Difference between E=mc^2 and K.E.=1/2mv^2?

Question

Difference between E=mc^2 and K.E.=1/2mv^2?

Answer 1

E=mc^2 :- This equation shows equivalence of mass and energy. It means how much energy can converted into mass and vice versa.

K.E.=1/2mv^2 :- This equation is of classical mechanics. It means when certain object is in motion by certain velocity v then How much energy formed by object during its moving path.

Answer 2

E = mc^2 is the rest energy of an object. It has energy even at rest. It's the energy you'd get if you converted the mass to energy.

KE is the energy of motion of a moving object, the energy due to the motion.



In relativity, one expression for total energy of a mass is E = gamma * mc^2 where gamma is the relativistic factor = 1/sqrt(1 - (v/c)^2). This is equal to 1 when v = 0, and it grows toward infinity as v approaches the speed of light.



So in relativity, KE is the difference between the total energy of a moving particle and its rest energy.

KE = (gamma - 1)*mc^2.



In classical physics, KE = (1/2)mv^2.



You can prove that when v is not close to the speed of light, say 10% or less of c, then (1/2)mv^2 is a good approximation to (gamma - 1)*mc^2.

Answer 3

E=mc^2 is eneregy realesed E on destroying completely mass m

but

K.E.=1/2mv^2 is energy of mass m moving with vel v

Answer 4

The difference? They are two completely unrelated equations. Simplistically the difference is classical mechanics vs. relativistic mechanics, but then your equations aren't even correct.



In classical mechanics, the kinetic energy of a particle is given by:



T = ½mv²



In relativistic mechanics, the energy of a particle is given by:



T = √((mc²)² + (pc)²)



where p is the relativistic momentum given by p = γmv, where γ = 1 / √(1 - (v/c)²)



E = mc² is the energy that a particle possesses when it has zero momentum (i.e. it's not moving). This is the "intrinsic" energy carried by the particle regardless of the reference frame--that is it always has AT LEAST this much energy (regardless of the frame of reference).