Survey of physical Science

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Shipman14e_9781305079137_chapter11.ppt

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James T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Omar Torres

Measurement

Chapter 1

Description leading to understanding of our environment
Description involves the measurement of the physical world
Understanding our environment demands the interpretation of accurate measurements (i.e., data)
Therefore, understanding measurement is essential

Intro

Science

Sophisticated methods of measurement have been developed
Measurements – movement, temperature, weather conditions, time, etc.
The constant use of measurements are in this book, including many examples
Can everything be measured with certainty?
As smaller and smaller objects were measured it became apparent that the act of measuring actually distorted the object

Intro

Measurement

Subset of the Natural Sciences, together with Biological Sciences
Physical Sciences: Physics, Chemistry, Geology, Meteorology, and Astronomy
This book covers the fundamentals of each of the five Physical Sciences

Section 1.1

What is Physical Science?

Section 1.1

The Major Physical Sciences

Measurements are the basis of scientific research/investigation
Phenomena are observed, resulting in questions of how or why these phenomena occur
Scientists assume that the universe is orderly and can be understood

Section 1.2

Scientific Investigation

Scientific Method – general methods of observations, rules for reasoning, and making predictions
Can be broken down into:
Observations & Measurements
Hypothesis
Experiments
Theory
Law

Section 1.2

Scientific Method

Quantitative data are gathered

Section 1.2

Observations & Measurements

Hypothesis – a possible explanation for the observations
Example: Matter consists of small particles (atoms) that simply rearrange themselves
A tentative answer or educated guess
New experiments are designed to test the validity of the hypothesis
The Hypothesis is supported if it correctly predicts the experimental results

Section 1.2

Hypothesis

The testing, under controlled conditions, to determine if the results support or confirm the hypothesis
Experimental results can be duplicated by other researchers
No concept or model of nature is valid unless the predictions are in agreement with experimental results.

Section 1.2

Experiments

Theory – tested explanation for a broad segment of basic natural phenomena
Example: Atomic Theory – This theory has withstood testing for 200+ years.
Depending on continued experimentation, theories may be accepted, modified, or rejected

Section 1.2

Theory

Scientific Law – after a series of experiments a concise statement (words/math) describes a fundamental relationship of nature
Example – Law of Conservation of Mass (no gain or loss during chemical reaction)
The law simply states the finding, but does not explain the behavior

Section 1.2

Scientific Law

Section 1.2

The Scientific Method

Sight, hearing, smell, taste, touch
Sight and hearing provide the most information to our brains about our environment
Sensory limitations – can be reduced by using measuring devices
Instruments extend our ability to measure and learn about our environment
Our senses can also be deceived

The Senses

Lines “a” and “b” are equal in length!

Some Optical Illusions

Optical Illusions

The lines are all horizontal!

Section 1.3

Some Optical Illusions

Section 1.3

Some Optical Illusions

Expressed in magnitude and units
Fundamental quantities – length, mass, & time
The study of Force and Motion requires only these three quantities
Standard Unit – fixed and reproducible value to take accurate measurements

Section 1.4

Standard Units
and Systems of Units

Two major systems of units
British (English) system – only used widely in the United States (miles, inches, pounds, seconds, etc.)
Metric system – used throughout most of the world (kilometers, meters, grams, etc.)
The U.S. “officially” adopted the metric system in 1893, but continues to use the British system

Section 1.4

Standard Units and Systems of Units (cont.)

The measurement of space in any direction
Space has three dimensions – length, width, and height
Metric Standard Unit = Meter (m), originally defined as 1/10,000,000 of distance from equator to north pole
British Standard Unit = Foot, originally referenced to the human foot

Section 1.4

Length

Originally defined as

a physical quantity of nature.

1/10,000,000 of the distance from the equator to the pole

Section 1.4

The Meter

The meter is now defined by the distance light travels in a vacuum/time.

The Meter

The amount of matter an object contains
An object’s mass is always constant
Mass is a fundamental unit that will remain constant throughout the universe
Metric Standard Unit = Kilogram (kg) – originally defined as the amount of water in a 0.1-m cube. Now referenced to a cylinder in Paris

Section 1.4

Mass (metric)

U.S. Prototype #20 Kilogram, at NIST in Washington, D.C. Actually – 0.999 999 961 kg

Section 1.4

Kilogram Standard

British Standard Unit = Slug (rarely used)
We use the Pound (lb)
The pound is actually not a unit of mass, but rather of weight, related to gravitational attraction (depends on where the object is!)
Object: Earth = 1 lb  Moon = 1/6 lb
In fact, the weight of an object will vary slightly depending on where it is on Earth (higher altitude  less weight)

Section 1.4

Mass (British)

Section 1.4

Mass is a Fundamental Quantity and Remains Constant – Weight Varies

Time – the continuous, forward flowing of events
Time has only one direction  forward
Second (s) – the standard unit in both the metric and British systems
Originally 1/86,400 of a solar day
Now based on the vibration of the Cs133 atom (Atomic Clock)

Section 1.4

Time

Originally defined as a fraction of the average solar day.

Section 1.4

A Second of Time

Defined by the radiation frequency of the Cs133 atom

Section 1.4

A Second of Time

Uses acronym “mks system” from standard units of length, mass, and time – meter, kilogram, second
It is a decimal (base-10) system – this is much better than the British system
Administered by – Bureau International des Poids et Mesures (BIPM) in Paris
International System of Units (SI)
Contains seven base units

Section 1.4

Metric System

The fundamental units are a choice of seven well-defined units which by convention are regarded as dimensionally independent:
meter, m (length)
kilogram, kg (mass)
second, s (time)
ampere, A (electrical current)
kelvin, K (temperature)
mole, mol (amount of a substance)
candela, cd (luminous intensity)

Section 1.5

Modern Metric System (SI)

Easy expression and conversion

Metric examples vs. British examples

1 kilometer = 1000 meters

1 mile = 5280 feet

1 meter = 100 centimeters

1 yard = 3 feet or 36 inches

1 liter = 1000 milliliters

1 quart = 32 ounces or 2 pints

1 gallon = 128 ounces

Section 1.5

Base-10  Convenient

Mega (M), 106  1,000,000 times the base
Kilo (k), 103  1,000 times the base
Centi (c), 10–2  1/100th of the base
Milli (m), 10–3  1/1000th of the base
See Appendix 1 for complete listing

Section 1.5

Commonly Used Prefixes

Liter – volume of liquid in a 0.1-m (10 cm) cube (10 cm×10 cm×10 cm = 1000 cm3)
A liter of pure water has a mass of 1 kg or 1000 grams
Therefore, 1 cubic cm (cc) of water has a mass of 1 gram
By definition 1 liter = 1000 milliliters (ml)
So, 1 ml = 1 cc = 1 g of pure water
1 ml = 1 cc for all liquids, but other liquids do not have a mass of 1 g

Section 1.5

Liter – Nonstandard Metric Unit

A liter is slightly more than a quart.

1 quart = 0.946 liter

1 liter = 1.06 quart

Section 1.5

Liter & Quart

(1 kg = 2.2046 lb on Earth)
The amount of water in a 0.10-m (10 cm) cube (0.10 m3)

Section 1.5

The Kilogram

Metric ton – mass of 1 cubic meter (1 m3) of water
1 m = 100 cm
(100 cm)3 = 1,000,000 cm3
Remember that 1000 cm3 = 1 liter
Therefore, there are 1000 liters in 1 m3 of water
Each liter has a mass of 1 kg
1 kg×1000 = 1 metric ton

Section 1.5

Metric Ton

It is difficult to make all measurements with only the 7 fundamental units
Derived units are therefore used, these are multiples/combinations of fundamental units
We’ve already used derived units: Volume  length3, m3, cm3
Area  length2, m2, ft2, etc.
Speed  length/time, m/s, miles/hour, etc.

Section 1.6

Derived Units and Conversion Factors

Density () = mass per unit volume

 = m/v [or mass/length3 (since v = length3)]

Measures how “compact” a substance is

Typical units used – g/cm3, kg/m3

Al = 2.7 g/cm3, Fe = 7.8 g/cm3, Au = 19.3 g/cm3

Average for the Earth = 5.5 g/cm3

Section 1.6

Density

Hydrometer – a weighted glass bulb
The higher the hydrometer floats the greater the density of the liquid
Pure water = 1 g/cm3
Seawater = 1.025 g/cm3
Urine = 1.015 to 1.030 g/cm3
Hydrometers are used to ’test’ antifreeze in car radiators – actually measuring the density of the liquid

Section 1.6

Liquid Densities

The denser the liquid the higher the hydrometer floats.

Section 1.5

Measuring Liquid Density

When a combination of units becomes complex and frequently used –
It is given a name
newton (N) = kg×m/s2
joule (J) = kg×m2/s2
watt (W) = kg×m2/s3

Section 1.6

Unit Combinations

Relates one unit to another unit

Convert British to Metric (inches  cm)

Convert units within system (kg  g)

We use “conversion factors”

1 inch is equivalent to 2.54 centimeters

Therefore “1 in. = 2.54 cm” is our conversion factor for inches & centimeters

Section 1.6

Conversion Factors

Question: How many centimeters are there in 65 inches?

Section 1.6

Since 1 in. = 2.54 cm 

Easy Conversion – Example

65 in. × = 165 cm (the inches cancel out!!)

Step 1 – Choose/Use a Conversion Factor, generally can be looked up.

Step 2 – Arrange the Conversion Factor into the appropriate form, so that unwanted units cancel out.

Step 3 – Multiply or Divide to calculate answer.

Use common sense – anticipate answer!

Section 1.6

Steps to Convert

for example

How fast in mi/h is 50 km/h?

Conversion Factor is 1 km/h = 0.621 mi/h

Starting Value

Conversion

Factor

Result

Section 1.6

50 km/h  ?? mi/h

Section 1.6

50 km/h  ?? mi/h

Starting Value

Conversion

Factor

Result

Either conversion factor can be used:

1 km/h = 0.621 mi/h or 1 mi/h = 1.61 km/h

How fast in km/h is 50 mi/h?

Section 1.6

50 mi/h  ?? km/h

Starting Value

Conversion

Factor

Same

Result

Section 1.6

50 mi/h  ?? km/h

Starting Value

Conversion

Factor

Same

Result

22 inches = ?? meters

Inches  centimeters  meters

Starting Value

Conv. Factor #1

in  cm

Conv. Factor #2

cm  m

Result

Section 1.6

Multi-Step Conversion –
No Problem!

Section 1.6

Starting Value

Conv. Factor #1

in.  cm

Conv. Factor #2

cm  m

Result

Multi-Step Conversion –
No Problem!

How would one express “First and 10” in meters?

Conversion Factor is 1 yd = 0.914 m

Section 1.6

Confidence Exercise 1.3

10 yd

Starting Value

Conversion

Factor

914

= ??

Result

Section 1.6

= 9.14 m

Result

Confidence Exercise 1.3 (cont.)

10 yd

Starting Value

Conversion

Factor

914

4843 m ×

= 15,885 feet above SL

(1775 feet higher than the top of Pikes Peak!)

Section 1.6

Peruvian Road Solution

Significant figures (“SF”) – a method of expressing measured numbers properly
A mathematical operation, such as multiplication, division, addition, or subtraction cannot give you more significant figures than you start with
For example, 6.8 has two SF and 1.67 has three SF

Section 1.7

Significant Figures

When we use hand calculators we may end up with results like: 6.8 ÷ 1.67 = 4.0718563
Are all these numbers “significant?”

Section 1.7

Significant Figures

General Rule: Report only as many significant figures in the result as there are in the quantity with the least significant figures.
6.8 cm ÷ 1.67 cm = 4.1 (round off 4.0718563)
6.8 is the limiting term with two SF
5.687 + 11.11 = 16.80 (round up 16.797)
11.11 is the limiting term with four SF

Section 1.7

Significant Figures

All non-zero digits are significant
Both 23.4 and 234 have 3 SF
Zeros are significant if between two non-zero digits (’captive’) – 20.05 has 4 SF, 407 has 3 SF
Zeros are not significant to the left of non-zero digits – used to locate a decimal point (leading zeros) – 0.0000035 has 2 SF
To the right of all non-zero digits (trailing zeros), must be determined from context – 45.0 has 3 SF but 4500 probably only has 2 SF

Section 1.7

Significant Figures – Rules

Exact Numbers – numbers of people, items, etc. are assumed to have an unlimited number of SF
In the process of determining the allowed number of significant figures, we must generally also ’round off’ the numbers.

Section 1.7

Significant Figures

If the first digit to be dropped is less than 5, leave the preceding digit unchanged.
Round off to 3 SF: 26.142  26.1
If the first digit to be dropped is 5 or greater, increase the preceding digit by one.
Round off to 3 SF: 10.063  10.1

Section 1.7

Rounding Off Numbers

Round off 0.0997 to two SF
0.0997  0.10
What about this? 5.0×356 = 1780
Round off 1780 to 2 SF
1780  1800

Section 1.7

Rounding off Numbers – Examples

Many numbers are very large or very small – it is more convenient to express them in ’powers-of-10’ notation
See Appendix VI
1,000,000 = 10×10×10×10×10×10 = 106

Section 1.7

Powers-of-10 Notation
(Scientific Notation)

Section 1.7

Examples of Numbers Expressed in Powers-of-10 Notation

The distance to the Sun can be expressed many ways:
93,000,000 miles
93×106 miles
9.3×107 miles
0.93×108 miles
All four are correct, but 9.3×107 miles is the preferred format

Section 1.7

Scientific Notation

The exponent, or power-of-10, is increased by one for every place the decimal point is shifted to the left.
360,000 = 3.6×105
The exponent, or power-of-10, is decreased by one for every place the decimal point is shifted to the right.
0.0694 = 6.94×10–2

Section 1.7

Rules for Scientific Notation

5.6256×0.0012 = 0.0067507

 round to 2 SF

0.0067507 rounds to 0.0068

 change to scientific notation

0.0068 = 6.8×10–3

Section 1.7

Example –
Rounding/Scientific Notation

0.0024/8.05 = 0.0002981

 round to 2 SF

0.0002981 rounds to 0.00030

 change to scientific notation

0.00030 = 3.0×10–4

**Note that the “trailing zero” is significant**

Section 1.7

Example –
Rounding/Scientific Notation

Read the problem, and identify the chapter principle that applies to it. Write down the given quantities w/ units. Make a sketch.

Determine what is wanted – write it down.

Check the units, and make conversions if necessary.
Survey equations – use appropriate one.
Do the math, using appropriate units, round off, and adjust number of significant figures.

Section 1.7

Problem Solving

The Earth goes around the Sun in a nearly circular orbit with a radius of 93 million miles. How many miles does Earth travel in making one revolution about the Sun?

Section 1.7

Problem Solving

The Earth goes around the Sun in a nearly circular orbit with a radius of 93 million miles. How many miles does Earth travel in making one revolution about the Sun?

Determine what parts of the question are important and how to attack the problem.

Section 1.7

Problem – Example

The Earth goes around the Sun in a nearly circular orbit with a radius of 93 million miles. How many miles does Earth travel in making one revolution about the Sun?

In order to solve this problem notice that you need an equation for a circular orbit (circumference, c)
The radius, r, of 93,000,000 miles is given
Our answer also needs to be in miles (convenient!)
Equation: ( = 3.14159…)

Section 1.7

Problem – Example

Circumference = ( = 3.14159…)
c = 2×3.14159×93,000,000 miles

c = 2×3.14159×9.3×107 miles
c = 58.433574×107 miles

round off and adjust to two SF

c = 5.8×108 miles
5.8×108 miles = distance that the Earth travels in one revolution around the Sun

Section 1.7

Problem Solving

Important Equation

Density:  = m/V

Section 1.7

2.54 cm

1 in.

1 inch

2.54 cm

1 inch

2.54 cm

1 inch

2.54 cm

0.621 mi/h

50 km/h31.05 mi/h

1 km/h

´=

0.621 mi/h

50 km/h31.05 mi/h

1 km/h

´=

1.61 km/h

50 mi/h80.5 km/h

1 mi/h

´=

1 km/h

50 mi/h80.5 km/h

0.621 mi/h

´=

1.61 km/h

50 mi/h80.5 km/h

1 mi/h

´=

1 km/h

50 mi/h80.5 km/h

0.621 mi/h

´=

2.54 cm1 m

22 in.0.56 m

1 in.100 cm

´´=

2.54 cm1 m

22 in.0.56 m

1 in.100 cm

´´=

3.28 ft

1 m

0.00000110

1,000,00010

===