Units of length?
The SI system of units
There are seven fundamental base units
which are clearly defined and on which all other derived units are based:
The metre
• This is the unit of distance. It is the distance traveled by light in a vacuum in a time of
The second
• This is the unit of time. A second is the
The ampere
• This is the unit of electrical current. It is
defined as that current which, when flowing in two parallel conductors 1 m apart,
produces a force of 2 x 10-7 N on a length of
The kelvin
• This is the unit of temperature. It is
The mole
• One mole of a substance contains as many molecules as there are atoms in 12 g of
carbon-12. This special number of
The candela (not used in IB)
The kilogram
• This is the unit of mass. It is the mass of a certain quantity of a platinum-iridium alloy kept at the Bureau International des Poids et Mesures in France.
Derived units
Other physical quantities have units that are combinations of the fundamental units.
Speed = distance/time = m.s-1
Acceleration = m.s-2
Force = mass x acceleration = kg.m.s-2 (called a Newton)
Some important derived units
(learn these!)
1 N = kg.m.s-2 (F = ma)
1 J = kg.m2.s-2 (W = Force x
distance)
Prefixes
Prefixes
Power Prefix Symbol Power Prefix Symbol
10-18 atto a 101 deka da
10-15 femto f 102 hecto h
10-12 pico p 103 kilo k
10-9 nano n 106 mega M
10-6 micro μ 109 giga G
10-3 milli m 1012 tera T
10-2 centi c 1015 peta P
Prefixes
Power Prefix Symbol Power Prefix Symbol
10-18 atto a 101 deka da
10-15 femto f 102 hecto h
10-12 pico p 103 kilo k
10-9 nano n 106 mega M
10-6 micro μ 109 giga G
10-3 milli m 1012 tera T
10-2 centi c 1015 peta P
10-1 deci d 1018 exa E
Don’t worry! These will all be in the
formula book you have for the
Examples
3.3 mA = 3.3 x 10-3 A
545 nm = 545 x 10-9 m = 5.45 x 10-7 m
Checking equations
Checking equations
For example, the period of a pendulum is given by
T = 2π l where l is the length in metres
g and g is the acceleration due to gravity. In units m = s2 = s
Errors/Uncertainties
In EVERY measurement (as opposed to simply counting) there is an uncertainty in the measurement.
This is sometimes
determined by the apparatus you're using, sometimes by the nature of the
Individual measurements
When using an analogue scale, the uncertainty is plus or minus half the smallest scale division. (in a best case
scenario!)
Individual measurements
When using an analogue scale, the uncertainty is plus or minus half the smallest scale division. (in a best case
Individual measurements
When using a digital scale, the uncertainty is plus or minus the smallest unit shown.
Repeated measurements
When we take repeated
measurements and find an average, we can find the uncertainty by finding the difference between the
average and the
measurement that is
Repeated measurements - Example
Iker measured the length of 5 supposedly identical tables. He got the following results; 1560 mm, 1565
mm, 1558 mm, 1567 mm , 1558 mm
Average value = 1563 mm
Uncertainty = 1563 – 1558 = 5 mm
Length of table = 1563 ± 5 mm
Precision
and
Accuracy
Precision
A man’s height was measured several times using a laser device. All the
measurements were very similar and the height was found to be
184.34 ± 0.01 cm
Accuracy
Height of man = 184.34 ± 0.01cm
This is a precise result, but not accurate (near the “real value”)
Accuracy
The man then took his shoes off and his height was measured using a ruler to the nearest
centimetre.
Height = 182 ± 1 cm
This is accurate (near the real value) but not
Precise and accurate
The man’s height was then measured
without his socks on using the laser device.
Height = 182.23 ± 0.01 cm
Random errors/uncertainties
Some measurements do vary randomly. Some are bigger than the actual/real value, some are smaller. This is called a random uncertainty.
Systematic/zero errors
Sometimes all measurements are
bigger or smaller than they should be.
This is called a
systematic
Systematic/zero errors
This is normally caused by not measuring from zero. For example when you all measured Mr Porter’s height without taking his shoes off!
For this reason they are also known as zero
errors/uncertainties. Finding an average
Systematic/zero errors
Uncertainties
In the example with the table, we found the length of the table to be 1563 ± 5 mm
We say the absolute uncertainty is 5 mm
The fractional uncertainty is 5/1563 = 0.003
Uncertainties
If the average height of students at BSH is 1.23 ±
0.01 m
We say the absolute uncertainty is 0.01 m
The fractional uncertainty is 0.01/1.23 = 0.008
Combining uncertainties
When we find the volume of a block, we have to multiply the length by the width by the height.
Because each measurement has an
Combining uncertainties
When multiplying (or dividing) quantities, to find the resultant uncertainty we have to add the percentage uncertainties of the
Combining uncertainties
Example: A block has a length of 10.0 ± 0.1 cm, width 5.0 ± 0.1 cm and height 6.0 ± 0.1 cm.
Volume = 10.0 x 5.0 x 6.0 = 300 cm3
% uncertainty in length = 0.1/10 x 100 = 1% % uncertainty in width = 0.1/5 x 100 = 2 % % uncertainty in height = 0.1/6 x 100 = 1.7 %
Uncertainty in volume = 1% + 2% + 1.7% = 4.7%
(4.7% of 300 = 14)
Volume = 300 ± 14 cm3
This means the
actual volume could be anywhere
Combining uncertainties
When adding (or
subtracting) quantities, to find the resultant
uncertainty we have to add the absolute uncertainties
Combining uncertainties
One basketball player has a height of 196 ± 1 cm and the other has a height of 152 ± 1 cm. What is the difference in their heights?