Illusion of Force and Mass

Let us start with the famous Newton’s second law of motion.

F = ma

   where

   F- net force acting on the body

   m- mass of the body

   a- acceleration of the body

What is the mass of a body? Generally, mass is attributed to the amount of matter in a body. How do we measure the mass of any body? Due to the unique property of gravitational force, on Earth’s surface weight (mg) of any body is proportional to mass. Dividing weight by constant g, the mass of a body can be obtained. While from the second law of Newton, we calculate force given the mass and acceleration, for measuring mass itself it is required to use some kind of force. This makes equation F=ma look like a cyclic illusion.

Even though we cannot measure mass directly without using some force, there is a way to verify the above equation. Let's say first we take a solid iron block and assume its mass to be m. We apply force F on it which results in the acceleration of the block. Now we brake the block into two halves. Assuming the mass of each resulting sub-block is m/2. We apply the same F force on the resulting block of mass m/2. Then we break this block into another two. Applied force F on the block of mass m/4. The acceleration for m/2 and m/4 should be 2a and 4a for the same force. Thus we can verify Newton's second equation by the method of cutting a standard block into pieces. Here it was assumed that mass is proportional to the volume of the body, as the block that is broken into two halves must have twice the matter than every two broken parts.

The important thing to note about equation F=ma is that force as such does not need to be defined by mass. There are four fundamental forces in nature 1. strong nuclear 2. weak nuclear 3. Electromagnetic 4. Gravitational. Force acting can be any one of them or derived from them. The consequence of this force on the body is acceleration which is related by the above equation. Where mass m is the intrinsic property of the body which decides how much acceleration will be generated for the given force. As seen in the previous example of a block, it is related to the amount of matter in a body but as such without force, there is no way to define mass.

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The Truth: part 1

Since the day, people are born, they have kept living each day after day, but what is life about? Of course money, relations, status, etc. are an essential part of life but is something beyond that to life. 

Every human by its very nature has got around 100 years of lifespan. Eventually, they die once their lifespan is reached and no one knows what happens after death. Scientifically there is no proof of the afterlife. Any scientific theory is accepted if its predictions match with observations, but there are no observations available about after-life. There is a possibility that observations about after-life cannot be made by simple physical means. So with probability, it is an equal chance of the afterlife being there or not being there.

If first is the case, then there is no a reason to be worried much, as it suggests the presence of supernatural powers or entities controlling the world and not only the laws of science, but it is still a question that what form of existence would it be in the afterlife? will the person be even conscious enough?

While people had the concepts of heaven and rebirth for a long time, the second possibility cannot be ignored. If the second case is true, that is world works all by-laws of science as it appears to be then sadly everyone is destined to be nothing but soil and ashes. It is not as bad to lose memories and rebirth as say ant than to never exist again.

So everyone has got about 100 years before going completely non-existent, nowhere to be found. This means everyone should live their life in the most meaningful way possible. To think, it seems so injustice that people work hard in life just to not exist forever. So why shouldn't some years of life be spent on researching on increasing human lifespan and knowing more about the universe? For people who might find this idea to be quite selfish, from an individual's perspective, even if failure comes it would be a pleasure to see the next generations of humanity solve this puzzle and die peacefully. But there is no wrong for one in trying to save his existence.

The goal here is not to live forever, but to understand intrinsically the world. And dying before that happens cannot be allowed. Until it is known what happens after death, where does our position stand in the universe, Is the world controlled by higher entities or world has no meaning as such, an intelligent decision about life cannot be made.

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Faraday's law of Electromagnetic Induction

Michael Faraday, who became one of the greatest scientists of the 19th century, began his career as a chemist. He worked as an assistant to famous chemist Humphry Davy. Faraday had no formal education beyond basic reading, writing and math, and he never went to college. 

At the age of 14, he became an apprentice to a local bookbinder and bookseller. During his seven-year apprenticeship, Faraday read many books and developed interest in science. His main discoveries include the principles underlying electromagnetic induction, diamagnetism and electrolysis and the invention of electric motor and dynamo.

Faraday's Law states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of the number of turns in the coil and flux associated with the coil.

Faraday's law can be understood in-depth from Maxwell's equation

        

The above equation means If there is time-varying magnetic flux passing through any arbitrary loop drawn in space, then there is an electric field established such that the line integral of electric field E on a closed loop is equal to the rate of change of flux.

Note here that it is not required for the conductor or coil to be present to establish the electric field and hence emf. But generally, no current flows due to the high resistance of air.

Let's say we place a circular copper coil in a time-varying magnetic field, then free electrons in the copper will start moving in the direction of the electric field created as stated above. The current flowing, in turn, produces its own magnetic field and tries to effectively cancel out variations in original magnetic field. This is in accordance with Lenz's Law.

If     

            ...............................................(1)

            .......................................................(2)

Equating 1 and 2, we get

          

      

Suppose one turn coil replaced with N turn coil, then induced emf is simply N times that of single turn emf. This is because for each turn    and so for N turns in series ,the emf will add up.

        

Here N being multiplied with the rate of change of flux is a very critical concept in Faraday's law. It is essential that to apply Maxwell's equation loop must be closed since phi is flux passing through a closed loop. A turn is almost circle, but it is not a closed-loop, though, as said before, it is not required the conductor to be present; hence we take an arbitrary circle in space that has the same radius as the turn and then electric field E obtained is same as single turn coil. It is as if the circles of the electric field are already present in space, and we are just placing a coil there.

        

        

         

Since N is a constant  

        

        

Psi is called flux linkage, and instead of adding emf of all turns in series, it is dealt with by taking emf induced equal to rate change of flux linkage.

Faraday's law explains the working of electrical elements like Inductor and Transformer and is the basis for converting mechanical motion into electrical energy in all electric generators. 

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What exactly is Archimedes' principle

Archimedes was a Greek mathematician and scientist. He was born in the Greece city-state of Syracuse in 287 BC. A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse. Archimedes' inventions include a proof of the principle of the lever, the widespread use of the concept of center of gravity, and the explanation of the law of buoyancy. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

If you put stone into a water container, volume of water displayed by stone is equal to volume of stone itself. When students are taught about Archimedes principle in class 8th or 9th they sometimes mistaken only above part as Archimedes principle but there is more to it. Lets look at more exact statement of the principle

"The upward buoyant force that is exerted on a body immersed in a fluid, is equal to the weight of the fluid that the body displaces".

Consider an experiment in which a stone of mass M attached to a sting is dropped into water. Let volume of stone be V which is also equal to volume of water displaced, density of stone ρ_s and that of water is ρ_w. Then according to Archimedes principle, 

Upward force on stone also called as buoyant force = weight of water displaced = ρ_wVg, 

while downward force on stone = Gravitational force = Mg = ρ_sVg.

Therefore net downward force on stone F = ρ_sVg - ρ_wVg = (ρ_s - ρ_w)Vg. 

This results into three cases depending on relative value between density of stone i.e. 

If ρ_s > ρ_w stone will sink into the water since F is positive. 

If ρ_s = ρ_w  stone will neither sink nor float since F=0. 

If ρ_s < ρ_w  stone will float into the water since F is negative

Actually, the origin of buoyant force can be understood as when stone wasn't there, water in that portion was prevented from falling down due to gravity by water below it . So to maintain the portion in equilibrium upward force equal to  ρ_wVg was always present and even after water was replaced by stone, there isn't any different treatment to it i.e. same upward force was applied on the stone.

Archimedes principle is useful measuring volume and density of irregular objects. It describes working of large ships and submarines.

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Hello blog world !!

Hey! My name is truedemon1101. Being a great fan of science and technology, after long time I finally started a science blog site. 

Solving logical math problem gives quite a joy, though they just numbers and symbols. It is natural for us to tie processes happening around to fit into certain pattern or logical operation . And we also think wondering about stars in the night sky - What is this universe exactly?  This blog quest have no limits. From atoms to the edge of the universe, we should explore everything. After all science is the most meaningful thing until the knowledge of truth of the universe.. and probably after that as well.

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