Einstein's energy equation and kinetic energy

  • Thread starter dirtydog
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Why is the kinetic energy given by [tex] E=\frac{1}{2}mv^2 [/tex]
yet Einstein's energy equation is [tex] E=mc^2 [/tex]?
Why is there a different constant (ie [tex] \frac{1}{2}[/tex] and [tex]1[/tex])?
 

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  • #2
ZapperZ
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dirtydog said:
Why is the kinetic energy given by [tex] E=\frac{1}{2}mv^2 [/tex]
yet Einstein's energy equation is [tex] E=mc^2 [/tex]?
Why is there a different constant (ie [tex] \frac{1}{2}[/tex] and [tex]1[/tex])?
Er... because they are NOT the same beast, so why should they be identical? One is the energy of motion, the other is the REST mass energy.

Zz.
 
  • #3
arildno
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You are confusing relativistic energy with classical kinetic energy.
If I remember correctly, the relativistic energy of a particle with rest mass m is given by:
[tex]E_{rel}=\frac{mc^{2}}{\sqrt{1-(\frac{v}{c})^{2}}}\approx{m}c^{2}+\frac{1}{2}mv^{2},v<<c[/tex]
(where v is the measured velocity of the particle)

In the low speed limit, we see that the relativistic energy can be written as the sum of the rest mass energy ([tex]mc^{2}[/tex]) and the classical kinetic energy.
 
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hi dirtydog,
as zapperz says, thery are not the same thing. kinetic energy (KE) is a form of energy that a body has due to its motion, while the other eqn describes the total amt of inherent energy that a body has due to its mass.

therefore for the KE, a body's KE can be increased by increasing its speed. a drop in speed would therefore cause the KE to drop. an obj at rest would then hav 0 KE.

as for E = mc^2, no matter the body is moving or not, the E here remains the same if the body's mass does not change. u can onli vary this E by varying the mass of that body. therefore this eqn gives u the total amt of energy that is 'associated' with a certain mass.

hope that helps to clarify things.
 

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