Earths force of gravity measured in Dynes

[Mordred]

I have a copy of a 1923 physics book so here is a question from it lol

" what is the force of gravity at the equator at sea level measured in Dynes ? "

Another question is

What is the definition of fusion in 1923 ?

what is the model of the atom and size assigned to each of its particles at 1923 ?

 

[HallsofIvy]

The force of gravity depends upon the mass being attacted by the earth. The acceleration due to gravity is about $9.81 m/s^2$ which, since there are 100 cm in a m, would be $981 cm/s^2$. If an object has mass M grams, then the gravitational force on it would be $981M dynes$.

 

[Mordred]

correct though back in 1923 the value was considered to be 980 Mdynes probably due to degree of accuracy. At least according to " Elements of Physics " publication date 1923 latest publication reprint was 1937 by F.W Merchant and C.A Chant who are the authors of this Canadian high school physics book I found recently. Still waiting to see if anyone wants to try the other two questions. The answers are kind of surprising. interesting side point this hard cover book cost one dollar back then lol. The truly neat thing is the amount physics has changed since then. This book also includes all the earlier experimental models on the topics it discusses complete with the details on how to build and replicate those experiments. Even shows how to build a single prism spectroscope. This book also refers to the Ether, and their value for the speed of light was 186,000 miles/sec but later corrects it by stating its value is 186,330 miles.sec or 299,860 km/sec. Xrays were still referred to as Rontgen rays.

 

[Ken G]

I don't know the answers but I'm waiting to hear them.

 

[Mordred]

to answer the other questions

Fusion was defined as the change from a solid to a liquid by means of heat.

the model of the atom had no neutron the mass of the electron was expressed as 1/1840th that of a hydrogen atom with its dimension 1/100000th those of hydrogen with the proton being 1/2000th the size of the electron.

The Dyne: A name has been given to that force which, when it has acted on a gram-mass for 1 sec will have given it a velocity of 1 cm. per sec is called a dyne.

 

[Ken G]

That's pretty bizarre, as recently as 1923, for physics to be that messed up! The definition of a dyne is bad enough-- the idea that a force would be quantified by what its effect would be on a given mass! It certainly seems to assume the force doesn't depend on mass, so would seem to be invalid for gravity unless their implication was that gravity was not a force at all so could not be characterized by any dyne amount, rather than 980 dynes.

 

[TurtleMeister]

That's pretty bizarre, as recently as 1923, for physics to be that messed up! The definition of a dyne is bad enough-- the idea that a force would be quantified by what its effect would be on a given mass! It certainly seems to assume the force doesn't depend on mass, so would seem to be invalid for gravity unless their implication was that gravity was not a force at all so could not be characterized by any dyne amount, rather than 980 dynes.

Eh?

The dyne is defined as the force required to accelerate a mass of one gram at a rate of one centimeter per second squared.

The Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

 

[Ken G]

Eh?

The dyne is defined as the force required to accelerate a mass of one gram at a rate of one centimeter per second squared.

The problem with this definition is, it only works on a given mass. What about other masses? The assumption must be that the force is staying the same when you change to a different mass, and then the acceleration will drop in inverse proportion and there is no problem with assuming you still have a dyne of force, because we are implicitly assuming we have not changed anything but the mass. But since gravity depends on mass, if you swap in a different mass you do not get less acceleration. The definition of the dyne has no way to tell us if we still have a dyne of force there or not, because nowhere in the definition does it say that a dyne must give less acceleration on more mass.

In other words, on a planet where g = 1 cm/s/s, there is absolutely no contradiction with that definition of a dyne of force to assert that the force of gravity on that planet is 1 dyne, because any 1 gram object will accelerate at 1 cm/s/s, no matter what the object is, and according to that definition, any force with that property is a dyne of force. The definition doesn't tell us what force we have if 2 grams accelerates at 0.5 cm/s/s, so it has to be making some assumption about what happens if you change the mass--i.e., that the force does not directly rely on mass.

 

[Doc Al]

In other words, on a planet where g = 1 cm/s/s, there is absolutely no contradiction with that definition of a dyne of force to assert that the force of gravity on that planet is 1 dyne, because any 1 gram object will accelerate at 1 cm/s/s, no matter what the object is, and according to that definition, any force with that property is a dyne of force.

You'd specify the gravitational field strength in terms of acceleration or force per unit mass, not simply force. Saying that the force of gravity is 1 dyne isn't very helpful, since the gravitational force depends on the mass of the object.

 

[Ken G]

That's my point. The above definition of a dyne is incorrect if gravity counts as a force-- the right definition must be that a dyne is any force that produces a unit product of the mass in grams and the acceleration in cm/s/s. Merely asserting what happens to 1 g can only be enough of a definition if one can assume that the acceleration scales in a certain way when you change the mass and nothing else, but that assumption is incorrect if gravity is viewed as a force.

 

[Doc Al]

I think we can safely assume Newton's law to apply that definition more generally.

 

[Ken G]

I am saying that we know F=ma, yet the definition is still not complete. It does not apply to gravity, unless it is framed the way I did.

Look, let's say we have 2 g and it accelerates at 0.5 cm/s/s. Can you say we have 1 dyne of force? Not by that definition. To apply that definition, we are forced to ask, "what would the acceleration be if it was only 1 g?" We have no choice, look at the definition-- knowing F=ma doesn't help us at all unless we know something about what happens to the force if it acted on 1 g, that's what the definition says. So how do we answer that? We are forced to make the assumption that the force would not change if all we did was change the mass from 2 g to 1 g. So let's do that-- and it's works just fine for any force but gravity. But if it was gravity, then the acceleration stays at 0.5 cm/s/s. So we must, by that definition, conclude that we did not have 1 dyne of force, because that force did not give us 1 cm/s/s when all we did was change the mass to 1 g.

No fair, you say, we should not have assumed the force would stay the same when we changed to 1 g. Well, then what should we have assumed? What assumption can we make that allows that definition to work for any force? None-- there is no assumption we can make about what happens to the force when it acts on only 1 g that allows that definition to be complete, unless we say gravity is not a force and then we can assume the definition works if all you do is change the mass and nothing else.

 

[Doc Al]

Look, let's say we have 2 g and it accelerates at 0.5 cm/s/s. Can you say we have 1 dyne of force?

Of course you can. The definition tells us that 1 dyne is the force that would accelerate 1 gram at 1 cm/s^2. Newton's 2nd law tells us that the same force would also accelerate 2 gms at .5 cm/s^2. No problem.

 

[Ken G]

Of course you can. The definition tells us that 1 dyne is the force that would accelerate 1 gram at 1 cm/s^2. Newton's 2nd law tells us that the same force would also accelerate 2 gms at .5 cm/s^2. No problem.

Yes, problem. What do you mean by the same force? You must have an operational definition of that, i.e., a definition that actually means something in the laboratory. Your definition gives you no way of knowing what the same force even means. You must make some assumption about how to get the same force, or else you need a definition that works on any amount of mass.

 

[cepheid]

Look, let's say we have 2 g and it accelerates at 0.5 cm/s/s. Can you say we have 1 dyne of force? Not by that definition.

Yes, we can say that we have 1 dyne of force, because 1 dyne ≡ 1 g*cm*s^-2, and using Newton's second law, we conclude that the net force acting on this object is equal to (2 g)(0.5 cm*s^-2) = 1 g*cm*s^-2 = 1 dyne.

To apply that definition, we are forced to ask, "what would the acceleration be if it was only 1 g?"

No. We are not forced to ask that. You misunderstand the definition. As Doc Al has already said, since we take it as a given (i.e. it is axiomatic) that Newton's 2nd Law is true, it is therefore implicit in the verbal statement that the force required to accelerate 1 gram by 1 cm*s^-2 must have a magnitude that is equal to the product of that mass and that acceleration. So, this definition IS stating that 1 dyne = 1 g*cm*s^-2.

 

[Ken G]

Again, see my answer to Doc Al. You are both making assumptions about what "the same force" means, and you have no definition of the same force to back you up. You have circular logic-- you want F=ma to quantify your force, but if the definition of a dyne explicitly uses 1 g of mass, then you have to know what will happen to the force you are trying to quantify when it does not act on 1 g, which you cannot do if the force depends explicitly on mass.

ETA: You're right, I'm mistaken. If you have a mystery force that accelerates 2g at 1 cm/s/s. You want to quantify that force. You know that if the force were 1 dyne, it would accelerate 1 g at 1 cm/s/s. You have 2 g, so that is like having 2 1g masses attached to each other. Each one is receiving 1 dyne of force, by your definition. So obviously, if each half is getting 1 dyne of force, the total must be getting 2 dynes. So the definition is OK, because you don't need F=ma so you don't need to know what happens to F when you change m.

 

[Doc Al]

Yes, problem. What do you mean by the same force? You must have an operational definition of that, i.e., a definition that actually means something in the laboratory. Your definition gives you no way of knowing what the same force even means. You must make some assumption about how to get the same force, or else you need a definition that works on any amount of mass.

The only assumption needed is Newton's 2nd law.

 

[cepheid]

Again, see my answer to Doc Al. You are both making assumptions about what "the same force" means, and you have no definition of the same force to back you up.

No, we're not making assumptions about what "the same force" means. We're saying that "the same force" is the force whose magnitude is such that, IF it were acting on 1 gram, then it would accelerate it at 1 cm/s² (regardless of what mass it is actually acting on in the situation being considered). That is how you define the magnitude of the force -- by what Newton's 2nd law says its effect on a unit mass would be. Please read that word in boldface and italics a few times.

You have circular logic-- you want F=ma to quantify your force,

No, I don't want "F = ma to quantify [my] force." I don't even know what that statement means.

but if the definition of a dyne explicitly uses 1 g of mass,

The definition of a dyne specifies what effect a force of that magnitude has on a unit mass. Newton's 2nd law then tells you what effect a force of that magnitude has on ANY mass.

 

[Ken G]

Note also that the above tells us that if mass is additive, and force is additive, then a=f(F/m) for some function f. That is all the definition needs, so it only needs that forces and masses be additive.

 

[Doc Al]

You seem to want to embed Newton's 2nd law into the definition of force. Not a good idea, in my opinion.

And what does this have to do with measuring gravitational field strength as 1 dyne, anyway?

 

[Ken G]

No, we're not making assumptions about what "the same force" means. We're saying that "the same force" is the force whose magnitude is such that, IF it were acting on 1 gram, then it would accelerate it at 1 cm/s² (regardless of what mass it is actually acting on in the situation being considered).

The problem in your argument persists-- that "if" is exactly the problem. The definition, if applied the way you mean, has no way to discuss that "if" because it doesn't know what it means for the "same force" to apply to a different mass, operationally, if it doesn't know how the force depends on the mass. For example, putting a different mass on the same spring gives the same force, but putting a different mass in the same gravity does not.

However, I gave a different argument that shows why the definition is in fact OK.

The definition of a dyne specifies what effect a force of that magnitude has on a unit mass. Newton's 2nd law then tells you what effect a force of that magnitude has on ANY mass.

Again the problem here is in what you mean by "a force." That part of your argument is indeed circular, you need an operational definition. The only way to get that is to notice that additivity of mass and force. Without that postulate, the definition wouldn't work. F=ma is not required, what you really need is a=f(F/m), because what you really need is the additivity of forces and masses.

 

[Ken G]

And what does this have to do with measuring gravitational field strength as 1 dyne, anyway?

The issue is how 1 dyne was defined in 1923, as in the OP. What I have concluded is that definition works because masses add, and forces add. If that were not true, the definition would not work, but it is, so the definition does. Note that this has nothing to do with saying "what if" the "same force" were applied to 1 g-- that is the thinking that leads to circularity. Since I originally thought that thinking was required, the definition fell apart. But in fact that is not the thinking that is required to see why the definition works, instead you need to divide your mass and force into subsets on the original object, without any "if" the force were acting on some other object. That's the key-- you must keep the same object to know that you have the same force, operationally, and only then can the definition help you to quantify that force.

 

[cepheid]

Look: the definition of a unit force is the force that would be required to accelerate a unit mass at a unit acceleration. Now, if we assume that Newton's 2nd Law is true (an assumption that is incredibly strongly motivated experimentally), then this gives us all we need to measure forces in a lab by measuring masses and accelerations. The preceding statement is true, because if we assume that acceleration just scales inversely with mass, then the definition in the first sentence of this post also tells us what acceleration would be experienced by any other mass when acted upon by a unit force. For that matter, it tells us how many units of force must be acting given any observed mass and acceleration.

If you're not willing to accept Newton's 2nd Law as true (which is the only argument you have to stand on in asserting that this definition is inadequate in providing a means to measure forces), then this thread will probably be locked in accordance with PF rules.

 

[Ken G]

Look: the definition of a unit force is the force that would be required to accelerate a unit mass at a unit acceleration.

Yes, and what I'm saying is, the sole reason that definition works in general is that masses add and forces add. That's it, that's the reason-- there's no "if the force were applied to a different mass" because then you'd have no way to know if it was the same force or not. It's more general than F=ma-- any situation where forces and masses add, that definition is OK, and in any situation where they do not, that definition will suffer the problem I mentioned. But since we live in a world where forces and masses do add, I was indeed mistaken that there is a problem with that definition.

 

[cepheid]

Okay, I don't know if I quite buy into (or understand) the whole "circular logic" argument, but I can see that what I am saying is problematic if you want some means of actually testing Newton's 2nd Law experimentally. So, taking it as a given that forces and masses are additive, how does that imply that a = f(F/m)? Apologies if this is really obvious, but I'm not getting it? Second question: how does that help us?

 

[Ken G]

I don't know if anything you were saying was really circular, because you knew that F=ma, and you knew that forces and masses were additive, so it's not terribly important which of these tidbits is the most important in making the definition fine. The additivity of forces and masses is the most fundamental way to support that definition, because if we have a body that has a net force F on it and a mass m, and we see that it is accelerating with a, then we can consider the body to be n identical parts each with mass m/n without loss of generality, given the additivity of mass. Those fragments must have forces on them that add up to F, and if they are not F/n on each one, then we have different forces on the same bodies making the same acceleration. That won't work if we are talking about n equivalent parts, there's nothing else that could be varying (barring some unusual complication we can idealize away as needed). So we must have F/n on each m/n, all giving the same a. Since n is arbitrary, a must only depend on the ratio of F to m, not on the magnitude of F or m independently of that ratio. We thus could never have a force law like F = m²a, it wouldn't work with additive masses and forces. We must have a = f(F/m), so we must also have a = f(F/F₁*m₁/m), and that justifies the concept of a unit mass and unit force, as you invoked above. So you were correct, I just didn't see why that would necessarily hold until I realized that forces and masses are additive.

 

[Mordred]

lol I'm happy to see so much discussion taken on earlier terms. I've decided to write down the entire passage including what this book states on Newtons 3 laws. I will replicate precisely how this book covers the matter.

The Dyne. A name has been given to that force which, when it has acted on a gram- mass for 1 sec will have given it a velocity of 1 cm. per sec it is caled a dyne.
It will be noticed that there is a distinction in nature between a gram-mass and a gram-force and when we use the term gram we must have clearly in mind whether it is a portion of matter or a force.
A gram-mass is the same wherever it is taken- to the North pole to the moon or to a distant star, it is just so much matter; but a gram-forc is not a constant all over the Earthe's surface, asw the Earth's atraction on a body on its surface is different at different placs. At the Equator it is slightly smaller than at the poles; but a dyne is constant everywhere in the universe and hence it is called an absolute unit of force.


LOL have fun with that half page in the book.

should have written this in order but kick back two pages.

Mass,intertia. The mass of a body has been defined as the quantity of matter in it. Just what is matter no one can say, we al understand it in a general way but we cannot explain it in terms simpler than itself. We must optain our knowledge regarding it by experience.
When we see a young man kicking a football high into the air, we know there is not much matter in it. If it were filled with water or sand, so rapid of a motion could not be given to it so rapid or so easily, nor would it be stopped orcaught so easily upn coming down. A Cannon ball of the same size as the gootball at the same speed, would simply plow through all the players on an athletic field before it would be brought to rest. ( key note here football refers to soccer )

Newton's laws of motion: The first law. In the previous section we have use the word effort a number of times when speaking of putting a body in motion of bringing it to rest. In Physics the word which is used in this manner is force. In 1687 Sir Isaac Newton published his " Principia" in which he gave his three Laws of Motion. " every body continues in its state of rest, or of unifrom motion in a straight line, unless it be compelled by external force to change that state.

The book then gives various examples then discusses a brief discussion of momentum.
finally defining momentum unfortunately he went a little haphazard in how he defined momentum so I'll simply copy the section here. (pleae note he interupted Newtrons 3 laws with an excerpt on momentum)

Momentum. Now from our experience we know that in estimating the greatness of the force required to put a body in motion, we must take into account not only the mass of the body but also the velocity which is given to it. It requires a much greater force to impart a great velocity than to give it a small one; and to stop a rabidly moving body is much harder than to stop a slowly moving one. We feel that there is something which depends on both mass and velocity, and which we can think of as a quantity of motion. This is known in physics as momentum. It is proportional to both mass and the velocity of the body, thus Momentum= mass*velocity=mv where m is its mass and v its velocity of translation.

How to Measure force Newtons second Law. Change in momentum, in a given time, is proportional to the impressed force and takes place in the direction the force acts.
( I'll skip the explanations and examples to the formula it provides. )

Force =m v/t = ma ie force = mass * acceleration.

Newtons third law is simply to every action there is an equal and opposite reaction. The section gets into tons of examples that are quite lengthy and I don't feel like typing 4 more pages to get to the result lol.

I shoud include what was then the two standards of measurement referred to as the English and the C.G.S system. IN the former the foot, the pound and the second IN the latter , which is used almost universally in purely scientific work, the units of length, mass ad time are the cetimetre, the gram and the second.

Several lessons can be taken from this post.

1) Even though formulas and definitions remain the same the interpretations of such may have changed.
2) units of measure has changed to higher precision historically so great care MUST be taken into account when you look at past values to include the accuracy of those units of measure. One key example is the units measuring time. So when you look at past historical data this must be taken into account.
3) names given to various matter,forces, radiation, etc also change as time moves on in human history so when researching for historical data understanding the history of its developent in Physics is also important ( example Rongten to x ray)
4) degrees of accuracy in measurements also change example speed of light although close is not quite the same as it was today.
5) Historically its been shown that there is gaps in our knowledge, where what was once understood had to be relearned a key example is the aztec calender, and the loss of information during Europes dark ages. So thinking we are more advanced simply because our understanding is later is also incorrect.

In order to work on theories that revolve around a long period of time from historical data all the above must be considered otherwise the data set becomes inaccurate so learning the history of a theories development is critical for accuracy. One good example is the original voltameter( no this is correct spelling the A was dropped later on) developed from a process of a silver voltameter electrolytic cell I'll include that process in this post.

Silver voltameter. The cell consissts of a platinum bowl, which is filled with a solution of silver nitrate in which is suspended a silver disc, When the Voltameter is placed int eh circuit, the platinum bowl is made the cathode and the silver disc the anode.
WEhen the current has been passed through the solution for a specific period of time the silver disk is removed , the solution poured off, and the bowl washed, dried and weighed, the increase in weight gives the mass deposited and the current strenght in amperes is easily calculated.
The definithion of amperes at this time is as follows
Ampere: the current that deposits silver at a rate of 0.001118 grams per second.

coper and hydrogen was also used the values for gain per second is 0.000328 for copper 0.000010384 for hydrogen.

 

[Mordred]

I forgot to include the reason I posted the question on the model of the atom in 1923. It should be noted that Einstein published his theory of relativety in 1905 and the final form in 1916 and yet publications of physics after that date show that they were not included in those literaltures nor did they completely understand the atom (absence of the Neutron)