Strange sum (riddle tread)
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11-09-2011, 07:43 AM
RE: Strange sum (riddle tread)
Quote:Now, weren't those Greeks very very clever?

Some of them - the ones that are remembered. But the rest believed in Zeus with the thunderbolts and Aphrodite with the big.... okay, maybe they weren't all that stupid.

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11-09-2011, 07:55 AM
RE: Strange sum (riddle tread)
The Greeks may have believed in all kinds of gods that did this, that, and the other thing, but at least their gods were freakin cool!

And like Pete said, they had gods like Aphrodite, with the big......well......ya.

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11-09-2011, 08:08 AM
 
RE: Strange sum (riddle tread)
(11-09-2011 07:43 AM)Peterkin Wrote:  
Quote:Now, weren't those Greeks very very clever?

Some of them - the ones that are remembered. But the rest believed in Zeus with the thunderbolts....

I said "those Greeks" -- like "those Greeks who were very clever, were very clever!"

Tongue
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13-09-2011, 05:52 AM
RE: Strange sum (riddle tread)
Place the mass in a particle accelerator, accelerate the mass until all has been converted to energy. Calculated mass associated with energy produced suing e=mc^2.

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13-09-2011, 07:31 AM
 
RE: Strange sum (riddle tread)
robotworld, you come up with the most ingenious ideas!

The quiz I posted has 2 parts:

1. The definition of mass (in Newton's Law)
2. The measurement of mass (based on this definition)

Richard Feynman best explains the problem in his “Lectures on Physics”:

“If we have discovered a fundamental law, which asserts that the force is equal to the mass times the acceleration, and then define the force to be the mass times acceleration, we have found out nothing.…Now such things certainly cannot be the content of physics, because they are definitions going in a circle….. One might sit in an armchair whole day long and define words at will, but to find out what happens when two balls push against each other or when a weight is hung on a spring, is another matter altogether, because the way the bodies behave is something completely outside any choice of definitions.”

Finally, Feynman tells us the solution to the dilemma:

“The real content of Newton’s laws is this: that the force is supposed to have some independent properties in addition to the law F=ma; but the specific independent properties that the force has were not completely described by Newton or by anybody else, and therefore the physical law F=ma is an incomplete law.”

As far as “what use is Newton’s Law” is concerned, Feynman states that:

“In order to use Newton’s laws, we have to have some formula for the force; these laws say pay attention to the forces. If an object is accelerating, some agency is at work; find it. Our program for the future of dynamics must be to find the laws for the force. Newton himself went on to give some examples. In the case of gravity he gave a specific formula for the force.”

When I read all this, my philosophical problems were solved: Now I knew what Newton meant and how to use his law to solve practical problems. Once you substitute the formula for the force (be it gravity, tension in springs, etc) then I could easily determine the motion of any object subjected to the force if I knew the mass of the object.

Next time I will talk about the second part: measurement. It is extremely important because we get to think about inertial mass and gravitational mass and the general theory of relativity and the destiny of the universe.

Bemore, aren't you happy you started this thread? Tongue
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13-09-2011, 08:59 AM
RE: Strange sum (riddle tread)
Technically Newton's Second Law states that the the force acting on an object is proportional to the rate of change of momentum of the object with respect to time and the force is acting in the same direction as the change in momentum. But we assume mass is constant in this case Smile

Hmm, so you are saying that to measure different types of forces, we have to use different formulae? For instance, spring force = spring constant x length of extension/compression, electrical force using Coulomb's Law, in which instead of mass, we just require the charge of the two interacting objects, or magnetic force = magnetic flux x current through wire x length of wire.

Maybe different forces have different natures, such as contact vs non-contact forces, and each can be measured using a wide variety of formulae?

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13-09-2011, 09:23 AM
 
RE: Strange sum (riddle tread)
(13-09-2011 08:59 AM)robotworld Wrote:  Technically Newton's Second Law states that the the force acting on an object is proportional to the rate of change of momentum of the object with respect to time and the force is acting in the same direction as the change in momentum. But we assume mass is constant in this case Smile

You are right, robotworld:

In Newton’s words in the Principia:

Definition II
“The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly”. (what we now call momentum)

Law II
“The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed”

By “The alteration of motion” Newton meant the deviation from the straight-line and uniform-speed inertial motion (which is the natural state of objects, according to Law I), resulting in a change in the "quantity of motion"

Quote:Hmm, so you are saying that to measure different types of forces, we have to use different formulae? For instance, spring force = spring constant x length of extension/compression, electrical force using Coulomb's Law, in which instead of mass, we just require the charge of the two interacting objects, or magnetic force = magnetic flux x current through wire x length of wire.

Actually, measuring forces is very simple, once we solved the problem of measuring mass, because then we can use the F=m*a law to measure the force.

What we need the force formula for is to be able to set up our equations. For example, knowing the gravitational force formula (as given by Newton) as F=G*m1*m2/r^2 – we can replace F in the F=m*a equation and have a new one that contains only mass (that we can presumably measure independently from the force) and acceleration – giving us a nice differential equation describing the trajectory of the objects.

To measure the mass, independently from the forces, we need to clarify some basic concepts first.

EDA:

Before I forget to conclude my answer on Newton's Second Law:

Usually mass is measured by weighing things, but it is completely incorrect conceptually, because weighing an object measures the force of gravitational attraction between the Earth and the body we weigh (gravitational mass). This is conceptually different from the ‘inertial mass’ which is defined as an object’s resistance to acceleration. To make it more clear: just think of how an object’s weight will drastically change (to about one-sixth of its value on Earth) if measured on the Moon, while its inertial mass (resistance to acceleration) will remain the same.

We are not completely defeated though because we have ways to measure inertial mass without weighing the object. For example, by measuring the acceleration of objects under identical forces (e.g. accelerating them by the same spring stretched to the same amount). If the force is identical on two objects (with masses mi1 and mi2), than F=mi1*a1= mi2*a2 which means that mi1/ mi2= a2/ a1.

This means that we can measure the ratio of inertial masses between any two objects (by measuring their accelerations under identical forces) and, if we arbitrarily select one particular object as a unit for inertial mass, then we can measure the inertial mass of any object as described above.

The International Prototype Kilogram, the IPK, which is roughly the size of a golf ball, is made of a platinum–iridium alloy and is stored in a vault at the International Bureau of Weights and Measures in Sèvres, France

Now that we have a unit of inertial mass (kg) we can define the unit of force as well: 1 unit of force (called a newton) is the force that causes one unit of inertial mass (1 kg) to accelerate at 1 meter per second per second. So now we have a way to measure both inertial masses and forces in their respective units.

Of course, measuring masses by accelerating them with springs is cumbersome and, luckily, we do not have to do that. Instead, as we will soon see, we can take advantage of what seems at first as a lucky coincidence: the inertial and gravitational masses of objects happen to be the same (if we choose the same unit for both inertial and gravitational mass), so we can measure both masses by weighing the objects, after all.

The experiment proving this was first performed by the Hungarian Lorand Eotvos in 1909 and other physicists at later times. The result of the experiments show that the ‘gravitational mass’ and ‘inertial mass’ of a material object is the same value within an error limit of 1 part in 1,000,000,000.

We can say that an object’s inertial mass and gravitational mass are the same, so from now on we will just simply talk about an object’s mass.

If we look back at our definition of an object’s inertial and gravitational mass, we will see, that the identity of the two means that: the attribute of a body that makes it resist acceleration is the same attribute as the one that responds to gravitational attraction.

This is a deeply philosophical, and by no means obvious conclusion, and will be used as one of the pillars on which Einstein built his General Theory of Relativity.

....and now I put myself in a straight jacket, so I can't type any more and bore the rest of you to tears!

Tongue
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13-09-2011, 03:39 PM
RE: Strange sum (riddle tread)
Change of pace, for non-science types.

A young knight named Aladair loved a princess and she loved him. But the king wanted a more advantageous marriage for his daughter. He called in his first minister to discuss ways and means of discouraging Aladair's suit, and they came up with a plan. The king would gather the whole court to settle the issue once and for all. Aladair would be presented with two identical sealed envelopes and told that one contained the word "Marriage" and the other "Banishment"; that he must choose his fate. Just as the prime minister was saying, "Only, i shall write Banishment on both papers." Aladair happened to pass under the window and overhear.
"Aha," he said to himself, I can out-trick these nasty old men."

How did he do it?

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13-09-2011, 03:47 PM
RE: Strange sum (riddle tread)
(13-09-2011 07:31 AM)Zatamon Wrote:  Bemore, aren't you happy you started this thread? Tongue

Im glad its adapted into this Zatamon........although TBH most of the puzzles on here im like "WTF".......which i like Big Grin

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13-09-2011, 03:55 PM
 
RE: Strange sum (riddle tread)
(13-09-2011 03:39 PM)Peterkin Wrote:  Aladair would be presented with two identical sealed envelopes and told that one contained the word "Marriage" and the other "Banishment"; that he must choose his fate. Just as the prime minister was saying, "Only, i shall write Banishment on both papers." Aladair happened to pass under the window and overhear.
"Aha," he said to himself, I can out-trick these nasty old men."

How did he do it?

That's easy, Peterkin.

He is standing there with the king and the prime minister and the princess and he is given 2 envelops with the instruction: "choose one"!

... upon which he grabs the hand of the princess and shouts: "I choose her!" -- and runs like hell!

Big Grin
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