In Physics why does eq: E = MC2 use the square function?

Question

In many equations in Physics the square and square root are so important. In E= MC2 why would mass * the speed of light be multiplied by itself for example. Why are so many other variables multiplied by themselves. Any Insights?

Answer 1

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When a physical object or fluid is moving, it contains momentum and kinetic energy.

Momentum is measured as mass x velocity.
Kinetic energy is measured by 0.5mass x velocity-squared.

Einstein asked the question, "Does a body at rest contain energy?" and concluded that it does in relation to the movement of atoms and sub-atom particles within its structure.

He then imagined what would be the sum of energies in the electrons and protons in an object of mass M, and derived the expression

E = MC-squared

because he believed that they would all be moving at the speed of light C.

The 0.5 in the kinetic energy formula disappears because the energies are acting in all directions, not just the direction of travel, since the mass is at rest. The vector sum of the energies gives rise to the Einstein formula.

See the Wiki below for a good description of Einstein's derivation of the formula. See especially the section named "Meanings of the mass–energy equivalence formula".

Also note that Einstein was not the first scientist to postulate an equivalence between mass and energy but only he had the imagination to "get inside the atom" and see what was happening.

Source(s):

http://en.wikipedia.org/wiki/Mass%E2%80%…

Answer 2

c represents the speed of light which is a HUGE value. This equation shows that the TINIEST amount of mass can produce an ENORMOUS amount of energy (like in the atom bomb), hence not just the speed of light but the s.o.l. squared

Answer 3

Why shouldnt they use the square function or the square root function?

There is no single reason why all these formulae use the squaring function since it all lies in the derivation of the formulae, but some of them use squaring because some things vary per square units, rather than per unit. Others are because we are working in 2 dimensions.

Answer 4

As this is an equation, one side must exactly equal the other. This applies not only to values (ie 3 = 2 + 1) but also units (ie 3kg = 2kg + 1kg but 3kg is not equal to 2kg + 1 km)

So looking at E =MC^2

Energy E is measured in Joules which under SI system is defined as (m^2*kg)/s^2

Mass M is measured in kg

and C is measured in m/s so c^2 is m^2/s^2

In terms of units the equation becomes

m^2 * kg / s^2 = kg * m^2 / s^2

As you can see the units balance

Hope this helps

Answer 5

Because Einstein proved that it is the correct way to calculate the amount of energy. It is mathematically calculated and you can't change it.