What is science

1
What is science?

• An introduction to physical science

2
Overview

• Quantitative description
• Measurement systems
• English/Metric
• Standard metric units
• Metric prefixes
• Understanding Data
• Exact/inexact numbers
• Significant figures
• Calculations
• Dimensional Analysis
• Density
• Proportionalities

• The nature of science
• The Scientific Method
• Explanations and investigations
• Laws and Principles
• Models and theories

3
Measurement systems(based upon standardized
units)

• English system
• Many units based upon parts of the human body
• Different units are not systematically related

• Metric (SI) system
• Established in 1791
• 7 base units meter (m), kilogram (kg), second
  (s), ampere (A), kelvin (K), mole (mol) and
  candela (cd)
• All other units derive from these

4
Fig. 1.5
5

• Ever wonder why there are 2 cups in a pint, 2
  pints in a quart, but 4 quarts in a gallon?

6
Table 1.1
7
Measurement systems(based upon standardized
units)

• English system
• Many units based upon parts of the human body
• Different units are not systematically related

• Metric (SI) system
• Established in 1791
• 7 base units meter (m), kilogram (kg), second
  (s), ampere (A), kelvin (K), mole (mol) and
  candela (cd)
• All other units derive from these

8
Metric prefixes

• Simplify the conversion process
• Help avoid writing large or small numbers
• A movie giving a perspective on powers of ten.

9
Table 1.3
Know these prefixes
10
Four Fundamental Properties

• Length, Mass, Time, Charge
• These cannot be defined in simpler terms.
• Can be used in combination to described
  everything observed in nature.
• Ex. Area length x length
• Speed length/time

11
SI units for the 4 fundamental properties

• Length meter (m)
• Distance light travels in 1/299,792,458s
• Mass kilogram (kg)
• Referenced to standard metal cylinder
• Time second (s)
• Referred to oscillation of cesium atom
• Charge (See electricity lecture)
• All other properties (e.g. volume) can be derived
  from these
• Physics calculations are done in these SI units!
• Speed m/s Force(Newtons) kgm/s2
• Work or Energy (Joule) kgm2/s2 Power (Watt)
  kgm2/s

12
Understanding Data

• Exact and inexact numbers
• Significant Figures

13
Exact and Inexact Numbers

• Numbers that have to be measured are always
  inexact. (how tall? 6.????....)most English to
  metric conversions are inexact
• Exact numbers have no uncertainty. They come
  from defined values (3ft/yd) or integer counts of
  values (14 students)  
• Inexact numbers limit calculations
• Exact number dont

14
Significant Figures

• Indicates the exactness of a measurement.
• The number of significant figures (digits) is a
  measure of the certainty of a measurement. The
  greater the number of significant digits, the
  less uncertain a number is.
• In calculations inexact data yields inexact
  answers. How exact is answer?

15
The Number of Significant Figures in a
Measurement Depends Upon the Measuring Device
Figure 1.14
16
Reading a Volumetric Device
Insert figure 3.13
Note the Meniscus
17
Rules for Significant Figures

• 1. nonzero digits always sig
• ex 45 - 2 sig figs , 1.37 - 3 sig figs
• 2. captive zeros must be significant
• ex 1001 - 4 sig figs , 1.0005 - 5 sig figs
• 3. leading zeros are not significant
• ex .004 - 1 sig digit, 0.0045 2 sig digits
• 4. trailing zeros are significant if there is a
  decimal point
• ex .00400 - 3 sig figs, 1000. - 4 sig figs
• 5. zeros at end, no decimal point ???
• ex 1000 1,2,3,or 4 sig figs?? must assume only 1
  s.f.

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If the Number Has No Decimal Point

• In the measurement 9500 m. It would be assumed
  that the zeros are not significant. Scientific
  notation is used to show which zeros are
  significant
• 9.5 x 103 has 2 significant digits.
• 9.50 x 103 has 3 significant digits.
• 9.500 x 103 has 4 significant digits

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How many significant figures does each of the
following have?

• .0005
• 10,000
• 1.230 x 105
• 53900.
• 10010
• 0.020
• .000300400500

• 1
• 1
• 4
• 5
• 4
• 2
• 9

20
How to write 1000 with varying significance.

• 1 s.f.
• 2 s.f.
• 3 s.f.
• 4 s.f.
• 7 s.f.

• 1000 or 1 x 103
• 1.0 x 103
• 1.00 x 103
• 1000. Or 1.000 x 103
• 1.000000 x 103

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Rules for Significant Figures in Answers
1. For addition and subtraction. The answer has
the same number of decimal places as there are
in the measurement with the fewest decimal
places.
Example adding two volumes
106.78 mL 106.8 mL
Example subtracting two volumes
863.0879 mL 863.1 mL
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Rules for Significant Figures in Answers
2. For multiplication and division. The number
with the least certainty limits the certainty of
the result. Therefore, the answer contains the
same number of significant figures as there are
in the measurement with the fewest significant
figures.
Multiply the following numbers
9.2 cm x 6.8 cm x 0.3744 cm
23.4225 cm3 23 cm3
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Issues Concerning Significant Figures
be sure to correlate with the problem
FIX function on some calculators
graduated cylinder
60 min 1 hr
numbers with no uncertainty
1000 mg 1 g
These have as many significant digits as the
calculation requires.
24
Significant Figures and Rounding
PLAN
In (a) we subtract before we divide for (b) we
are using an exact number.
SOLUTION
2.104 cm
4.16 g/ cm3
25
How many Sig. Figs should be in the following
answer?

• 19.3 18.4
• 1.07

• .841121495

.8 1s.f.
26
Dimensional Analysis

• Method by which units (dimensions) are used to
  help solve problems, and check answers.

27
Calculations with Dimensional Analysis

• 1. Use equivalence statement to get conversion
  factor.
• 2. Pick conversion factor that cancels
  appropriate unit.
• 3. Multiply quantity by conversion factor.
• 4. Check Sig Figs.
• 5. Ask whether your answer makes sense.

28
Relationships to Know

• English unit relationships
• Metric prefixes
• 1cm3 1mL
• 2.54 cm 1 in.
• 454 g 1 lb.
• 1L 1.057 qt.

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Example Conversions

• Convert
• .3704 m to cm
• 5.6 cm to inches
• .0478 mg to ?g
• 351 in3 to cm3, and L
• 200. ml to fluid ounces
• 95 kmph to ft/s

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Example Problems

• Solve
• A faucet dripping 53 drops every minute adds how
  many gallons to your monthly water bill? It
  takes approximately 19 drops to equal 1 ml.
• How much does it cost a month to run a 100W light
  that only runs about 10 hours every night? The
  cost of electricity is .06048/KWHr

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Density

• Which is heavier a pound of feathers or a pound
  of lead?
• What is density?
• Mass per unit volume
• Density mass/volume
• Intensive/characteristic property
• Solids g/cm3, liquids g/ml, gases g/L
• An object will float in/on another if it is less
  dense.
• Q A student took an unknown liquid and
  discovered that a volume of 9.02 mL had a mass of
  8.31g. Calculate the density.
• A d m/v 8.31g/9.02mL 0.921 g/mL

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Densities of Some Common Substances
Table 1.5
Substance Physical State
Density (g/cm3)
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Density

• Q Calculate the mass of a 30.0 mL sample of a
  substance which has a density of 0.92 g/mL.
• A d m/v m d x v (0.92g/mL)x(30.0mL)

28 g
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Density

• What is the mass of 2.5 L of ethanol?
• A d m/v m d x v
• (0.789g/mL)x(2.5L)x(1000mL/L)
• 1972.5 g
• 2.0 x 103 g

35
Proportionality Statements

• Direct proportionality
• How is the circumference of a circle related to
  its diameter?
• As the diameter of a circle gets larger, so does
  its circumference.
• Therefore the circumference of a circle is
  directly proportional to its diameter.
• C ? D

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Proportionality Statements

• Inverse proportionality
• How are the speed you drive and the time it takes
  you to get to class related?
• Faster speed means shorter time.
• This is an inversely proportional relationship
• Speed ? 1/Time

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Proportionality Statements

• Proportionality constants
• Constants can often turn a proportionality
  statement into an equation.
• The equation for the circumference of a circle
• Remembering that C ? D
• C kD
• Where k 3.14159.
• Often symbolized ?

38
Box Fig. 1.2
Light intensity with distance. An inverse
square relationship.
39
The nature of science

• Beginnings 300 years ago
• Associated with Galileo and Newton
• Ancient natural philosophers - thinking only
• Additional component here - understanding based
  upon experimental evidence

40
Scientific Laws

• Law - a statement that summarizes experimental
  facts, where behavior is consistent and has no
  known exceptions
• ex. Law of Conservation of Mass
• Laws summarize facts, but do not explain.

41
Hypothesis

• a tentative, reasonable explanation of the facts,
  or a law

42
Theory

• A well established explanation that has withstood
  extensive testing
• Does not represent absolute truth
• Explains phenomena and makes accurate predictions