Transcript Basic Science Information - Mr. Sapone's SHHS Portfolio

Basic Science Information
•Exponent Rules & Scientific Notation
•Units and the M-K-S System
•Dimensional Analysis
•Significant Figures
•Variables and the Scientific Method
By Vincent Sapone
What is Science?
• Study of the world around us.
• Uses observation and experimentation, logic,
reason.
• Makes predictions, is testable and is generally
repeatable.
Types of Science
• There are a ton of different branches to science:
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If it stinks its probably Chemistry.
If its Slimy its probably Biology.
If its Broken its probably Physics.
If you can’t lift it its probably geology.
If you can’t predict its probably meteorology.
If you can’t get there its probably Astronomy
If it makes no sense its quantum mechanics or relativity.
If it assumes cows are spherical its probably Mathematics.
Scientific Notation
Exponential Notation is useful to science because
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Very small numbers are used.
Very large numbers are used
It is also easier to solve large numbers adding exponents.
It uses factors of ten and accommodates metric system.
• Example: Rest Mass of Electron =
• Compare that to 9.11x10^-31
0.000000000000000000000000000000911 kg
Exponential Numbers: Powers of 10
• Any Number written as A x 10B
• A is usually between 1 and 10
• B is usually an integer.
• Example I: 93,450,000 
9.345 x 107
• 7th power means move the decimal place right 7 places.
• Example II: 0.0001728  1.728 x 10-4
• The - 4th power means to move the decimal place to the left
4 places.
Exponent Rules
• Rule 1
• Example
Exponent Rules
• Rule 2
• Example
Exponent Rules
• Rule 3
• Proof from Rule 1:
Exponent Rules
• Rule 4
• Example
Why Scientific Notation is Easier
Example:
6,350,000,000 x 424,000,000 = 6.35 x10^9 x 4.24x10^8.
• Using rule one we add the exponents (8+9) and multiply the
leading numbers (6.35 x 4.24). This is an easier calculation to
perform.
• Answer =
(6.35 x 4.24) x 10^17
Scientific Notation
• Example Problems
• Homework Assignment
Units, Conversions & M-K-S System
System
Length
Mass
Time
MKS
Meter (m)
Kilogram (kg)
Second (s)
CGS
Centimeter (cm)
Gram (g)
Second (s)
British
Foot (ft)
Pound (lb)
Second (s)
• In science we use the MKS system
•The mks system is preferred because its
units are divisible by 10.
Metric
Prefixes
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yotta- (Y)
zetta- (Z)
exa- (E)
peta- (P)
tera- (T)
giga- (G)
mega- (M)
kilo- (k)
hecto- (h)
deka- (da)
deci- (d)
centi- (c)
milli- (m)
micro- (µ)
nano- (n)
pico- (p)
femto- (f)
atto- (a)
zepto- (z)
yocto- (y)
1024 1 septillion
1021 1 sextillion
1018 1 quintillion
1015 1 quadrillion
1012 1 trillion
109 1 billion
106 1 million
103 1 thousand
102 1 hundred
10 1 ten
10-1 1 tenth
10-2 1 hundredth
10-3 1 thousandth
10-6 1 millionth
10-9 1 billionth
10-12
1 trillionth
10-15
1 quadrillionth
10-18 1 quintillionth
10-21
1 sextillionth
10-24
1 septillionth
Conversion is Easier
Three Yards into Feet
Three Meters into Centimeters
• 3 goes to 36
• We have a new number.
• 3 goes to 300
• Decimal moves two places
The MKS jut moves the decimal to the right two places. Much more convenient
especially when dealing with the very large and small numbers of science.
Universal System
• It is convenient to use one system so that we
understand the numbers.
• If I said tomorrows High will be 283 kelvins what
does that tell you?
• Likewise, if I said it will be 10 degrees C?
• Also if I said John has a speed of 7 what does that
tell you? You need to ask 7 what?
Special Units:
• Example: Newton
• Example: Joule
(kg m/s^2)
(kg m^2/s^2 )
[F=MA]
[KE = (1/2)mv^2
• Do KE and PE have the same Units? (mgh and 1/2mv^2).
Dimensional Analysis & Unit Conversion
• We often need to convert between units in science.
• Suppose a truck on the highway was traveling at 65
km per hour and I wanted to know its speed in miles
per hour or meters per second.
Problem 1 (Level I)
• Problem 1: Convert 10 miles into centimeters.
• Solution: First we must find a Conversion Factor and
set it up so the units cancel. A conversion factor is
essentially equal to One.
• Conversion Factor: 1 Mile = 1.609 Kilometers so we
first convert the 10 miles into kilometers:
•1.609 kilometers = 1 mile is the conversion factor
•The units of miles cancel in division.
•Now we convert kilometers to meters and then meters to centimeters
Problem 2 (level II)
• Problem 2: Convert 60 milers per hour into meters
per second.
• Solution: We must convert both miles into meters
and hours into seconds.
• Conversion Factor: 1 Mile = 1.609 Kilometers so we
first convert the 60 miles into kilometers:
Problem 3 (level II)
• Problem 3: Determine the units of the gravitational
constant
Solution: the left hand of an equation must always have the same unit
Gravitational Constant = 6.67 x 10^-11 ((m^3)/ (s^2* kg)
Problem 4 Level (II)
• Problem: Show that G also = (N*M) / KG^2
• Solution: Find the units for Newtons the same way we did for the
Gravitational Constant.
Significant Figures
• Important b/c of measured vs. known numbers.
• E.g., the length of a desk versus the # of desks in a room.
• Think of some other examples…
• There are ALWAYS errors in measurements.
• Sigfigs tell us that the result of any experiment cannot be
more accurate than the data used.
• Sigfig’s let readers know the accuracy you used in an
experiment.
SigFig Example
• Suppose I ask you to measure the length of a
desk with a meter stick.
• You tell me it is 0.756563874 meters.
• Should I applaud you for your high level of
precision and accuracy?
Significant Figures
• Did you really read the meter stick with your
naked eye to a hundred millionth of a meter?
• Your naked eye is not that precise and your
value is suspect.
Reading a Meter Stick
• A meter sticks’ smallest division is usually cm.
• The best we can do is estimate one doubtful
figure after centimeters.
• An object is between 45 and 46 centimeters and
you estimate it at 45.6 cm.
• 45 can be considered a known or number while
the .6 is a measured or doubtful one.
• The Significant Figures of a measured value
include those numbers directly readable from
a measuring device plus one doubtful figure.
• Calculators make errors since they assume all
numbers are known.
Measured Numbers
When you use a measuring tool is used to
determine a quantity such as your height or
weight, the numbers you obtain are called
measured numbers.
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)
=2
cm
2.?? cm
Second digit (known) = 0.6 2.6? cm
Third digit (estimated) between 0.05- 0.07
Length reported
=
2.65 cm
or
2.66 cm
or
2.67 cm
Known + Estimated Digits
 Known digits 2 and 6 are 100% certain
 The third digit 5 is estimated (uncertain)
 In the reported length, all three digits
(2.65 cm) are significant including the estimated
one
Learning Check
. l8. . . . I . . . . I9. . . .I . . . . I10. .
cm
What is the length of the line?
How does your answer compare with your
neighbor’s answer? Why or why not?
Solution
. l8. . . . I . . . . I9. . . . I . . . . I10. .
cm
Estimate to the hundreth’s place (0.01 cm)
The estimated digit may be slightly different.
Learning Check
l5. . . . I . . . . I 6. . . . I . . . . I 7. .
What is the length of the line?
1) 6.2 cm
2) 6.199 cm
3) 6.18 cm
cm
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
What is the length of the line?
First digit
4.?? cm
Second digit
4.5? cm
Last (estimated) digit is
4.50 cm
cm
Exact Numbers
Obtained when you count objects
2 soccer balls
1 watch
4 pizzas
Obtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cm
Not obtained with measuring tools
Learning Check
A. Exact numbers are obtained by
1. measuring
2. counting
3. definition
B. Measured numbers are obtained by
1. measuring
2. counting
3. definition
Solution
A. Exact numbers are obtained by
2. counting
3. definition
B. Measured numbers are obtained by
1. Using a measuring tool
Learning Check
Classify each of the following as an exact (1)
or a measured (2) number.
A.___Gold melts at 1064°C
B.___1 yard = 3 feet
C.___A red blood cell with diameter 6 x 10-4 cm
D.___There were 6 hats on the shelf
E.___A can of soda contains 355 mL of soda
Solution
Classify each of the following as an exact (1) or a
measured(2) number. Give reason.
A. 2 Requires a thermometer(measuring tool)
B. 1 From a definition in U.S. system
C. 2 Need measuring tool to determine
D. 1 Counted the hats
E. 2 Measured
Significant Figures
1. All non-zero numbers are always significant (e.g. 123456789)
2. All zeroes between non-zero numbers are significant (7007).
3. All zeroes both to the right of a decimal point and at the end of a
number are significant. (.007 has 1 sf and 700 = 1 but 7.00 = 3)
4. All zeroes left of a decimal point in a number > 10 are significant.
(700.4 = 4 sf)
To check #3 and #4 write the number in scientific notation. If you can
get rid of the zeroes they are not significant.
SigFig examples…
Sigfig Products and Quotients
• When multiplying or dividing, the answer
cannot have more significant figures than the
term with the least number of significant
figures.
• For example 25.2 x 2.543 = 64.0836 in a
calculator.
• The answer is 64.1 however.
Sigfig Addition and Subtraction
• In addition and subtraction the number of
decimal places is what is important.
• The answer cannot have more decimal places
than the term with the least number.
• 25 + 1 = 26 but
• 25.331 + 1.33 = 26.66 not 26.661
Sigfigs’s
• Do sample problems on the board
• Assign Homework Problems
Scientific Method
• Hypothesis is an educated guess to solve a problem.
• Theory is a better hypothesis that is backed by physical
data, etc.
• A Scientific Model is a combination of Theories
• Stellar Evolution combines theories and laws pertinent
to Nuclear Physics, Gas laws, thermodynamics and
Gravity into a cohesive whole.
SCIENTIFIC METHOD
Control Variable– stays constant in an experiment
Independent Variable – manipulated by observer
Dependent Variable – effects of the independent variable are measured
Step 1.
Observe / experiment (gather data).
Step 2.
Hypothesize (explain).
Step 3.
Test the hypothesis by prediction.
Step 4.
Modify or reject the hypothesis.
GENERALIZE to many situations
Occam’s Razor: The explanation that makes the
fewest assumptions is the preferred one.
Variable Identification Ex. 1
Can blueberries slow down aging?
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A study indicates that antioxidants found in blueberries may slow down the
process of aging. In this study, 19-month old rats (equivalent to 60-year old
humans) were fed either their standard diet or a diet supplemented by either
blueberry, strawberry, or spinach powder. After eight weeks, the rats were given
memory and motor tests. Although all supplemented rats showed improvement,
those supplemented with blueberry powder showed the most notable
improvement.
• What is the independent variable? (diet: blueberries or no blueberries)
• What are the dependent variables? (memory test and motor skills test)
• What are the Control variables? (same rates, same equipment used in
tests, et al)
Variable Identification Ex. 2
Does beta-carotene protect against cancer?
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Beta-carotene supplements have been thought to protect against cancer.
However, a study published in the Journal of the National Cancer Institute
suggests this is false. The study was conducted with 39,000 women aged 45
and up. These women were randomly assigned to receive a beta-carotene
supplement or a placebo, and their health was studied over their lifetime.
Cancer rates for women taking the beta-carotene supplement did not differ
systematically from the cancer rates of those women taking the placebo.
• Independent variable? (supplements, beta-carotene, placebo)
• What are the dependent variables? (occurrence of cancer)
• What are the Control variables? (same equipment used in
tests, et al)
Variable Identification Ex. 3
How bright is right?
• An automobile manufacturer wants to know how bright brake lights
should be in order to minimize the time required for the driver of a
following car to realize that the car in front is stopping and to hit the
brakes.
• What is the independent variable? (brightness of brake light)
• What is the dependent variable? (time to hit brake)
• What are some control variables (same equipment, same driver, same
cars, the same lighting is used during the test)
Variable Identification Ex. 4
Class Activity!!
• We will now come up with something we want to test. It can be anything,
e.g. how does temperature impact how high a basketball bounces. Once
the issue and method are figured out we will label the following:
• What is the independent variable?
• What is the dependent variable?
• What are some control variables?