## reducing joules to elementary units

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### reducing joules to elementary units

kinetic energy is 1/2 mass * velocity^2, or 1/2 kilograms * meters^2/seconds^2

wolfram alpha agrees: http://www.wolframalpha.com/input/?i=kg ... +in+joules

except... where did the 1/2 term go? what happened to the coefficient?

Thesh
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### Re: reducing joules to elementary units

That formula only comes in when you have mass and velocity and want to calculate energy. You are converting kg * m^2/s^2, which is the dimension of energy in SI base units, to Joules, where a Joule is defined to be 1 kg * m^2/s^2.
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### Re: reducing joules to elementary units

I'm not sure i understand. What's the difference between kg * m^2/s^2 and 1 kg * m^2/s^2?

jaap
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### Re: reducing joules to elementary units

>-) wrote:kinetic energy is 1/2 mass * velocity^2, or 1/2 kilograms * meters^2/seconds^2

wolfram alpha agrees: http://www.wolframalpha.com/input/?i=kg ... +in+joules

except... where did the 1/2 term go? what happened to the coefficient?

You are mixing up units and measurements expressed in those units.

If something with a mass of 10 kg has a velocity of 10 m/s, its kinetic energy is 1/2 * 10kg * (10m/s)^2 = 500 kg m^2/s^2 = 500 J.
The compound unit kg m^2/s^2 is equal to the joule by definition. The factor 1/2 just remains right there in the numerical value of the measurement, as it is 500 and not 1000.

Maybe it is easier if you think about other formulas that involves coefficients, e.g. the area of a triangle:

"The area of a triangle is 1/2 base * height, or 1/2 meters * meters
wolfram alpha agrees: http://www.wolframalpha.com/input/?i=m+m+in+m%5E2
except... where did the 1/2 term go? what happened to the coefficient?"

Or of a circle:

"The area of a circle is pi * radius^2, or pi meters * meters
wolfram alpha agrees: http://www.wolframalpha.com/input/?i=m+m+in+m%5E2
except... where did the pi term go? what happened to the coefficient?"

The fact that a formula for calculating a particular value has a coefficient, is totally unrelated to what the units are doing. Sure, changing from one system of units to another often involves an extra conversion factor, but going from kilograms * meters^2/seconds^2 to joules does not (or has conversion factor 1 if you prefer).

Qaanol
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### Re: reducing joules to elementary units

Energy is already one of the most elementary units around, but if you really want to simplify it then a joule is about six and a quarter trillion MeV. Alternatively, if you prefer natural units then there are about two billion joules in a Planck energy.
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### Re: reducing joules to elementary units

jaap wrote:The fact that a formula for calculating a particular value has a coefficient, is totally unrelated to what the units are doing. Sure, changing from one system of units to another often involves an extra conversion factor, but going from kilograms * meters^2/seconds^2 to joules does not (or has conversion factor 1 if you prefer).

that makes sense, thanks