Transcript How many different units of length can you think of? Units of length? Light year, parsec, AU, mile, furlong, fathom, yard, feet, inches, Angstroms, nautical miles, cubits, cm,

How many
different
units of
length can
you think
of?
Units of length?
Light year, parsec, AU, mile, furlong,
fathom, yard, feet, inches, Angstroms,
nautical miles, cubits, cm, mm, km, μm, nm
The SI system of units
There are seven fundamental base units
which are clearly defined and on which all
other derived units are based:
You need to know these,
but not their definitions.
The metre
• This is the unit of distance. It is the distance
traveled by light in a vacuum in a time of
1/299792458 seconds.
The second
• This is the unit of time. A second is the
duration of 9192631770 full oscillations of
the electromagnetic radiation emitted in a
transition between two hyperfine energy
levels in the ground state of a caesium-133
atom.
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
1 m of the conductors.
Note that the Coulomb is NOT
a base unit.
The kelvin
• This is the unit of temperature. It is
1/273.16 of the thermodynamic temperature
of the triple point of water.
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
molecules is called Avogadro’s number and
equals 6.02 x 1023.
The candela (not used in IB)
• This is the unit of luminous intensity. It is
the intensity of a source of frequency 5.40 x
1014 Hz emitting 1/683 W per steradian.
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.
THE kilogram!
SI Base Units
Can you
copy this
please?
Quantity
Unit
distance
metre
time
second
current
ampere
temperature
kelvin
quantity of substance
mole
luminous intensity
candela
mass
kilogram
Note: No Newton or Coulomb
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)
(note in IB we write m.s-1 rather than m/s)
Some important derived units
(learn these!)
1 N = kg.m.s-2
(F = ma)
1 J = kg.m2.s-2
(W = Force x distance)
1 W = kg.m2.s-3
(Power = energy/time)
Guess
what
Prefixes
It is sometimes useful to express units that
are related to the basic ones by powers of
ten
Prefixes
Power Prefix
10-18 atto
10-15 femto
10-12 pico
10-9 nano
10-6 micro
10-3 milli
10-2 centi
10-1 deci
Symbol
a
f
p
n
μ
m
c
d
Power Prefix
101
deka
102
hecto
103
kilo
106
mega
109
giga
1012 tera
1015 peta
1018 exa
Symbol
da
h
k
M
G
T
P
E
Don’t
worry!
These will
all be in the
formula
Power Prefix Symbol book you
101
deka da
have for the
exam.
102
hecto h
103
kilo k
106
mega M
109
giga G
1012 tera T
1015 peta P
1018 exa
E
Prefixes
Power Prefix
10-18 atto
10-15 femto
10-12 pico
10-9 nano
10-6 micro
10-3 milli
10-2 centi
10-1 deci
Symbol
a
f
p
n
μ
m
c
d
Examples
3.3 mA = 3.3 x 10-3 A
545 nm = 545 x 10-9 m = 5.45 x 10-7 m
2.34 MW = 2.34 x 106 W
Checking equations
If an equation is correct, the units on one
side should equal the units on another. We
can use base units to help us check.
Checking equations
For example, the period of a pendulum is
given by
T = 2π l
g
In units
where l is the length in metres
and g is the acceleration due to gravity.
m
m.s-2
=
s2
=
s
Let’s try some questions for a
change
Can you
finish
these for
Monday
11/9/12
please?
Tsokos Page 6
Questions 15, 16, 18,
20, 21, 24, 26, 29.
Let’s do some measuring!
Do the
measurements
yourselves, but leave
space in your table
of results to record
the measurements of
4 other people from
the group
Errors/Uncertainties
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
measurement itself.
Estimating uncertainty
The intelligent
ones are
always the
cutest.
As Physicists we
need to have an idea
of the size of the
uncertainty in each
measurement
Individual measurements
When using an analogue scale, the uncertainty is plus or
minus half the smallest scale division. (in a best case
scenario!)
4.20 ± 0.05 cm
Individual measurements
When using an analogue scale, the uncertainty is plus or
minus half the smallest scale division. (in a best case
scenario!)
22.0 ± 0.5 V
Individual measurements
When using a digital scale, the uncertainty is
plus or minus the smallest unit shown.
19.16 ± 0.01 V
Repeated measurements
When we take repeated
measurements and find an
average, we can find the
uncertainty by finding the
difference between the
highest and lowest
measurement and divide
by two.
Repeated measurements - Example
Pascal 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 = (1567 – 1558)/2 = 4.5
This means the actual
length is anywhere
between 1558 and
mm 1568 mm
Length of table = 1563 ± 5 mm
Average of the differences
• Imagine you got the following results for
resistance (in Ohms)
• 13.2, 14.2, 12.3, 15.2, 13.1, 12.2.
Precision and Accuracy
The same thing?
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
This is a precise result (high
number of significant figures,
small range of measurements)
Accuracy
Height of man = 184.34 ± 0.01cm
This is a precise result, but not
accurate (near the “real value”)
because the man still had his shoes
on.
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 (only 3 significant figures)
Precise and accurate
The man’s height was then measured
without his socks on using the laser device.
Height = 182.23 ± 0.01 cm
This is precise (high number of significant
figures) AND accurate (near the real value)
Precision and Accuracy
• Precise – High number of significent
figures. Repeated measurements are similar
• Accurate – Near to the “real” value
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.
Finding an average can produce a more reliable
result in this case.
Systematic/zero errors
Sometimes all measurements are
bigger or smaller than they should be
by the same amount. This is called a
systematic error/uncertainty.
(An error which is identical for each reading )
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
doesn’t help.
Systematic/zero errors
Systematic errors are sometimes hard to
identify and eradicate.
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
The percentage uncertainty is 5/1563 x 100 = 0.3%
Uncertainties
If the average height of students at BSW 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
The percentage uncertainty is 0.01/1.23 x 100 = 0.8%
Let’s try some questions.
Let’s read!
Pages 7 to 10 of
Hamper/Ord ‘SL
Physics’
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
uncertainty, the uncertainty increases when
we multiply the measurements together.
Combining uncertainties
When multiplying (or dividing) quantities,
to find the resultant uncertainty we have to
add the percentage (or fractibnal)
uncertainties of the quantities we are
multiplying.
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
between 286 and
314 cm3
Combining uncertainties
When adding (or
subtracting) quantities, to
find the resultant
uncertainty we have to add
the absolute uncertainties
of the quantities we are
multiplying.
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?
Difference = 44 ± 2 cm
Who’s going to win?
New York Times
Latest opinion poll
Bush 48%
Gore 52%
Gore will win!
Uncertainty = ± 5%
Who’s going to win?
New York Times
Latest opinion poll
Bush 48%
Gore 52%
Gore will win!
Uncertainty = ± 5%
Who’s going to win?
New York Times
Latest opinion poll
Bush 48%
Uncertainty = ± 5%
Gore 52%
Gore will win!
Uncertainty = ± 5%
Who’s going to win
Bush = 48 ± 5 % = between 43 and 53 %
Gore = 52 ± 5 % = between 47 and 57 %
We can’t say!
(If the uncertainty is greater than the difference)
Let’s try some more questions!
Error bars
• X = 0.6 ± 0.1
• Y = 0.5 ± 0.1
Gradients
Minimum gradient
Maximum gradient
y = mx + c
Hooke’s law
• F = kx
Hooke’s law
• F = kx
F (N)
x (m)
Kinetic energy
• Ek = ½mv2
y = mx + c
• Ek = ½mv2
Ek (J)
V2 (m2.s-2)
Period of a pendulum
T = 2π l
g
Period of a pendulum
T = 2π l
g
T (s)
l½ (m½)
Period of a pendulum
T = 2π l
g
T2 (s)
l (m)
Let’s try an investigation
Can you read
the sheets that
Mr Porter is
giving you?
Data collection and processing
• Heading, Units, Uncertainties
• Decimal places consistent between data and
also with uncertainties
• Repeated measurements
• Averages (with uncertainties)
• Graph(s) with units and labels
• Lines of best fit – maximum and minimum
gradients if possible/required
Homework
• Complete „Oscillating Mass” investigation.
• Due Monday 26th September