an object sitting still on a pan balance. A more useful definition of g is that it is the gravitational field strength."

Oooh, that's wierd. It is as if I wrote it. (But I didn't. They explained their views better than I did.)

Thanks for the references.

 

[woodysooner]

If accuracy is what you desire then we should drop Newton's second law altogether and use general relativity to solve classical physics problems.

Johndubya, what GR equation do you use to do this?

 

[pmb_phy]

By the way, the term "acceleration due to gravity" is a misnomer, because it assumes g is an acceleration. It is not. The correct term, in my opinion, should be "gravitational field constant."

Since this is in the Classical Physics forum then I'm assuming that this is a discussion on Newton's Law of gravity.

In that sense = What is your justification for your statement it assumes g is an acceleration. It is not.

g(r) is a vector function of a vector variabe and as such varies from place to place and therefore can't be considered to be a constant. g(r) is an acceleration vector as a function of position since

\bold g(\bold r) = \frac{d^2\bold r}{dt^2}

The only constant is G in

\bold F_{12} = \frac{Gm_{1}m_{2}}{r^2} \bold e_{12}

Pete

 

[pmb_phy]

Given that the book is in equilibrium2 it has no acceleration due to gravity, nor has anything else in the figure, so the statement is self-contradictory.

That seems to be a common error in thinkng in physics. Its a result of a misuse/misunderstanding of the principle of superposition. F = mg refers to that acceleration what would occur if this were the only force acting on the body in the absense of all other forces. This same thing carries over to EM. Griffitth quite nicely explains all this in a most beautiful fashion.

Pete

 

[JohnDubYa]

What is your justification for your statement it assumes g is an acceleration. It is not.

The fact that the constant g can factor into a non-accelerating system. When students are told that g is an acceleration, then they assume that a body with a weight mg must accelerate at g.

Sure, WE know better.

 

[JohnDubYa]

woody, I'm not sure what you are asking.

Are you a Sooner?

 

[woodysooner]

A Sooner I am, can't wait to get back to Norman only few more days.

If accuracy is what you desire then we should drop Newton's second law altogether and use general relativity to solve classical physics problems.

I just meant how in the instance do we use GR, guess I need to get with it and learn the math behind GR, just thought if you gave me the equation for that instance in GR i could run with it.

Thanx

 

[JohnDubYa]

Gawd, I miss Oklahoma. Are you a physics major at the University?

My allusion to GR was a jab at those that conjure GR to explain the most elementary physics.

 

[woodysooner]

good question, at the present I'll be a junior in chemical eng. and eng physics, but bout to give all that up and start over lol in Physics and Math.

if dad let's me, he runs the show sadly, but he shouldn't cause he don't pay for it the state and a lot of other do.

 

[JohnDubYa]

Take all the classes that Bruce Mason teaches. I had him as an undergraduate and he may be the best Prof I have ever had at any level. Doc Watson and Mike Morrison too.

 

[cepheid]

I'm a student and I'd just like to offer my two cents on this debate over terminology:

When we began our study of physics in high school, we began with kinemetics. Certain problems (involving freefall and later projectile motion) involved use of the physical quantity g, which I learned was the acceleration of objects in freefall. (Our physical model for falling objects always neglected air resistance, so I did not trouble myself over it). My teacher referred to this as the acceleration due to gravity, which made perfect sense to me, because it meant that gravity caused objects to accelerate at 9.81m/s^2. More precisely, when gravity was the sole force on an object, it's resulting acceleration would be g. I accepted this to be true, even though I had no idea how or why it was so, i.e. was was the nature of the graviational force and why did all objects under it's influence accelerate like so?

Later, when we studied dynamics, we attempted to determine how such 'action at a distance' was possible, and we were introduced to the notion of fields. From Newton's Universal Law of Gravitation, we derived the 'graviational field strength' at the Earth's surface to be g. I must admit to being mometarily confused. Why should these two quantities with totally different names be represented by the same symbol? I decided that the quanitites must actually be one and the same, and set about explaining it to myself. I asked myself the question: "Why is the acceleration of objects under the sole influence of Earth's gravity equal to the strength of the graviational field at the Earth's surface? The answer is simple: From the definition of a field, we see that the Earth's graviational field exerts a force of 9.81 Newtons on every kilogram of an object's mass. It therefore exerts a force of 9.81 Newtons on a 1kg object in freefall. Since the definition of a Newton is the force required to accelerate a 1kg object at 1 m/s^2, it stands to reason that our 1kg object in freefall will accelerate at 9.81 m/s^2, since 9.81 N of force are being exerted on every kilogram of mass. Therefore, the two quantities are one and the same: the acceleration of an object in freefall is equal to the strength of the gravitational field. I was sure this was true when I observed that

\frac{N}{kg} = \frac{m}{s^2}

In short, I sorted it out on my own and I really don't care whether you call g 'acceleration due to gravity' or 'gravitational field strength' since the fact that the two must have the same magnitude (and direction) at the Earth's surface is direct consequence of the Law of Gravitation and Newton's Second Law.