Exercises: The International System

When the D&T teacher says that the workshop table measures "6 handspans", she is comparing its length to that of her hand, as shown in the figure.

Explain in your own words what it means to measure a quantity and give a new example, different from the table.

From this list of words, state which are quantities and which are units: length, second, mass, metre, temperature, ampere, time, kilogram.

Write the name and symbol of the International System unit corresponding to each fundamental quantity: length, mass, time, temperature, electric current, and amount of substance.

Lucía's little brother wrote in his notebook: "My mass is $42\ \text{Kg}$ and my height is $1,45\ \text{M}$". There are two errors in the unit symbols. Find them and write the sentence correctly.

Complete the sentence with the missing words: "A $\dots$ is any property of a body that can be measured, such as length or mass. The $\dots$ is the fixed quantity taken as a reference to compare when measuring."

Which quantity is measured with each of these instruments? Observe them in the figure:

1. a) A ruler.
2. b) A balance.
3. c) A stopwatch.
4. d) A thermometer.

On the fridge at home there is a dial marked "$4\ \celsius$". a) What quantity does this dial regulate? b) What is the International System unit for this quantity? c) In what unit do we usually give it at home and on the news?

On the label of Hugo's mobile charger it says "output: $2\ \text{A}$". a) What quantity is measured in amperes? b) Chemists use another fundamental quantity to count particles: what is it called and what is its International System unit?

In the final of the $100\ \text{m}$ sprint, the scoreboard showed only this: "WINNER: $9,98$", as seen in the figure.

1. a) What is missing from this value for it to be a complete measurement? b) Complete the scoreboard with the appropriate unit and its symbol.

Speed is calculated by dividing the distance travelled by the time taken. a) Is it a fundamental or a derived quantity? Explain the difference. b) Deduce its unit in the International System from those of the metre and the second, and write its symbol correctly.

In grandmother's croquette recipe it says "a splash of oil" and "a pinch of salt". a) Are "splash" and "pinch" good units of measurement? b) Why wouldn't two different cooks make the same croquettes following that recipe? c) What quantity is measured in each case and in what unit should it be given for the recipe to be accurate?

In a warehouse, three measurements without units are recorded: $3$; $40$; $45$. They correspond to the length of a shelving unit, the mass of a bag of animal feed, and the time taken for the goods lift to go up, but they are out of order. Assign each number to its quantity and add the most suitable International System unit.

Classify these quantities as fundamental or derived: length, surface area, mass, volume, time, speed. Explain what criterion you used to decide.

A team of scientists from Japan sends a report to another in Spain stating: "the cable measures $12$". a) What problem is there with this value? b) How is it solved if everyone uses the International System? c) Why do you think the SI is used worldwide instead of each country having its own?

In an American online shop, a rucksack weighs "$3\ \text{lb}$" (pounds) and measures "$18\ \text{in}$" (inches). a) Are these International System units? b) What do you need to know to get an idea of its weight and size? c) What advantage would there be if the shop also provided kilograms and centimetres?

In the word "kilogram", the prefix "kilo-" appears, which means thousand. a) What do the prefixes in $\text{km}$, $\text{mm}$, and $\text{ms}$ mean? b) Write the full name of each unit and the quantity it measures. c) How many millimetres are in a metre?

Centuries ago, length was measured in "feet" and "cubits", which depended on each person's body. a) What problems could this cause when several carpenters were building a house together? b) What is the advantage of defining the metre so that it does not depend on anyone's body? c) Today the metre is defined based on the speed of light, which is always the same: why does this make it unnecessary to keep a "reference ruler" in a museum?

For a long time, the "standard metre" and "standard kilogram" existed: metal objects kept in a museum in Paris that served as the global reference. a) What problem arises if the standard kilogram gets dirty or wears down a little? b) Today units are defined using natural constants, such as the speed of light: why is this a better system? c) If all old standard prototypes in the world disappeared at once, would the units be lost? Explain your reasoning.

Imagine that the International System stops existing and your class has to invent its own unit system to measure lengths, masses, and times. a) Choose a unit for each quantity using classroom objects or phenomena. b) What problems would your system have if people in a school in another city wanted to use it? c) Relate these problems to the reasons that led to the creation of the International System.

Surface area is obtained by multiplying two lengths, and volume by multiplying three. a) Deduce the International System unit for surface area from the metre and write its symbol. b) Do the same for volume. The figure shows the cube referred to in part c:

1. c) The litre is not an SI unit, but it is widely used: knowing that $1\ \text{L}$ is the volume of a cube with an edge of $10\ \text{cm}$, calculate how many cubic metres $1\ \text{L}$ is equivalent to.

A weather presenter says: "Today was twice as hot as yesterday: $20$ degrees compared to $10$". a) What quantity is he measuring? b) In what unit does the TV give it and what is the International System unit? c) Convert $10\ \celsius$ and $20\ \celsius$ to kelvin by adding $273$ and use the result to explain why saying "twice as hot" does not make much sense.

State whether these properties are quantities or not, and justify your answer: the classroom temperature, how pretty a painting is, the mass of a rucksack, the taste of a pizza, the duration of a song, and the speed of a train. What condition must a property meet to be a quantity?

A German screw factory and a Japanese one exchange blueprints with all measurements in millimetres. a) Why do they use a specific unit rather than words like "small" or "medium"? b) What would happen if one factory worked in inches and the other in millimetres without notice? Invent a numerical example of the disaster, for instance with a part that should measure $25\ \text{mm}$. c) Relate this problem to the purpose of the International System.

In 1999, the Mars Climate Orbiter space probe was lost on Mars because one team of engineers made calculations in pounds and another in newtons, and nobody converted the units. a) Explain in your own words what went wrong. b) If one pound-force is equal to about $4,45\ \text{N}$, how many newtons is a thrust of $100$ pounds-force equal to? c) The probe's computer expected the value in newtons and received the bare number $100$: was the applied thrust greater or smaller than expected? By how many times?