Saturday, 20 July 2013

From mass to energy

In physics, mass–energy equivalence is the concept that the mass of a body or system is a measure of its energy content. In particular, any physical system has a property called energy and a corresponding property called mass; the two properties are always present in the same (i.e. constant) proportion to one another. This means (for example) that the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable unit conversion factor which transforms units of mass to proportionate units of energy.


As we approach speed of light we start loosing our mass as the lesser the mass the more the speed and more the speed the less the mass. Since we would loose mass, we would be turning ourselves to energy. When we reach the speed of light we would be completely mass-less and could completely turned ourselves to energy. Einstein also showed that an object gains mass as its energy increases and losses mass as its energy decreases. This made him to conclude with the most famous equation of the century : E = mc2

2006 Walk of ideas, Berlin, Germany.
In 1905, Einstein gave his equation E = mc2, which says that E is the amount of energy released when mass m is destroyed at squared speed of light, c. This relation between mass and energy has seen enormous application in Nuclear physics.
E = mc

One of the most important implication of Mass-Energy relation is the development of atomic bombs and nuclear fuels. An Atomic Bomb contains elements of very high mass. For example Uranium, Thorium, Neptunium and Plutonium. They have very high mass, moreover they are radioactive (Refer Types of Radiation) so they can be destroyed easily. Also the energy released in enormous, all the energy released in however not consumed. In most Nuclear Power plant, only 10 to 20 % is hardly used. Rest all are excreted in form of Radioactive wastes. It is so bad to see that the same technology is being used to develop Nuclear Bombs some of which are so strong that they can destroy a Mega City completely.

Nuclear devastation
                                                  

Derivation of E=mc2

This derivation has been provided by adamauton.com. Please refer www.adamauton.com/warp/emc2.html for more details about this proof.


Let us try and think about this experiment mathematically. For the momentum of our photon, we will use Maxwell’s expression for the momentum of an electromagnetic wave having a given energy. Remember that p = mv is not applicable for photons. If the energy of the photon is E and the speed of light is c, then the momentum of the photon is given by:
                               

 (1.1)
The box, of mass M, will recoil slowly in the opposite direction to the photon with speed v. The momentum of the box is:
                               

 (1.2)
The photon will take a short time, Δt, to reach the other side of the box. In this time, the box will have moved a small distance, Δx. The speed of the box is therefore given by
                               

 (1.3)
By the conservation of momentum, we have
                               

 (1.4)
If the box is of length L, then the time it takes for the photon to reach the other side of the box is given by:
                               

 (1.5)
Substituting into the conservation of momentum equation (1.4) and rearranging:
                               

 (1.6)
Now suppose for the time being that the photon has some mass, which we denote by m. In this case the centre of mass of the whole system can be calculated. If the box has position x1 and the photon has position x2, then the centre of mass for the whole system is:
                               

 (1.7)
We require that the centre of mass of the whole system does not change. Therefore, the centre of mass at the start of the experiment must be the same as the end of the experiment. Mathematically:
                               

 (1.8)

The photon starts at the left of the box, i.e. x2 = 0. So, by rearranging and simplifying the above equation, we get:

                               

 (1.9)
Substituting (1.4) into (1.9) gives:
                               

 (1.10)
Rearranging gives the final equation:
                               




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