Put Christmas Lego to good use: Measure Planck’s Constant with it
Lego is a popular Christmas gift, and young and old alike can derive hours of pleasure building with those little plastic blocks. But, like a lot of playthings, the novelty wears off soon enough and you find yourself drifting back to watch Christmas TV re-runs. But what if you could use that Lego to construct real scientific equipment; would that maintain your enthusiasm? Well hang on to your plastic blocks, because engineers have designed an experiment that uses Lego and a few other bits and pieces that allows any keen tinkerer to build a device that not only determines Planck's Constant but may also help quantify the international standard unit of mass.
To help explain all of this, let's start with a bit of background.
The last remaining unit of the International System of Units (SI) which is still based on a physical artifact is the kilogram. Since 1899, a representative kilogram has been stored in a vault at the Bureau International des Poids et Mesures (BIPM) in France along with six official copies which are used as calibration weights against which countries around the world may test their own official kilogram reference.
Unfortunately, the long term stability of the mass of these copies has actually increased over more than a century so that – in respect to the original official kilogram – they have all accumulated mass to the tune of around 50 micrograms.
As such, a better method is needed to make sure that the long-term stability of the mass unit is maintained. In this regard, in 1999 the General Conference for Weights and Measures (CGPM) recommended that national laboratories develop and refine experiments that link the unit of mass to fundamental or atomic constants so that the degradation of a physical reference may be avoided.
Further, as other important base units that require exceptionally fine definitions (specifically: the ampere, the mole, and the candela) also depend on the mass definition of the kilogram to determine their base accuracy, then more rigorous definitions of the kilogram would fundamentally improve the accuracy and usefulness of these measures.
So, one of the ways that has been mooted to solve this dilemma is to measure mass based on Planck’s constant or using a value of Planck’s constant based on a known mass. Planck’s constant describes the relationship – in an equation known as the Planck-Einstein relation – between the energy and frequency of an electromagnetic wave. That equation is E = hv, where E is energy, h is Planck’s constant, and v is frequency.
This is where our team of Lego brick-wielding researchers comes in. Working at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland, engineers wanted to do some rapid prototyping of a device to conduct their Planck's constant experiments. Rather than use conventional, time-consuming, and costly methods of construction, however, the researchers opted for a more unconventional method: Lego.
As this worked quite well, the team built three of these instruments and, just for good measure, also decided it would be a good idea to share the design with others wanting to explore this field. The device the engineers created for their experiment in Lego is known as a watt balance. So named because it uses both electrical and mechanical energies in its measurements, both of which are expressed in watts.
In principle, the device itself is relatively simple mechanism. Constructed so that it balances the force exerted on a mass due to gravity by using the force generated by an electrically-energized coil in a magnetic field, the device allows the calculation of the mass by comparing the mechanical power exerted to the electrical power required to balance it out.
In detail, the experiment requires measurements of both the voltage and current running through the coil as well as the velocity of the mass moving through that coil. As such, this means that an accurate local value for the acceleration due to gravity is required. Luckily, this can be easily obtained by entering a location on the gravity page on the National Oceanic and Atmospheric Administration (NOAA) website.
Ordinarily, in Physics, the use of Planck's constant is linked with quantum theory, and one does not ordinarily equate it with determination of SI units due to the uncertainty in the value dependent upon the location of its measurement. However, by being able to determine a known value of Planck's constant using local gravity values from the NOAA website and the watt balance described, mass and Planck's constant can be conversely determined with high accuracy.
"By comparing electrical power in conventional units to mechanical power in SI units, h can be determined," said the researchers.
Building a working watt balance could be achieved by the average tinkerer with the right parts, some technical plans, and access to the appropriate tools. But an even easier way would be to build one using Lego, and the researchers at NIST describe how to do just that, and even provide a complete list of parts, most of which can be ordered directly from Lego’s Pick-a-Brick website. The team also provides a list of websites that the constructor may use to find the more specialized, non-Lego, components.
According to the team, the overall cost of components required to build the watt balance as described is US$634. But this figure assumes that you'll want to buy a $300 data acquisition instrument and an accompanying $90 analog output device. The researchers say that those on a budget could forgo the expensive devices they used, and opt for a single piece of equipment that does both jobs for around $189, which, with luck, should put the cost within the reach of schools and even individual constructors.
"We hope to encourage many enthusiasts to build a Lego watt balance and have fun toying with the science of measurement, metrology," said the team.
The team has put together a paper on their instrument along with detailed plans on how to build it, and have made it available on the Cornell University Library website in PDF format.
So, this holiday season, when everyone else is building the same old cars and planes with their little plastic blocks, with a bit more work you could build yourself the ultimate Lego machine for yourself or give the gift of science to the significant other physicist in your life.