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José Vicente Pacheco

on 16 September 2016

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The observation of a phenomenon and scientists' curiosity make them
ask questions
Before doing anything else, it's necessary to look for the
previous knowledge
about the phenomenon.
Formulating hypothesis
Hypothesis are
possible answers
for the question we asked before.
They are
testable predictions
about the phenomenon.

Testing hypotheses
Scientists make
prove the hypotheses
to be true or false
They reproduce the phenomenon under
controlled conditions
In experiments, we need to
different variables and collect the data in
tables and graphs
Getting conclusions
Two things can happen after doing an experiment.
If the hypothesis is proved to be true, it becomes a law.
If the hypothesis is proved to be false: let's start again!

E. g: Galileo proved that heavy and light bodies spend the same time on falling from the same height
What science is
Common characteristics of all sciences:
They have the same aim: knowledge of
They work in the same way: the
All of them make
possible that make our lives easier.

Physics and Chemistry
Both, Physics and Chemistry, research about matter and its changes.
Chemistry studies natural phenomena that change the composition of matter.
Physics studies natural phenomena that don't change the composition of matter.
Scientific Method
Why does the hammer fall faster than the feather?
Hypothesis: heavier bodies fall faster than lighter ones
Three kinds of variables
Independent variable: we can change it.
Dependent variable: we just measure it.
Controlled variables: they don't change during the experiment.
The International System of units (SI)
The SI is based on seven units
Some meausres are too large or too small
Size of a cell = 0.000001 m
Diameter of Earth = 6370000 m
We use prefixes that multiply the base unit by a power of 10
American and British units
British people and Americans have a unit system that is not based in powers of 10.

Units for length
1 mile = 1760 yards
1 yard = 3 feet
1 feet = 12 inches

Changing units
Ratio factors are fractions with the same quantity in their denominator and in their numerator but expressed in different units
A unit is a value of a quantity that is used as a patron to measure.
We need units
The length of the classroom is 10 meters
The length of the classroom is 10 times the length of 1 meter
Derived units. Examples:
Speed: meters / second (m/s)
Area: squared meters (m2)
Volume: cubic meters (m3)
Significant figures
They indicate the precision of a measurement.
Sig Figs in a measurement are the really known digits.
Counting sig figs
Which are sig figs?
All non-zero digits. [
4 sig figs
Zeros between non-zero digits.

3 sig figs
Final zeros at the right side of the decimal point. [
4 sig figs
Final zeros at the end of the number with decimal point. [
. has
4 sig figs
Which aren't sig figs?
Zeros at the beginning of a number [0.000
3 sig figs
Final zeros at the end of the number without decimal point. [
00 has
2 sig figs
Calculating with sig figs
Scientific notation
Scientific notation consist on using powers of ten to write easily too large or too small number

Dealing with numbers in Science
29.2 cm has three sig figs
Adding and subtracting
The number with the fewer number of decimal places determines the number of decimal places of the result.
Example 1
3.456 m + 2.35 m = 5.806 m
3.456 has
3 decimal digits
2.35 has
2 decimal digits
The re
sult must be written
2 decimal digits
3.456 m + 2.35 m = 5.806 m = 5.81 m
Example 2
14.50 m - 11.181 m = 2.319 m
14.50 has
2 decimal digits
11.181 has
3 decimal digits
The result must be written
2 decimal places
14.50 m - 11.181 m = 2.319 m = 2.32 m
Multiplying and dividing
The number with the fewer number of sig figs determines the number of sig figs of the result.
Example 1
2.345 m · 4.55 m = 10.66975 m2
2.345 has
4 sig figs
4.55 has
3 sig figs
The re
sult must be expressed
3 sig figs
2.345 m · 4.55 m = 10.66975 m2 = 10.7 m2
Example 2
2.345 m / 4.55 s = 0.5153846... m/s
2.345 has
4 sig figs
4.55 has
3 sig figs
The re
sult must be expressed
3 sig figs
2.345 m / 4.55 s = 0.5153846... m/s = 0.515 m/s
To express a number in scientific notation:
Move the decimal point until there is an only integer digit.
The exponent is the number of places that the decimal point has been moved.
positive exponent -> a big number
negative exponent -> a small number
Experimental errors
The value we get in a measurement doesn't equal the real value of the quantity:
The instruments have a limited accuracy. They appreciate a few decimal digits.
Sometimes the instruments...
... aren't used properly.
... don't work well.
Kinds of errors
How to express the error
Absolute error
The absolute error is the difference between the value of the measurement and the real value of the quantity
How to express the error
Relative error
The relative shows how good a measurement is.
It shows how great the absolute error is in relation with the value of the measurement.
It is usually expressed as a percentage.
Er = [Ea / Vr]·100
Random errors
Random errors are provoked by factors we can't control
They are unavoidable.
Because of them, we should repeat every measurement several times.
We will take as a real value the average value of all measurements
Systematic errors
They have always the same sense: by excess or by defect.
We can avoid them by using properly the instrument.
Calculating the absolute error
Four people have measured the length of a table and they got the results: 85.7 cm, 86.1 cm, 86.0 cm and 86.6 cm.
We calculate the average value of all measurements:
average value = (85.7 cm + 86.1 cm + 86.0 cm + 86.6 cm) / 4 = 86.1 cm
The absolute error of the first measurement is:
Ea = |85.7 cm - 86.1 cm| = 0.4 cm
Calculating the relative error
The length of a road is 500 km. How large is the relative error if we measure it with an absolute error of 0.1 km?
Er = [Ea/Vr]·100
Er = [0.1 / 500] · 100 = 0.2 %
Analyzing experimental data
We use them to register the experimental data in a organized way.
The length of a spring is modified by the weight of a mass hung on its end. Different masses produce different stretchings in the spring.
Graphs let us find relationships between variables easily
A graph helps us to find a mathematical equation that describes the relationship between two variables.
The straight line in the graphs means that both variables are proportional:
x = C · m
C is the stretching produced by a mass of 1 gram
Fortunately we study the SI that is much easier.
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