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20 July 2010

Article: Redefining the kilogram

We use kilograms to measure how much things weigh. But how much is a kilogram, anyway?

There is only one object in the world that weighs exactly one kilogram. It is a cylinder of metal locked away in a cabinet in France. Standards labs from around the world take copies of this kilogram, and use them to make sure that a kilogram in Australia is the same as a kilogram anywhere else.

But what if something happens to the kilogram? If the weight in France was lost, or damaged, we would no longer have a standard to compare to. We would be less certain that our measurements were the same. Mathematicians and scientists are trying to find a new way of defining a kilogram, so that anyone can make one.

Other approaches

There are other scientists trying to redefine the kilogram using different techniques. One group is trying by making a set of scales, not a weight. The scales, called a Watt Balance, use electricity to measure the mass of the object being weighed. If their method is more successful, the kilogram will be redefined as an amount of energy, using Einstein’s most famous equation: E=mc2. This formula states that mass can be turned into energy, so we can define mass as being a certain amount of energy.

Scientists working at the National Measurement Institute in Sydney and CSIRO are part of a world wide effort called the Avogadro Project. They want to define the kilogram as a certain number of atoms of silicon. Because you can make an object composed only of silicon atoms that all weigh exactly the same, this would allow scientists to make their own kilograms without having to compare to the original.

However, there are around 2.15 x 1025 (21 500 000 000 000 000 000 000 000) atoms of silicon in one kilogram. This is far too many to count individually. So instead, the scientists made two spheres that were the roundest (most like a sphere) objects ever made. Because they were so round, they could work out the volume very accurately, and then they could calculate how many atoms were inside. Knowing the number of atoms, and how much one atom weighed, they could work out how much the whole sphere weighed.

The two spheres are now being monitored to see if they stay the same weight over time. Maybe someday soon, the meaning of a kilogram will change.

More information

The Avogadro Project

Sphere of influence: CSIRO redefines the kilo

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Events: Pi day!

Do you love Pi?

Pi is the ratio between a circle’s perimeter (circumference) and its width (diameter). Pi is a decimal number that starts out 3.141592… and never stops or repeats. It can’t be written as a fraction, or even a sum of surds, but people use Pi every day in everything from decorating cakes to deigning electronics.

Every year, on July 22, (22/7) people from all around Australia join together to celebrate Pi. Check out one of these Pi day events:

In Adelaide:

Pi Day @ the Science exchange:

Pi day schools session:

In Canberra:

World Pi Day bake off - starts at 8:00 AM

Pies @ the pub -

Or if you want, you can hold your own celebration, by making -

Try this: Imperial Pie!


The measurements in this recipe are in non-metric units. You will need to change them into metric before you can make the recipe!

ingredients
What you will need:
breaking biscuits with a rolling pin
If you don't have a food processor, you can break the biscuits with a rolling pin
mixing the base
Mix the ingredients for the base together. Make sure the biscuits have been broken down to crumbs
whipped cream
Use a clean bowl when you make the topping!
the finished pie
The finished pie

Download the recipe for printing

Download a conversion chart

Try this activity online

WARNING: This activity involves melted butter, hot water, electric beaters and a food processor. Younger mathematicians should ask an adult to help.

 

For the base:

  • A mixing bowl
  • Wooden spoon
  • A food processor, or a rolling pin and a tea towel
  • A springform pan, 8 inches across
  • some butter to grease the pan
  • 8 ounces of gingernut biscuits
  • 4 ounces of butter
  • 2/3 fluid ounces of brown sugar
  • 1 fluid drachm of ground ginger
  1. Grease the springform pan
  2. Crush the gingernut biscuits with a food processor. If you don’t have one, wrap the biscuits in a teatowel, and crush them with a rolling pin.
  3. Melt the butter in a microwave or on a stove
  4. Mix all the ingredients in a bowl
  5. Press the mixture into the pan to make a crust
  6. Put the pan into the fridge

For the filling:

  • A mixing bowl
  • Electric beaters
  • Wooden spoon or spatula
  • 1/4 pint of cream
  • 14 fluid ounce can of sweetened condensed milk
  • The juice of two lemons, and the rind of one
  • 3/4 pint can of evaporated milk, chilled
  • 1 fluid drachm of vanilla essence
  • 2 fluid drachms of gelatine dissolved in 2 fluid ounces of hot water
  1. Whip cream with the beaters
  2. Carefully mix (fold) in the condensed milk
  3. Add the lemon juice and rind
  4. Beat in the evaporated milk, vanilla and dissolved gelatine
  5. Pour the filling into the base
  6. Put the pie into the fridge and chill well

What’s happening:

When you try this activity, you might find it takes almost as long to make the conversions as it does to make the pie, and we’ve even given you a conversion sheet! Measurement is a lot easier when everyone agrees on what units to use.

In Australia, and in almost all the rest of the world, we use the metric system. But fifty years ago, Australia used a system of measures called the Imperial system. The Imperial system uses ounces and pounds to measure weights, and feet and miles to measure distances.

The Imperial system evolved over hundreds of years, with different groups of people comparing weights with each other. Because some groups tended to trade between themselves, sometimes the meanings of weights changed between groups. In 1850 in England, there were three different ounces: troy ounces for measuring precious metals, apothecary ounces for measuring chemicals, and avoirdupois ounces for measuring everything else.

Currently, there are three countries in the world that don’t use the metric system. They are Liberia, Burma, and the United States of America. The United States uses a system called American Customary, which uses avoirdupois ounces and pounds to measure weights. However, some of the larger measurements are different to Imperial. For example, a US ton is 2000 pounds and an Imperial ton is 2240 pounds. A metric tonne is 1000 kg, which is about 2205 pounds.

The main reason for using the metric system is that converting between units is easy. But the metric system also allows everyone to compare measurements without getting confused. A metre in France is the same as a metre in Australia, and the same with kilograms, and litres. But there are even some metric units that change from country to country. For example, in many countries, including New Zealand, a tablespoon is 15 mL, but in Australia it is 20 mL. Even some terms for numbers can have different meanings. A dozen usually means 12, but a baker’s dozen is 13!

More information:

English weights and measures

Conversion table for most measurements

Avoirdupois on Wikipedia (more advanced)

Brainteaser question

Imagine a rope tied in a loop running all the way around the world, along the equator. If you wanted to put the rope on poles so it was one metre above the Earth all the way around, how much longer would the rope have to be?

Websites

Read maths!

Fifty years ago, Russell Kirsch made one of the first digital pictures, out of little squares. Now he’s trying to change how digital pictures are made.

Do maths!

See if you can work out what’s happening with this puzzling device

Brainteaser answer

It would only need to be about 6 metres longer!
The rope is a circle, so we can use the circle formula to work out its length.
The Earth’s radius is about 6400 000m
Initially, the rope’s length is 2 x Pi x 6 400 000
After you lift the rope up one metre all way around the Earth, the length becomes 2 x Pi x 6 400 001
The difference in length is 2 x Pi, which is about 6m

Did you know?

In 1610, a mathematician named Ludolph van Ceulen worked out the first 35 digits of Pi, by hand. This is enough digits to calculate the circumference of our galaxy to an accuracy of one atom!

Scientriffic

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