Idea Seeds #08 - Choose the words you use with care.
The Importance of words
Lewis Carroll’s ‘Humpty Dumpty’ had this to say about words: “When I use a word it means just what I choose it to mean neither more nor less.” It is critically important that you do the same. When you use ‘words’ make very sure they are clear and unambiguous. I hope that you will never again confuse ‘mass’ and ‘weight’ and are clear about their role in ‘Archimedes Principle’.
Mass and Weight
If you understand; that a fat man with a ‘mass’ of 100 kg becomes ‘weightless’ when he is swimming or in outer-space but is never anything other than a 100 kg fat man; that when he goes on diet it is to lose mass − reduce his kilograms; that on the surface of the earth he will have a ‘weight’ of approximately 980 Newtons (N); on the surface of the moon his ‘weight’ will be down to about one-sixth of this at 165 Newtons (N). Put another way, the ‘weight’ of an object is affected by its environment while the ’mass’ of an object remains unaffected. In Cape Town his weight will be 980 N and in Johannesburg where gravity is slightly lower because of its height above sea-level, his weight will be 979 N. If all this is clear to you then read on, if not I suggest you go through Idea Seeds #07 again.
Below are some further examples for you to ponder.
A ‘Galilean thermometer’ is shown in the picture on the right. It was invented by a group of Italian scientists that included a former student of Galileo. They published their invention it in 1666. My father believes it should have been named after Archimedes as it is based on his principle of buoyancy. Small sealed glass bulbs containing coloured fluids to help identify them are immersed in a liquid in a long sealed glass tube. Each bulb has been made with a slightly different density. Changes in temperature of the liquid in which the glass bulbs are immersed result in changes in the liquid’s density; colder − more dense; warmer − less dense; causing the bulbs with greater or lesser densities to rise or sink. Hanging from the bottom of the glass bulbs are metal tags each with a temperature engraved on it. The temperature is read by averaging the temperatures marked on the lowest floating bulb and highest bulb from the bottom. The bulbs in the example shown have temperatures 5, 10, 15, 20, 25, 30, and 35 degrees Celsius marked on their tags. The temperature on the lowest floating would be 20 and the highest from the bottom 15 so the temperature of the fluid would be about 17,5 degrees Celsius. If one of the bulbs is floating alone in the gap then the temperature of the liquid will be equal to that on the tag. The ‘maximum density of water occurs at 4 degrees Celsius’. This ‘property’ of water has great significance and plays a huge role in what makes our world work in the way it does. The density of ice is less than water, the reason why it floats.
When you next go to the docks look for the Plimsoll line mark on the sides of cargo ships. It will look similar to that shown in the adjacent diagram. Samuel Plimsoll, a member of parliament in England, in 1870 started a crusade against what he called ‘coffin ships’ − overloaded cargo ships that became unstable in bad weather and sank resulting in the drowning of hundreds of English sailors every year. He finally got it made law in 1890 to get a surveyor to paint a mark indicating the safe loading depth on the side of every cargo carrying ship; a circle 300 mm in diameter with a 450 mm load line drawn through it. Where money is involved, things are never that easy as attested by the additional lines to the right of the circle that have since been added. TF = Tropical fresh water, F = Fresh, T = Tropical salt water, S = Summer temperate salt water, W = Winter temperate sea water, and WNA = Winter North Atlantic sea water. Here again we see ‘Archimedes Principle’ in action. As explained previously fresh water has a ‘density’ of 1000 kg/m^3. Sea water depending on the salt concentration has a ‘density’ of about 1025 kg/m^3. As just explained the densities of both are affected by temperature. A ship that is loaded in sea water will sink deeper in fresh water and deeper still in Tropical fresh water. Despite all these regulations there are still regular reports of overloaded ferries capsizing and hundreds drowning each year due to ignorance and greed. More on this and why they capsize in a future article.
Testing a Car Battery's Charge: Hydrometers
Hydrometers are used to check the density of many liquids. In the diagram a hydrometer is being used to check the density of the liquid in a lead acid car battery. Here it is usual to express the measurement as ‘Specific Gravity’ which is the ‘ratio’ of the ‘density’ of a substance to the ‘density’ of some ‘reference substance’, most often pure water. As you have just learnt ‘temperature’ affects density of a fluid so it must be specified for both the sample and the reference. Battery acid in a discharged battery has a lower density than when the battery is fully charged. The bulb sinks deeper in the liquid in an uncharged battery than a charged battery giving a good indication of the state of the battery. But be careful when interpreting the readings; is it a hot summers day and the car has been standing out in the sun or is it a freezing winters day? Think ‘Galilean thermometer’.
For All People for All Time
To measure mass accurately it is best to use a balance as it is unaffected by any change in gravity. The mass of an unknown object is found by bringing it into balance using objects with ‘known masses’. Where do these ‘known masses’ come from? In South Africa the National Metrology Institute is responsible for calibrating masses and providing the certification. They get their calibrated masses from the original ‘prototype kilogram’, a metal cylinder of platinum-iridium kept in France. Why France?
Until the 18th century weights and measures were mainly used for local trade and varied greatly from country to country. The rapid rise in scientific discoveries and engineering endeavours round that time called for a more universal and more ‘precise’ system. A decimal system based on the ‘kilogram’ and the ‘metre’ was proposed and adopted in France during the French Revolution “For all people for all time". Its use quickly spread to other European countries but the English, regularly at war with the French, decided to stay with their own system, which in hindsight was not a very clever move. They are now slowly starting to change to the metric system. The United States have still a long way to go and still have some very different measures like the volume of a ‘US Gallon’ is about 3,8 litres while the English ‘Imperial Gallon’ is about 4,5 litres. All very confusing if you are studying from American or English textbooks
The kilogram was originally based on the mass of water having a volume of 1 litre under certain specified conditions. Today the volume of one litre is the volume contained in a cube with 100 mm sides or one thousandth of a cubic metre. Remember the density of water 1000 kg/m^3. It was later found that due to the conditions specified there was a very small error in this measurement and so the ‘prototype kilogram’ was changed from water to a metal cylinder of platinum-iridium. However, for everyday use you can safely use a measuring jug to measure 1 litre of fresh water and say it has a mass of 1 kg. I urge you to ‘benchmark’ these numbers and commit them to memory.
A ‘Calibrated’ Spring Balance.
The other way of measuring the mass of something is to use a ‘calibrated’ spring balance. Robert Hooke (1635 – 1703) discovered that a spring elongates in direct proportion with the ‘force’ applied to it. Many materials obey this law as long as the extension does not exceed the ‘elastic limit ‘of the material. So if a mass is suspended from a spring it is the force produced by its weight that is causing the spring to elongate. The weight, as explained above, is caused by gravity and so a spring balance will only give the right reading if the gravity at that place is the same as that where it was calibrated.
The drawing on the right is a ‘schematic depiction’ of a balance used to compare masses resting on level ground with nothing on its pans
The lost Kilogram
The next drawing is a ‘schematic depiction’ of a balance with a one cubic metre block of polystyrene in balance with a known calibrated mass made from cast iron.
A person has just been to a shop to purchase the block of polystyrene where he was told that it had a density of 10 kg/m^3 and a price of R10,00 per kg. He paid the shop owner R100,00 and when he got home decided to check the mass of the block and found it to be slightly less than 9 kg. Angry at having been wrongly charged he stormed back to the shop where he was told the story of Archimedes and the King’s gold. I hope you understand why? The polystyrene is displacing one cubic metre of air which has a density of about 1,2 kg/m^3 while the much smaller balancing mass is only displacing a small amount of air, the reason for the lost kg. When you establish the mass of an object with a very different density to that of the balancing mass, an air buoyancy error will be introduced that needs to be accounted for when high accuracy is required. I hope you realise by now why it is so important to understand exactly what Archimedes was on about and don’t forget to start making a set of ‘benchmarks’ for yourself and committing a range of them to memory. The ‘benchmarks’ my father has committed to memory include the approximate densities of
- air, 1 kg/m^3
- water, 1 Ton/m^3
- concrete, 2½ Tons/m^3
- steel, 8 Tons/m^3
- gold, 20 Tons/m^3