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Unit 1
THE SCIENTIFIC WORK
Physics and Chemistry
What do they have in common? Physicists and Chemists study
the same: matter. Physicists, Chemists and other
scientists work in the same way: SCIENTIFIC METHOD
Physics and Chemistry What makes them different?
Physics studies phenomena that don't change the composition of matter.
Chemistry studies phenomena that change the composition of matter.
SCIENTIFIC METHOD
SCIENTIFIC METHOD
The observation of a phenomenon and curiosity make scientists ask questions.
Before doing anything else, it's necessary to look for the previous knowledge about the phenomenon.
SCIENTIFIC METHOD
Hypotheses are possible answers to the questions we asked.
They are only testable predictions about the phenomenon.
SCIENTIFIC METHOD We use experiments for
checking hypotheses. We reproduce a
phenomenon in controlled conditions.
We need measure and collecting data in tables or graphics
SCIENTIFIC METHOD We study the relationships
between different variables.
In an experiment there are three kinds of variables
Independent variables: they can be changed.
Dependent variables: they are measured.
Controlled variables: they don't change.
SCIENTIFIC METHOD
After the experiment, we analyse its results and draw a conclusion.
If the hypothesis is true, we have learnt something new and it becomes in a law
If the hypothesis is false. We must look for a new hypothesis and continue the research.
Magnitudes, measurements and units
Physical Magnitude: It refers to every property of matter that can be measured.
Length, mass, surface, volume, density, velocity, force, temperature,...
Measure: It compares a quantity of a magnitude with other that we use as a reference (unit).
Unit: It is a quantity of a magnitude used to measure other quantities of the same magnitude. It's only useful if every people uses the same unit.
Magnitudes, measurements and units
Length of the classroom = 10 m
means
The length of the classroom is 10 times the length of 1 metre.
The International Systemof Units
The SI has: a small group of magnitudes whose units
are fixed directly: the fundamental magnitudes.
E.g.: Length → meter (m); Time → second (s)
The units for the other magnitudes are defined in relationship with the fundamental units: the derivative magnitudes.
E. g.: speed → meter/second (m/s)
The International Systemof Units
The fundamental magnitudes and their units
Length meter m
Mass kilogram kg
Time second s
Amount of substance mole mol
Temperature Kelvin K
Electric current amperes A
Luminous intensity candela cd
The International Systemof Units
Some examples of how to build the units of derivative magnitudes:
Area = Length · width → m·m = m2
Volume = Length · width · height → m·m·m = m3
Speed = distance / time → m/s Acceleration = change of speed / time →
(m/s)/s = m/s2
The International Systemof Units
Some examples of how to build the units of derivative magnitudes:
Area = Length · width → m·m = m2
Volume = Length · width · height → m·m·m = m3
Speed = distance / time → m/s Acceleration = change of speed / time →
(m/s)/s = m/s2
The International Systemof Units
More derivative units.
Area square meter m2
Volume cubic meter m3
Force Newton N
Pressure Pascal Pa
Energy Joule J
Power Watt W
Voltage volt V
Frequency Hertz Hz
Electric charge Coulomb C
Quantity Name Symbol
The International Systemof Units
Prefixes: we used them when we need express quantities much bigger or smaller than basic unit.
Power of 10 for Prefix Symbol Meaning Scientific Notation_______________________________________________________________________
mega- M 1,000,000 106
kilo- k 1,000 103
deci- d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- 0.000001 10-6
nano- n 0.000000001 10-9
The International Systemof Units
Prefixes: the whole list Factor Name Symbol Factor Name Symbol
10-1 decimeter dm 101 decameter dam
10-2 centimeter cm 102 hectometer hm
10-3 millimeter mm 103 kilometer km
10-6 micrometer m 106 megameter Mm
10-9 nanometer nm 109 gigameter Gm
10-12 picometer pm 1012 terameter Tm
10-15 femtometer fm 1015 petameter Pm
10-18 attometer am 1018 exameter Em
10-21 zeptometer zm 1021 zettameter Zm
10-24 yoctometer ym 1024 yottameter Ym
Changing units
We can change a quantity into another unit. Conversion factors help us to do it.
A conversion factor is a fraction with the same quantity in its denominator and in its numerator but expressed in different units.
1h60min
=1
60min1h
=1
1 km1000m
=1
1000m1 km
=1
Changing units
Let's see a few examples of how to use them
30ms=30
ms·
1 km1000m
·3600 s
1h=30 ·3600 km
1000h=108
kmh
500 cm² · 1m100 cm
2
=500 cm² · 1m²10000 cm² =500m²
10000=0,05m²
3500 s ·1h
60min·1min60 s
= 3500h3600
=0,972h
2570m·1 km
1000m= 2570 km ·1
1000=2,570 km
Significant figures
They indicate precision of a measurement. Sig Figs in a measurement are the really
known digits.
2.3 cm
Significant figures Counting Sig Figs:
Which are sig figs? All nonzero digits. Zeros between nonzero digits
Which aren't sig figs? Leading zeros – 0,0025 Final zeros without
a decimal point – 250 Examples:
0,00120 → 3 sig figs; 15000 → 2 sig figs 15000, → 5 sig figs; 13,04 → 4 sig
figs
Significant figures
Calculating with sig figs Multiplicate or divide: the factor with the
fewer number of sig figs determines the number of sig figs of the result:
2,345 m · 4,55 m = 10,66975 m2 = 10,7 m2
(4 sig figs) (3 sig figs) → (3 sig figs)
Add or substract: the number with the fewer number of decimal places determines the number of decimal places of the result:
3,456 m + 2,35 m = 5,806 m = 5,81 m (3 decimal places) (2 decimal places) → (2 decimal places)
Significant figures
Calculating with sig figs Exact number have no limit of sig fig:
Example: Area = ½ · Base · height. ½ isn't taken into account to round the
result. Rounding the result:
If the first figure is 5, 6, 7, 8 or 9, the last figure taken into account is increased in 1
If not, it doesn't change.
Scientific notation
Is used to write very large or very small quantities: 385 000 000 Km = 3.85·108 Km 0,000 000 000 157 m = 1,57·10-10 m
Changing a number to scientific notation: We move the decimal point until there is an only
number in its left side. The exponent of 10 is the number of places we
moved the decimal point: The exponent is positive if we move it to the left side It's negative if we move it to the right side.
Measurement errors
It's impossible to measure a quantity with total precision.
When we measure, we'll never know the real value of the quantity.
Every measurement has an error because: The measurement instrument can only see
a few sig figs. It may not be well built or calibrated. We are using it in the wrong way.
Measurement errors
There are two ways for expressing the error of a measurement:
Absolute error: it is the difference between the value of the measurement and the value accepted as exact.
Relative error: it is the absolute error in relationship with the quantity.
Measurement errors
How to calculate the error. EXAMPLE 1: We have measured several times the mass of a ball:
20,17 g, 20,21 g, 20,25 g, 20,15 g, 20,28 g It's supposed that the real value of the ball of the
mass is the average value of all the measurements: Vr = (20,17 g + 20,21 g + 20,25 g + 20,15 g + 20,27 g )/5 = 20,21 g
The absolute error of the first measurement is: Er = |20,17 g – 20,21 g| = 0,04 g
The relative error is calculate dividing the absolute error by the value of quantity.
Ea = (0,04 g / 20,21 g) = 0,002 = 0,2 %
Measurement error
How to calculate the error. EXAMPLE 2: We have measured once the length of a
piece of paper using a ruler that is graduated in millimetres: 29,7 cm
We suppose that the real value is the measured value.
The absolute error is the precision of the rule:
Ea = 0,1 cm
Relative error: Er = 0,1 cm / 29,7 cm = 0,0034 = 0,34 %