New units for old
Can you match up the entries from this table of units?
Age
16 to 18
Challenge level
Problem
There are seven different Standardised International (SI) units of measurements from which all others are derived. These are:
|
Name
|
Phenomenon
|
Units
|
|
metre
|
Length
|
m
|
|
second
|
time
|
s
|
|
kilogram
|
mass
|
kg
|
|
ampere
|
electric current
|
A
|
|
kelvin
|
thermodynamic temperature
|
K
|
|
mole
|
Amount of substance
|
mol
|
|
Luminous intensity
|
candela
|
cd
|
There are 22 derived physical phenomena, shown below. The names, phenomena, units and base units have been mixed up.
- Sort them into the correct order and work out how their units may be represented with base SI units.
- For each pheonomena, how many examples of biological application can you find? Can you find an example from biology for each one of these processes?
|
Name
|
Phenomenon
|
Units
|
Base units |
|
becquerel, Bq
|
capacitance
|
A / V
|
$\quad\quad$m$^2$m$^{-2}$cd |
|
degrees Celsius, $^\circ$ C
|
electric
conductance |
C / V
|
$\quad\quad$K |
|
coulomb, C
|
electric
potential |
cd sr
|
$\quad\quad$kg s$^{-2}$ A$^{-1}$ |
|
farad, F
|
electric
resistance |
J / kg
|
$\quad\quad$m kg s$^{-2}$ |
|
gray, Gy
|
electrical
charge |
J / kg
|
$\quad\quad$m$^{1}$m$^{-1}$ |
|
henry, H
|
energy
|
J / S
|
$\quad\quad$m$^{2}$ m$^{-4}$ cd |
|
Hertz, Hz
|
flux of light
|
$\quad\quad\quad$lm / m$^2$ | $\quad\quad$m$^{2}$ kg s$^{-2}$ |
|
joule, J
|
force
|
$\quad\quad\quad$N / m$^{2}$ | $\quad\quad$m$^{2}$ kg s$^{-2}$ A$^{-1}$ |
|
katal, kat
|
frequency
|
N m
|
$\quad\quad$m$^{2}$ kg s$^{-2}$ A$^{-2}$ |
|
lumen, lm
|
illuminance
|
V / A
|
$\quad\quad$m$^{2}$ kg s$^{-3}$ |
|
lux, lx
|
inductance
|
V s
|
$\quad\quad$m$^{2}$ kg s$^{-3}$ A$^{-1}$ |
|
newton, N
|
magnetic flux
|
W / A
|
$\quad\quad$m$^{2}$ kg s$^{-3}$ A$^{-2}$ |
|
ohm, $\Omega$
|
magnetic
flux density |
Wb / A
|
$\quad\quad$m$^{-2}$ kg$^{-1}$ s$^{3}$ A$^{2}$ |
|
pascal, Pa
|
plane angle
|
$\quad\quad\quad$Wb / m$^2$ | $\quad\quad$m$^{-2}$ kg$^{-1}$ s$^{4}$ A$^{2}$ |
|
radian, rad
|
power
|
$\quad\quad$m$^{2}$ s$^{-2}$ | |
|
siemens, S
|
pressure
|
$\quad\quad$m$^{2}$m$^{-2}$ | |
|
sievert, Sv
|
radiation
dose |
$\quad\quad$sA | |
|
steradian, sr
|
solid
angle |
$\quad\quad$s$^{-1}$ | |
|
tesla, T
|
temperature
|
$\quad\quad$s$^{-1}$ mol | |
|
volt, V
|
unit of catalytic activity
|
||
|
watt, W
|
|||
|
weber, Wb
|
(data sourced from the Bureau International des Poids et Mesures http://www.bipm.org/)
Other problems
Try Universal Time, Mass, Length to investigate the units implicit in the fundamental constants of nature.
Getting Started
As with any complex, sorting exercise try to make sense of the
complexity by searching for familiar elements and dealing with them
first.
Student Solutions
| Name | Phenomenon | Units | Base units |
| becquerel, Bq | (radioactivity) | $(\textrm{s}^{-1})$ | $\textrm{s}^{-1}$ |
| degrees Celsius, $^\circ$ C | temperature (relative) | $(\textrm{K}$) | $\textrm{K}$ |
| coulomb, C | electrical charge | ($\textrm{A s})$ | $\textrm{A s}$ |
| farad, F | capacitance | $\textrm{C V}^{-1}$ | $\textrm{A}^2 \textrm{ kg}^{-1} \textrm{ m}^{-2} \textrm{ s}^4$ |
| gray, Gy | radiation dose (absorbed) | $\textrm{J kg}^{-1}$ | $\textrm{m}^2\textrm{ s}^{-2}$ |
| henry, H | inductance | $\textrm{Wb A}^{-1}$ | $\textrm{A}^{-2}\textrm{ kg m}^{2} \textrm{ s}^{-2}$ |
| hertz, Hz | frequency | $(\textrm{s}^{-1})$ | $\textrm{s}^{-1}$ |
| joule, J | energy | $\textrm{N m}$ | $\textrm{kg m}^2 \textrm{ s}^{-2}$ |
| katal, kat | catalytic activity | $(\textrm{mol s}^{-1})$ | $\textrm{mol s}^{-1}$ |
| lumen, lm | flux of light | $\textrm{cd sr}$ | $\textrm{cd m}^2 \textrm{ m}^{-2}$ |
| lux, lx | illuminance | $(\textrm{cd sr m}^{-2})$ | $\textrm{cd m}^2 \textrm{ m}^{-4}$ |
| newton, N | force | $(\textrm{kg ms}^{-2})$ | $\textrm{kg ms}^{-2}$ |
| ohm, $\Omega$ | resistance | $\textrm{V A}^{-1}$ | $\textrm{A}^{-2} \textrm{ kg m}^2 \textrm{ s}^{-3}$ |
| pascal, Pa | pressure | $\textrm{N m}^{-2}$ | $\textrm{kg m}^2 \textrm{ s}^{-2}$ |
| radian, rad | plane angle | (dimensionless) | $\textrm{m m}^{-1}$ |
| siemens, S | conductance | $\textrm{A V}^{-1}$ | $\textrm{A}^2 \textrm{ kg}^{-1} \textrm{ m}^{-2} \textrm{ s}^3$ |
| sievert, Sv | radiation dose (equivalent) | $(\textrm{m}^2\textrm{ s}^{-2})$ | $\textrm{m}^2\textrm{ s}^{-2}$ |
| steradian, sr | solid angle | (dimensionless) | $\textrm{m}^2 \textrm{ m}^{-2}$ |
| tesla, T | magnetic flux density | $(\textrm{A}^{-1} \textrm{ m}^{-1} \textrm{ N})$ | $\textrm{A}^{-1} \textrm{ kg s}^{-2}$ |
| volt, V | electrical potential | $\textrm{W A}^{-1}$ | $\textrm{A}^{-1} \textrm{ kg m}^2 \textrm{ s}^{-3}$ |
| watt, W | power | $\textrm{J s}^{-1}$ | $\textrm{kg m}^2 \textrm{ s}^{-3}$ |
| weber, Wb | magnetic flux | $\textrm{V s}$ | $\textrm{A}^{-1} \textrm{ kg m}^2 \textrm{ s}^{-2}$ |
(date sourced from the Bureau International des Poids et Mesures http://www.bipm.org/)
Items in parenthesis () not present in original table
Teachers' Resources
Why do this problem ?
This important problem will lead to a thorough understanding, and demystification of, the various units which exist. Students will enage in a variety of problem solving strategies in its solution.Possible approach
This question initially appears to be quite demanding. Provide
a printout of the data to each student. Which units are already
known? Suggest that these first be crossed off, with the results
tabulated elsewhere. This will significantly reduce the scale of
the problem.
Key questions
Are there any obvious pieces of data with which to start?Possible extension
Extension activities are given in the question. Can students find examples for each of the units?Possible support
Create cards for a team card sorting exercise, allowing
students to move the various data around physically.
As a warm-up, you might try Choose
your units.