E = mc^2? Units dont work?

Question

Okay so here it goes:

E = Energy

Unit of Energy = Joule = Kg *m/s^2

However the equation E = mc^2

m = mass (kg)

c = speed of light (m/s^2)

if you square the units of the speed of light you get m^2/s^4

so the equation E = mc^2 yields the units Kg*m^2/s^4, when it should yield Kg*m/s^2

What the hell?

Answer 1

Look at it this way -

Force = mass*acceleration = ML/T^2
Energy = Force* Distance = ML^2/T^2


Mc^2= M L^2/T^2

So it is right after all.

You have got the dimensions of speed wrong.

Have faith in Dr Einstein !

Answer 2

The problem you're having seems to be that you're attributing the wrong units to the speed of light. Light is measured in m/s since it travels at a fixed velocity, anything in m/s^2 is the rate of acceleration. Light has no acceleration, so it's velocity is only measured in m/s.

Now if you put that into the equation it works out.

E = MC^2

E = M*(C)^2

E = kg * m^2/s^2

E = Kg * (m/s)^2

1 Joule = Kg * m/s^2

So it actually works out the way it should.

I hope this helps you out.

Answer 3

Just a little unit confusion.. energy can also been seen as the measurement necessary to do a certain amount of work: work = force * distance

E = Energy = joule = force*distance = [kg m/s^2] * [m] = kg m^2/s^2

mc^2 = [kg] * [m^2/s^2]

E = mc^2

Answer 4

c= m/s not m/ s^2

Answer 5

When you said that the speed of light was c = m/s^2, you were incorrect. It is actually c = m/s. c, or the speed of light is a velocity and a constant at that unless it travels through some other medium. m/s^2 is actually acceleration such as gravity of 9.8m/S^2. So basically light does not accelerate!

Answer 6

E=joule = newton*m = mass*meter/s^2*m=mass*meter^2/s^2
E= m*c^2 = mass*meter^2/s^2 so the units are correct
your units of speed are wrong

Answer 7

joule is a (newton meter)=kgm^2/s^2 e=mc^2=kgm^2/s^2 it's the same units to me.

Answer 8

You have the wrong units for speed of light -- it should be meters per second.

Answer 9

E=mc2 wherein E stands for potential launched throughout the time of fission and 'm' stands for mass of the particle it somewhat is used as gasoline and "c" is the speed of sunshine so the potential launched is the made from the mass of the gasoline and the sq. of the speed of sunshine

Answer 10

J=Kgm^2/s^2 not Kgm/s^2

E=mc^2 (c=m/s)

Kgm^2/s^2=Kgm^2/s^2 - not WTF.