Basic Usage

As an examples, let us consider a rock of mass $m = 2\,\mathrm{kg}$. We know that on earth, a force of $F = m g$ is required to lift the rock, where approximately $g = 10\,\mathrm{m/s^2}$. We would like to use Julia with the Alicorn module to calculate the energy $E = Fh$ we have to invest to raise the rock above our heads to a height of $h = 230\,\mathrm{cm}$. Alicorn comes with a wide range of predefined units and unit prefixes compatible with the International System of Units. To access them, we load Alicorn and start by initializing a default UnitCatalogue:

julia> using Alicorn

julia> ucat = UnitCatalogue()
UnitCatalogue providing
 21 unit prefixes
 43 base units

We can then define the quantities given in the problem

julia> mass = 2 * (ucat.kilo * ucat.gram)
2 kg

julia> acceleration = 10 * ucat.meter * ucat.second^-2
10 m s^-2

and have Julia calculate the required force:

julia> force = mass * acceleration
20 kg m s^-2

Note that Alicorn made no assumption about the unit we would like to express the energy in. Instead, it simply combined the units by multiplying them. We decide we would like to express the force in units of kilonewton

julia> inUnitsOf(force, ucat.kilo * ucat.newton)
0.02 kN

and the resulting energy in units of joule:

julia> energy = force * height
4600 kg m s^-2 cm

julia> inUnitsOf(energy, ucat.joule)
46.0 J

Now, while we are holding the rock up there, we wonder what would happen if we were to accidentally drop it on our nose. Assuming that our nose is $h_n = 1.7\,\mathrm{m}$ above the ground, we can calculate the energy transferred after a drop of height $h - h_n$ as follows:

julia> noseHeight = 1.7 * ucat.meter
1.7 m

julia> dropDistance = height - noseHeight
60.0 cm

julia> energyToNose = force * dropDistance
1200.0 kg m s^-2 cm

julia> inUnitsOf(energyToNose, ucat.joule)
12.0 J

Note that Alicorn used the unit of height to express the quantity dropDistance resulting from taking the difference.

Finally, let us check how the transferred energy compares to the rest energy of an electron-positron pair. We recall that the rest energy of an electron-positron pair is around $E_p = 1022\,\mathrm{MeV}$ and express our results in the according unit:

julia> inUnitsOf(energyToNose, ucat.mega * ucat.electronvolt)
7.489810889352916e13 MeV