If E=mc^2, how does it relate to Ek+1/2 mv^2?
How does it work when v = c?
thanks
I don't know what your question is exactly
E=mc^2 can mean two things:
a) the energy equivalent of a rest mass, or
b) the energy equivalent of a mass exchange for energy. Energy is mass, and mass is energy. That is what we call mass equivalency.
On the Ek=1/2 mv^2, that does not work of for v approaching the speed of light, relativity takes over, and mass itself changes as speed of light is approached.
Thank you
The equation E=mc^2 is the famous mass-energy equivalence equation proposed by Albert Einstein. It states that the energy (E) of an object is equal to its mass (m) times the speed of light (c) squared. This equation shows that mass and energy are interchangeable.
Now, let's examine how this equation relates to Ek + 1/2 mv^2, where Ek represents the kinetic energy of an object with mass (m) and velocity (v).
Kinetic energy (Ek) is given by the equation Ek = 1/2 mv^2, where m is the mass of the object and v is its velocity. This equation describes the energy possessed by an object due to its motion.
When we consider the case where v = c (the speed of light), let's substitute v = c into the equation Ek + 1/2 mv^2.
Ek + 1/2 mc^2 = 1/2 mc^2 + 1/2 mc^2
Notice that the term 1/2 mc^2 in the equation is equivalent to the rest energy (E) in the equation E=mc^2. So, we can rewrite the equation as:
Ek + 1/2 mv^2 = E + E
This reveals that the total energy (Ek + 1/2 mv^2) of an object with velocity approaching the speed of light is equal to twice its rest energy (E=mc^2). This result shows that an object's total energy includes its kinetic energy and its rest energy.
In conclusion, when v = c, the equation Ek + 1/2 mv^2 simplifies to 2E, which means that the total energy is equivalent to twice the rest energy of the object.