Transcript 10 -1

What is Physics?
Physics answers the questions 3
year olds ask – WHY??
Dictionary:
“the study of matter, energy, and
the interaction between them”
Physics
“the study of matter, energy, and the
interaction between them”
Matter
anything that has mass and takes up space or
the amount of stuff that makes up an object
Physics
“the study of matter, energy, and the
interaction between them”
Energy - Ability or capacity to do work
Work – process of moving an object
Energy - Ability or capacity to move an object
Physics
“the study of matter, energy, and the
interaction between them”
Physics
“the study of matter, energy, and the
interaction between them”
Key concept of course
The source of all
energy on Earth is the
conversion of mass
into energy
PHYSICS
Most basic of the sciences
Study of EVERYTHING

Motion (mechanics)
 Fluids
 Heat
 Sound
 Light and Optics
 Electricity and Magnetism
 Waves and Oscillations
 Relativity
 Atomic Structure
 Nuclear Physics
 Elementary Particle Physics
 Astrophysics
AP Physics1 BIG IDEAS
1. Objects and systems have properties such as mass and
charge. Systems of objects may have internal structure.
2. The interaction of an object with other objects can be
described by forces.
3. Fields existing in space can also be used to explain
interactions.
4. Interactions between systems can result in changes of
those systems.
5. Changes that occur as a result of interactions are
constrained by conservation laws.
6. Waves can transfer energy and momentum from one
location to another without the permanent transfer of
mass, and serve as a mathematical model for the
description of other phenomena.
How is Science Practiced?
Ask questions (science) OR define a problem (engineering)
Develop or use a model
(expected)
Plan and carry out an
experimental investigation
Analyze and interpret data using
mathematical and computational
techniques
Compare
experimental results and
expected model to
construct explanations
(science)
OR design solutions
(engineering)
Engage in argument (make conclusions) from evidence
Communicate information
Science is NOT just a
mechanical process of
collecting facts and
making theories
It is a CREATIVE PROCESS
Theory
Theories are never derived directly from
observations
Theories are inspirations that come from the
creativity of the human mind
Examples





Atomic Theory of Matter
Copernicus’ Heliocentric Theory
Theory of Relativity
Electromagnetic Theory of Light
Newtons Law of Universal Gravitation
Math Review
Dimensions and units
SI base units
Quantity
SI unit
symbol
Length
Mass
Time
Electric current
temperature
Luminous intensity
Amount of substance
meter
kilogram
second
ampere
kelvin
candela
mole
m
kg
s
A
K
cd
nol
All other units can be derived
from the 7 base units
Metric Prefixes and Symbols
Astronomical
1 000 000 000 000 000 000 = 1018 exa
1 000 000 000 000 000 = 1015 peta
1 000 000 000 000 = 1012 tera
1 000 000 000 = 109 giga
1 000 000 = 106 mega
1 000 = 103 kilo
100 = 102 Hecto
10 = 101 deca
0.1 = 10-1 deci
0.01 = 10-2 centi
0.001 = 10-3 milli
0.000 001 = 10-6 micro
0.000 000 001 = 10-9 nano
0.000 000 000 001 = 10-12 pico
0.000 000 000 000 001 = 10-15 femto
0.000 000 000 000 000 001 = 10-18 atto
Sym
E
Sun
P
(1.4x109m)
T
G
M
Earth
k
(1.3x107m)
h
da
Softball (10-1m)
d
c
cells (10-5m)
m
proteins
m
(5-10nm)
n
H atom (10-10m)
p
f
Proton (10-15m)
a
Subatomic Electron, quarks
Human
prefix
Atomic
Cellular
Quantity
Milky Way
(1021m)
Scientific Notation: Used to
express very large or very small
numbers. Based on powers of 10
Examples:
20,000 = 2 x 10,000 = 2 x (10 x 10 x 10 x 10) = 2 x 104
497,100,000 = 4.971 x 108
move decimal right 8 times
0.000000582 = 5.82 x 10-7
move decimal left 7 times
Scientific Notation:
Try these
Try these
5.3 x 10-3 = 0.0053
351000 =
6.34 x 105 = 634,000
0.00000877 = 8.77 x 10-6
5.56 x 107 = 55,600,000
3.51 x 105
Rules for multiplication and
division in Scientific Notation:
Multiplication
1. Multiply coefficients
2. Add exponents
8
3
(83)
11
12
(2 x10 )(8x10 )  (2 x8)(10 )  16 x10  1.6 x10
Division
1. divide coefficients
2. subtract exponents
8
8
(6 x10 )  6  10 
( 8 3)
5




3
(
10
)

3
x
10
  3 
3
(2 x10 )  2  10 
Express in Scientific Notation:
(5 x 10-5)(7 x 1010) = 3.5 x 106
(5 x 10-5)(8 x 1010) (4 x 104) = 1.6 x 1011
7
2
5
(4 x10 )(2 x10 )(6 x10 )
15

1.6
x
10
4
3 x10
3 4
(3x10 ) 
81 x 10-12
Dimensional Analysis
problem-solving method that uses the fact
that any number or expression can be
multiplied by one without changing its value
1 inch = 2.54 cm
1 cm = 10 mm
How many cm long is a 100 yard football
field?
3 ft 12in 2.54cm
100 yd 
x
x
 9144cm
1yd 1 ft
1in
Dimensional Analysis
1 inch = 2.54 cm
1 cm = 10 mm
5280ft = 1mi
1. A fish tank is 20in x 12in x 12in.
What is its volume in mm3?
4.7 x 107 mm3
2. The speed of light is 3 x 108 m/s.
What is the speed of light in mph?
6.7 x 108 mph
Being able to manipulate formulae to solve for a variable is
an extremely important skill in Physics. It is done to isolate
a single variable to make problem solving easier. The
formulae below are a few used during the course.
Manipulate the variables algebraically and solve for the
variable indicated.
v  v  2a ( x  x0 ),
2
2
0
m
T  2
,
k
Fg  G
m1m 2
r
2
a  _________________
k  _________________
,
r  _________________
E  12 mv 2  mgh, v  _________________
Manipulate the variables algebraically and solve for the
variable indicated.
2
mv
 mf  T
r
a) Isolate m: m = ?
b) Isolate f: f = ?
c) If the units of m are [kg], the units of v are [m/s], the
units of r are [m] and the units of T are [kg m/s2],
what are the units of f?
Algebra Review
The following are ordinary physics problems. Place
the answer in scientific notation when appropriate
and simplify the units.
Fg  (9.0 x10
9
9 N m 2
C2
9
(3.2 x10 C )(9.6 x10 C )
)

2
(0.32m)
4.5 x10  2 kg
T  2

3 kg
2.0 x10 s 2
1.33 sin 25.0  1.50 sin  ,   ____________
o
Right Triangle Trigonometry
Using the generic triangle to SOHCAHTOA
the right, Right Triangle
Trigonometry and
Pythagorean Theorem solve
the following. Your calculator
must be in degree mode.
a) =55o and c=32m. Solve for a and b
b) a=250m and b=180m. Solve for θ and c.
Experimental Design
How is Science Practiced?
Ask questions (science) OR define a problem (engineering)
Develop or use a model
(expected)
Plan and carry out an
experimental investigation
Analyze and interpret data using
mathematical and computational
techniques
Compare
experimental results and
expected model to
construct explanations
(science)
OR design solutions
(engineering)
Engage in argument (make conclusions) from evidence
Communicate information
Ask questions (science) OR define a problem (engineering)
Experimental Question (or objective) – how does one
quantity (variable) affect another quantity (variable)
Variable- Any factor that might affect the behavior of an
experiment.
• Independent Variable
- Factor that is changed or manipulated during the
experiment
- Always plotted on the x-axis
• Dependent Variable
- Factor that depends on the independent variable
- Always plotted on the y-axis
Experimental Investigation
Procedure – describe what is measured and how its measured
Collect Data • At least 6 data points are necessary for a good graph.
• Independent variable should cover a range of at least 10 fold
if possible (eg. 0.2 to 2.0 m)
• Record data in a data table immediately as its collected
Data Table should be organized and self-explanatory
• Construct data table before collecting the data
• There should be a column for every measured variable with
Independent variable in leftmost column of data table
• Every column is headed with the variable name being
measured with the units in parentheses
• All data should be recorded with appropriate sig figs to
indicate the precision of measurement (Same number of
decimal places in each column)
ANALYSIS and interpretation of data using mathematical and
computational techniques
GRAPH DATA
The purpose of a graph is to show the relationship between
variables
• Plot data as scatter plots (do not connect the data points)
• Always include a title in words
(typically Indep vs Dep var for ….)
• Label each axis with the variable and units in parentheses
• Recognize the mathematical relationship shown between the
variables
• Fit the data points with a line or curve of best fit to model the
relationship between the variables. Include the equation of
best fit.
Graphing Data
Title
Force Applied vs. Mass
(words)
20
Dependent
variable
F (N)
F=2m
Direct
Relationship
15
10
5
Axes labeled
with variable
symbols (not
words) and
units
0
0
2
4
6
m (kg)
Independent
variable
8
10
ERROR ANALYSIS
And
Significant Figures
How is Science Practiced?
Ask questions (science) OR define a problem (engineering)
Develop or use a model
(expected)
Plan and carry out an
experimental investigation
Analyze and interpret data using
mathematical and computational
MEASUREMENTS
and
techniques
Compare
experimental results and
expected model to
construct explanations
(science)
OR design solutions
(engineering)
comparing those
measurements to expected values lie at
Engage
argument
conclusions)
from evidence
theinheart
of all(make
scientific
endeavors
No measurement
is exact
Communicate information
Two issues must be confronted when taking a
measurement:
1.
the possibility of ERROR during the measurement
ERROR = difference between a measured value
and the true or accepted value.
Error is a measure of ACCURACY
2.
CAUSE-Systematic errors that bias results in one
direction. CAN be eliminated
some unavoidable UNCERTAINTY in measurement
UNC can only be estimated as ± ____
It is a measure of PRECISION
CAUSE- Random errors that have no pattern.
CANNOT be eliminated, only reduced
Accurate
Inaccurate
(low systematic error) (high systematic error)
Precise - repeated
measurements
closely cluster
around a single value
that may not be the
correct value
Precise
(low random error)
Imprecise
(high random error)
Accurate repeated
measurements
cluster around
the true value
Systematic errors are not
random and can therefore
never cancel out. They
affect the accuracy but
not the precision.
2 issues to be confronted when taking measurement
1. ERRORS caused by SYSTEMATIC ERRORS
consistently cause measurement to be too large or
too small. Some common systematic errors:
- imperfections in equipment (mis-calibrated
balances, inaccurate metersticks /stopwatches),
- improper equipment use (did not tare a scale),
- presence of unaccounted for physical effects such
as air resistance, friction, drag, …
Error  measured  accepted
Error
% Error  Accepted
x100
Error is a measure of the accuracy of the measurement.
Systematic errors CAN be eliminated.
ERROR- Difference between a measured
value and actual or accepted value. It is a
measure of the accuracy of a measurement
Absolute Error  measured  accepted
Error
Re lative Error (%) 
100
Accepted
2.
Two issues must be confronted when taking a
measurement:
UNCERTAINTY caused by RANDOM ERRORS
variations in measurements that have no pattern
(reaction time, reading a scale, unavoidable
variations in starting conditions …).
Uncertainty in a measurement cannot be calculated
exactly. It must be ESTIMATED and is expressed as
Average ± Unc %Unc  Unc x100
Avr
Uncertainty is a measure of the precision of the
measurement.
Random errors can be reduced but never eliminated