Math: How to Convert Energy in Mass Units to Joules?

[imsmooth]

I was reading Spacetime Physics, second edition by Edwin Taylor. In the chapter Energy: "time part" of momenergy, page 203, Energy (E) has been equated to mass, m. The section STILL MORE UNITS then reads "In order to convert energy in units of mass to energy in conventional units, such as joules, multiply the expressions above by the square of the light speed, c^2."

Thus, Econv = Ec^2 = mc^2

How does multiplying energy by c^2 come out as joules? If the square of the velocity is needed for the units then why the speed of light?

 

[ghwellsjr]

See this thread:

https://www.physicsforums.com/showthread.php?t=449463

 

[imsmooth]

I understand that velocity^2 is needed to get the correct units. I want to know why the value for "v" was chosen to be the speed of light, c? In the chapter I am reading, the formula E=mc^2 was not derived - it is being derived. So, for one to answer, "well, c is chosen because of the equation E=mc^2". So, how does one jump to say we have to multiply mass by light squared, instead of any random velocity?

 

[LBrandt]

I was reading Spacetime Physics, second edition by Edwin Taylor. In the chapter Energy: "time part" of momenergy, page 203, Energy (E) has been equated to mass, m. The section STILL MORE UNITS then reads "In order to convert energy in units of mass to energy in conventional units, such as joules, multiply the expressions above by the square of the light speed, c^2."

Thus, Econv = Ec^2 = mc^2

How does multiplying energy by c^2 come out as joules? If the square of the velocity is needed for the units then why the speed of light?

You don't multiply energy by c^2. You get energy, by multiplying mass by c^2. And as far coming out as joules, ergs or whatever units of energy you prefer, you must use the appropriate units of measure on both sides of the equation.