**SCIENCE AND ITS METHOD**

MEASURING MAGNITUDES

MEASURING MAGNITUDES

Observation

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

experiments

to

prove the hypotheses

to be true or false

They reproduce the phenomenon under

controlled conditions

.

In experiments, we need to

measure

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

nature

.

They work in the same way: the

SCIENTIFIC METHOD.

All of them make

inventions

possible that make our lives easier.

They have the same aim: knowledge of

nature

.

They work in the same way: the

SCIENTIFIC METHOD.

All of them make

inventions

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.

CHEMISTRY

PHYSICS

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

Prefixes

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

means

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. [

2.356

has

4 sig figs

]

Zeros between non-zero digits.

[

1.06

has

3 sig figs

]

Final zeros at the right side of the decimal point. [

23.50

has

4 sig figs

]

Final zeros at the end of the number with decimal point. [

1400

. has

4 sig figs

]

Which aren't sig figs?

Zeros at the beginning of a number [0.000

234

has

3 sig figs

]

Final zeros at the end of the number without decimal point. [

14

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

SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION

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

with

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

with

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

with

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

with

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

INSTRUMENTS AND ERRORS

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

Example:

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

Example:

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**

Tables

We use them to register the experimental data in a organized way.

Example:

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

Graphs let us find relationships between variables easily

Equations

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.