Fun with Units

Random derivations (some false) based on unit multipliers.

Einstein taught us `E` = `m``c`^{2}.
In that equation `E` stands for energy, and
Calories is a measure of energy;
`m` stands for mass, and kilograms is a measure of mass;
and `c` is just some constant.
To consume 1 kilogram requires about 2.15 × 10^{13}
21.5 trillion, or 21,500,000,000,000
Calories.
That’s a number too big to comprehend,
even if we do hear numbers nearly that large in economic news all the time,
so let’s rework it a bit.

If you use 2000 Calories per day it will take about 29,400 days to lose a single gram.

A small (3mg) grain of dry rice, consumed at a rate or 2000 Calories a day, would last for almost 90 years.

It would take seven billion people each working hard (3000 Calories hard) all day long to jointly burn a kilogram in a single day.

Moral of this story: it is more appropriate to talk about losing weight then to talk about burning it. Also, if you had an antimatter stomach a single meal would be enough to keep you and several generations of your descendants full of energy well into old age.

Say I put ten gallons of gasoline into my car, drive 300 miles, then find all ten gallons are gone. Where did the gasoline go? Out my tailpipe, after a bit of chemical reaction. In fact,

10 gallons |

300 miles |

When my gar is driving at 60mph on the freeway it uses about 35 horsepower (or 26 kilowatts) to do that.

35 horsepower |

60 miles per hour |

Moral of this story: if we didn’t let the gasoline expand into the air before it pushed against the pistons in the engine we could be dribbling a trail of hair-width diamonds from our tailpipes instead of fumes. Also, chemistry is more complicated than unit multipliers suggest.

One pound = 4.448 Newtons = 4.448 kg m / s.
One pound = 0.4536 kg.
Thus 0.4536 kg = 4.448 kg m / s.
Canceling terms by dividing both sides by 0.4536 s / kg, This derivation contains multiple errors; see the comments below.
we find 1 second = 2.0176 kilograms.
This looks like a useful constant; let’s use it to find the age of the earth.
The earth is 5.972198×10^{24} kilograms,
so it is 2.96×10^{24} seconds
or 93.86 quadrillion years, about seven million times older
than current estimates of the age of the universe.

Moral of this story: If the earth is older than the universe but the universe was created first then the earth must just age really really fast. As dog-years are shorter than person years, so earth-years are shorter than universe-years. Or is it universe years that are shorter? Also, there are several kinds of pound.

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