In the formula of KE - 1/2 mv^2, is mass expressed in g or kg?

Question

In the formula of KE - 1/2 mv^2, is mass expressed in g or kg?

Answer 1

Probably kg, but let's make sure.

The units on the left side of the equation must match those on right. If you have (or want) the energy in Joules:

1 Joule = 1 kg*m²/s² and so, since velocity is measured in m/s, mass is in kg. This is an example of the mks unit systems where all units are derived from meters, kilograms, and seconds.

Alternatively, if you are looking for energy in units of ergs:

1 erg = 1g*cm²/s² and so, (since velocity is measured in cm/s), mass is in g. This is an example of the cgs unit systems where all units are derived from centimeters, grams, and seconds.

Answer 2

If you use the SI units for mass (kg) and for velocity (m/s) then the results will be the SI units for energy (joules or J).

However, the equation is not applicable only to SI units. As an engineer, I was trained using English units and the equation works fine. You just need to be aware of the appropriate conversion factors.