relationship between e=mc2 and e=1/2mv2?

Question

Anyone can explain using words and equation about the relationship of these 2 equations?

Why this two cannot be related if both of the equation is true?

Answer 1

E = m c^2 is the total energy of a mass m moving with a speed v,

Its total energy ( internal energy) when v= 0, is m0c^2.

The kinetic energy of a mass m moving with speed v is, therefore,
= (m-m0) c^2.

m and v are related by the equation

m = m0/ √ (1 – β^2). where β = v/c.

Using this and expanding 1/ √ (1 – β^2) in a series,

We can show that the kinetic energy

(m-m0) c^2 = m0 c^2 {β ^2/2 + 1*3 β ^4 / 2*4 + 1*3*5 β ^6 / 2*4*6 + ...........


When v is small compared to c, β is small and hence

(m-m0) c^2 = (1 / 2) m0 v^2

Thus in the equation E = Mc^2, if M = (m-m0) then the equation represents the kinetic energy of the mass m and if M = m then it represents the total energy and if M = m0 it represents the rest mass energy of the mass m.

The accurate formula to calculate the kinetic energy is E = Mc^2 where M= (m-m0) and when v is small we can use the formula E = ½ m0 v^2.

Answer 2

These two are not related equations. In the first equation

E = m.c^2 the equivalence of mass and energy is stated.

In the second equation E = 1/2 m.v^2 the relationship between the kinetic energy and velocity of a mass m is stated. If you try to equate those two, you end up with c^2 = 1/2 v^2 which is an absurd and meaningless relationship.

Answer 3

E = mc^2 is the statement of energy and mass equivalence, that all mass has an energy value counterpart. Energy(E) is equivalent to an mass(m) multiplied by the speed of light squared (c^2).

E = 1/2mv2 is the statement of kinetic energy, the value of energy when an object is moving i.e. has a velocity. Energy (E) is 0.5 x mass (m) x velocity squared (v^2).

The energy values of both equations cannot be related as one is based on relativistic mechanics (E = mc^2) and the other Newtonian mechanics, one implies an object at rest has no energy, whilst the other implies a rest mass has an energy value (E = mc^2).

Answer 4

e=mc2 and e=1/2mv2
well,
mc^2=1/2mv^2?
c^2 = 1/2 v^2

Does that help?