# Earths force of gravity measured in Dynes

1. Sep 4, 2011

### 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 ?

Last edited: Sep 4, 2011
2. Sep 4, 2011

### 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 $981M dynes$.

3. Sep 4, 2011

### 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.

Last edited: Sep 4, 2011
4. Sep 4, 2011

### Ken G

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

5. Sep 4, 2011

### Mordred

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.

6. Sep 5, 2011

### 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.

7. Sep 5, 2011

### TurtleMeister

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.

8. Sep 5, 2011

### Ken G

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.

Last edited: Sep 5, 2011
9. Sep 5, 2011

### Staff: Mentor

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.

10. Sep 5, 2011

### 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.

11. Sep 5, 2011

### Staff: Mentor

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

12. Sep 5, 2011

### 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.

13. Sep 5, 2011

### Staff: Mentor

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.

14. Sep 5, 2011

### Ken G

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.

15. Sep 5, 2011

### cepheid

Staff Emeritus
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.

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.

16. Sep 5, 2011

### 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.

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17. Sep 5, 2011

### Staff: Mentor

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

18. Sep 5, 2011

### cepheid

Staff Emeritus
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.

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

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.

19. Sep 5, 2011

### 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.

20. Sep 5, 2011

### Staff: Mentor

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?