Transcript Mathematics and Physics

1.1
Physics

Physics is a branch of science that
involves the study of the physical world:
energy, matter, and how they are
related.
Areas Within Physics
Name
Subjects
Examples
Mechanics
Motion and its causes
Falling objects, friction,
weight, spinning objects
Thermodynamics
Heat and temperature
Melting and freezing
processes, engines,
refrigerators
Vibrations and wave
phenomena
Specific types of repetitive Springs, pendulums,
motions
sound
Optics
Light
Mirrors, lenses, color,
astronomy
Electromagnetism
Electricity, magnetism,
and light
Electrical charge, circuitry,
permanent magnets,
electromagnets
Relativity
Particles moving at any
Particle collisions, particle
speed, including very high accelerators, nuclear
speeds
energy
Quantum mechanics
Behavior of
submicroscopic particles
The atom and its parts
Physics Best Friend?

THE SCIENTIFIC METHOD!
Scientific
Method
Scientific Method

Observation
 (pre-research)
Hypothesis
 Experiment

 Independent and dependent variable
 Controlled experiment
Results - data , graphs, tables, etc.
 Conclusion – is hypothesis supported?

Importance of Models

Physicists often use simple models to
explain the most fundamental features
of various phenomena, because it is
basically impossible to describe all
aspects at the same time.
Importance of Models

Physicist break the phenomena down
into different parts, decide which parts
are important to what they want to study,
and disregard the rest.
Models and Experiments

Models help guide experimental design
by focusing what you are testing and
keeping all other variables the same.

This is an example of a controlled
experiment, where you change only one
variable.
1.2
Numbers as Measurements

Systeme International (SI) is a system
of units used for measurements by
scientists all around the world.

Why do we all use the same system?
SI Units
Prefixes Used with SI Units
Scientific Notation

Scientific notation is a way we show
large and small numbers.

The measurement is recorded to a
power of 10, and all of the figures given
are significant.
 EX: c = 3.00 x 108 m/s = 1 sig fig (3)
Uncertainty in Measurements

Results are often reported with an
uncertainty to allow for a minimal
difference in measurement readings.

Ex: 14.6 ± 0.2 cm. --- the reading can
be anywhere between 14.4cm and
14.8cm.

The larger the uncertainty, the less the
precision.
Accuracy vs. Precision

Accuracy describes how close a
measurement is to reality.

Precision describes the limitations of the
measuring device used.
Significant Figures

Significant figures are used to indicate
precision ( the degree of exactness of a
measurement).

In calculations, the number of significant
figures in your result depends on the
number of significant figures in each
measurement.
Rule
Examples
1. Zeros between other nonzero digits
are significant.
a. 50.3m has three sig figs
b. 3.0025s has five sig figs
2. Zeros in front of nonzero digits are not
significant.
a. 0.892kg has three sig figs
b. 0.0008ms has one sig fig
3. Zeros that are at the end of a number
and also to the right of the decimal are
significant.
a. 57.00g has four significant figures.
4. Zeros at the end of a number but to
the left of a decimal are significant if they
have been measured or are the first
estimated digit; otherwise, they are not
significant. (we treat them as not
significant)
a. 1000m may contain from one to four
significant figures, depending on the
precision of the measurement, but we
will be assumed that measurements
like this have one significant figure.
b. 2.000000kg has seven sig figs
b. 20m may contain one or two
significant figures, but we will assume
it has one sig fig.
Significant Figures
Type of Calculation
Rule
Example
Addition or subtraction
The final answer should
have the same number
of digits to the right of
the decimal as the
measurement with the
smallest number of digits
to the right of the
decimal.
97.3
+5.85
103.15
The final answer has the
same number of
significant figures as the
measurement having the
smallest number of
significant figures.
123
X 5.35
658.05
Multiplication or division
Round off to 103.2
Round off to 658
Significant Figures

Calculators do not pay attention to
significant figures.

Calculators often exaggerate the
precision of your final results by
returning answers with as many digits as
the display can show.
PRACTICE!

1. Convert the following measurements:
a) 6.20 mg in kg
b) 3 x 10-9 s in ms
c) 88.0 km in m
PRACTICE!

Perform these calculations, following the
rules for significant figures.
a) 26 x 0.02584
b) 15.3 ÷ 1.1
c) 782.45 – 3.5328
d) 63.258 + 734.2
Measurement Lab

Follow Directions!
1.3
Mathematics and Physics

Tables, graphs, and equations can make
data easier to understand.

Physics equations indicate relationships
through variables.

Variables and other specific quantities
are abbreviated with letters that are
boldfaced or italicized.
Mathematics and Physics
Quantity
Symbol
Units
Unit Abbreviations
Change in position
Δx, Δy
Meters
m
Time interval
Δt
Seconds
s
Mass
M
Kilograms
kg
Evaluating Expressions

Dimensional analysis can weed out invalid
equations.

Treating the units as algebraic quantities,
which can be cancelled, is called
dimensional analysis.


EX: quantities can be added or subtracted only if
they have the same dimensions.
Its used in choosing conversion factors (a
multiplier equal to 1).
PRACTICE!
•
1. How many megahertz is 750 kilohertz?
•
2. Convert 5021 centimeters to kilometers.
•
3. How many seconds are in a leap year (1
extra day)?
•
4. Convert the speed 5.30 m/s to km/h.