I might just be stupid because math is not my strong suit, but it seems like the fact that metric units are able to convert between mass and energy so cleanly is astounding. Especially since the metric system was invented so long before relativity, meaning these units were obviously not designed with this in mind.
What’s am I missing here? Is it possible to write an equivalent equation for imperial units?
In: Mathematics
I’ll explain the neatness the same way i explained it to my students. Although they tend to have much neater equations with units.
When we put our numbers into an equation, it’s not just the digits we include, we also bring the units along! So it’s energy = mass * velocity^2. We plug in the same types of units whether it’s metric or Imperial.
In the metric system, we would have an energy unit of a joule, which is equal to a kilogram-meter^2 per second^2, or a kilogram-(meter per second)^2. The kg is a unit of mass, and the m/s is a unit of velocity. The joule was made to fit neatly with the other units, so the calculations are super simple!
In the imperial system, it’s harder. The energy unit is ft-lbf (foot-pound force if you want to be specific), which works just fine if we are using feet and pounds (force)… but we are using mass in our equation. So we would have to do something like slug * (ft/s)^2. We can see that this equation is just as simple as the metric! And it actually is as simple as that, the slug-(ft/s)^2 is equal to the ft-lbf. The key problem: when are you given the mass of something in slugs? So you’ll need to remember to convert your pounds into slugs.
A bigger problem comes up when you are given bigger or smaller units. If it becomes kilometers per second, we just have to change the decimal place. But if it’s miles per second, we now have to account for a conversion of (5280 ft per 1 mile)^2.
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