Physics
Fifth Edition
Lecture Outline
Chapter 1
Introduction to Physics
Lecture Outlines by
Douglas Sherman,
San Jose State University
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Chapter 1: Introduction to Physics
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Units of Chapter 1
• Physics and the Laws of Nature
• Units of Length, Mass, and Time
• Dimensional Analysis
• Significant Figures, Scientific Notation, and Round-Off
Error
• Converting Units
• Order-of-Magnitude Calculations
• Scalars and Vectors
• Problem Solving in Physics
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1-1 Physics and the Laws of Nature
• Physics: the study of the fundamental laws of nature
– These laws can be expressed as mathematical
equations
– Much complexity can arise from relatively simple laws
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1-2 Units of Length, Mass, and Time (1 of 6)
• SI units of length (L), mass (M), time (T):
– Length: the meter
▪ Was: one ten-millionth of the distance from the
North Pole to the equator
▪ Now: the distance traveled by light in a vacuum in
1 299,792,458 of a second
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1-2 Units of Length, Mass, and Time (1 of 6)
– Mass: the kilogram
– Was: based on the weight of a cubic centimeter of
water at sea level and pressure. The “gram” was 1
cm3, but was deemed too small for many practical
larger scale uses, so the SI unit became the
“kilogram” and remains the only SI unit to have a
prefix.
NOW: One kilogram is the mass of a particular
platinum-iridium cylinder kept at the International
Bureau of Weights and Standards, Sèvres, France.
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1-2 Units of Length, Mass, and Time (2 of 6)
– Time: SI unit is the “second”
▪ WAS defined as “1-60th of a “minute”, which was
“1-60th” of an hour, which was “1-12th” of the length
of sunlight seen during either solstice (or 1/24th of
the length of one entire day). This made it so: 1
second = 1 / 86 400th of one day.
▪ NOW: One second is the time for radiation from a
cesium-133 atom to complete 9,192,631,770
oscillation cycles.
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1-2 Units of Length, Mass, and Time (3 of 6)
Table 1-1 Typical Distances
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1-2 Units of Length, Mass, and Time (4 of 6)
Table 1-2 Typical Masses
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1-2 Units of Length, Mass, and Time (5 of 6)
Table 1-3 Typical Times
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1-2 Units of Length, Mass, and Time (6 of 6)
Table 1-4 Common Prefixes
Power
Prefix
Abbreviation
1015
peta
P
1012
tera
T
109
giga
G
106
mega
M
103
kilo
k
102
hecto
h
101
10 raised to power 1
deka
da
10 −1
deci
d
10 −2
centi
c
10 −3
milli
m
10 −6
micro

10 −9
nano
n
10 −12
pico
p
10 −15
femto
f
10 raised to power 15
10 raised to power 12
10 raised to power 9
10 raised to power 6
10 raised to power 3
10 raised to power 2
10 raised to power negative 1
10 raised to power negative 2
10 raised to power negative 3
10 raised to power negative 6
10 raised to power negative 9
10 raised to power negative 12
10 raised to power negative 15
mu
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1-3 Dimensional Analysis
• Any valid physical formula must be dimensionally consistent—each
term must have the same dimensions
Table 1-5 Dimensions of Some
Common Physical Quantities
• From the table:
Distance = velocity  time
Quantity
Dimension
Velocity = acceleration  time
Distance
[L]
Energy = mass  ( velocity )
Area
[L2 ]
2
Volume
left bracket L right bracket
left bracket L squared right bracket
[L3 ]
left bracket L cubed right bracket
Velocity
[L] [T]
Acceleration
[L] [T 2 ]
Energy
start fraction left bracket L right bracket over left bracket T right bracket end fraction
start fraction left bracket L right bracket over left bracket T squared right bracket end fraction
[M] [L2 ] [T 2 ]
start fraction left bracket M right bracket left bracket L right bracket over left bracket T squared right bracket end fraction
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1-3 Dimensional Analysis
• Any valid physical formula must be dimensionally consistent—each
term must have the same dimensions
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1-3 Dimensional Analysis
• Any valid physical formula must be dimensionally consistent—each
term must have the same dimensions
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (1 of 4)
• Accuracy of measurements is limited
• Significant figures: the number of digits in a quantity
that are known with certainty
• Examples:
– The event took 12.56 seconds
– He jumped a height of 57cm
– The whale had a mass of 3451 kg
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (2 of 4)
d=Vxt
• Significant figures:
– Example: A tortoise travels at 2.51 cm s for 12.27 s.
How far does the tortoise go?
– Answer:
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
• RULES for Significant Figures:
– For x or / : can only keep the number of digits
found in the least precise element of the calculation
– For + or - : can only keep the largest placeholder
decimal found in any elements in the calculation
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
Try this: Take the handout page with the ruler dimensions
printed on them, and find the area of the page (in cm2) and also
the perimeter of the page (in cm). Determine how you would
choose the significant digits to get the most acceptable answer
for each.
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
Try this: Find the total height (in cm) of everyone in your row. What
happens to the significant figures in this case?
Eg)
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
Some other factors to consider:
You want to use a measurement that shows 750 km. How many significant
digits is this? (it depends on the method that was used to determine this
number).
* if the measurement method is unknown, you can only keep 2 significant digits. (the "0" is
only a placeholder)
* if the measurement came from a car's odometer, and it is accurate to the nearest
kilometer, the "0" counts, and you can keep all 3 significant digits.
* if the measurement was from a trip meter accurate to the nearest 100 meters, it would
need to be displayed as 750.0 km, and the trailing "0" indicates that this value is known,
and we can now use 4 significant digits.
* If the measurement came from modern GPS, accurate to the nearest meter, it would be
written as 750.000 km and contains 6 significant digits.
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (3 of 4)
A rectangular solid has dimensions of 4.5cm
long, 1.87cm tall and 2.2cm thick. What is
its volume?
If this same block has a mass of 48.453g,
what is the density of the block?
m
-
p V
m (mass)
p (density)
V (volume)
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V=d/t
1-4 Significant Figures
Context is important. Sometimes, the apparent
precision is not the actual precision.
Eg) The current world record for the 100m freestyle swimming race was
just broken last month and currently stands at 46.40 seconds. What is
the average speed for the swimmer who broke this record?
Problem – what assumptions should we make about
the distance “100 m” for the precision and significant
digits of the answer?
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (3 of 4)
• Scientific notation
– Leading or trailing zeroes can make it hard to determine
number of significant figures: 2500, 0.000036
▪ Each of these has two significant figures
– Scientific notation writes these as a number from 1–10
multiplied by a power of 10, making the number of
significant figures much clearer: 2500 = 2.5  103
▪ If we write 2.50  103 , it has three significant figures.
0.000036 = 3.6  10 –5
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1-4 Significant Figures, Scientific
Notation, and Round-Off Error (4 of 4)
• Round-off error:
– The last digit in a calculated number may vary
depending on how it is calculated, due to rounding off
of insignificant digits
• Example:
–
$2.21 + 8% tax = $2.3868, rounds to $2.39
–
$1.35 + 8% tax = $1.458, rounds to $1.46
–
Sum : $2.39 + $1.46 = $3.85
–
$2.21 + $1.35 = $3.56
–
$3.56 + 8% tax = $3.84
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1-5 Converting Units
• Converting feet to meters:
1 m = 3.281 f t
eters
ee
(this is the conversion factor)
The Zlin 242 has a wingspan of 29ft 10in and a 23ft 2in. What are these
dimensions in meters?
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1-5 Converting Units
1 kn = 1.852 km/h
1 m = 3.2808 ft
Converting blended (multi) units:
The Zlin has a cruising speed of 108 knots and a climb rate of 850 feet
per minute (fpm). Convert both of these values to the SI units for
speed (m/s).
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1-5 Converting Units
1 ha = 10 000 m2
1 m = 3.2808 ft
RULES for significant digits and converting units:
The answer in any unit conversion MUST HAVE the same number of
significant digits as the value you started with (the answer can't become
more precise or less precise just because you converted the units).
Eg) A homeowner measures his property and discovers that he has a
rectangular lot with a length of 1212 ft and a width of 442 ft. What is the
area of the property in hectares?
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1-5 Converting Units
Converting multi-variable units:
* Identify which unit is a numerator and which is the denominator if the unit has
fractions identifying it (like m/s, lbs/in2, ft/s2), and match those to the target unit
you want to end up with.
Eg) Your car was travelling 32.3 m/s in a 90km/h zone. Are you speeding in this zone?
Eg) Human hair grows about 0.35mm per day. If you have about 100 000 hairs on your
head, how much hair (in m) do you grow if you wait 3 months between hair cuts?
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1-7 Scalars and Vectors
• Scalar: a numerical value. May be positive or negative.
Examples: temperature, speed, height
• Vector: a quantity with both magnitude and direction.
Examples: displacement (e.g., 10 feet [north]), force,
magnetic field, velocity
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1-7 Scalars and Vectors
• Scalar:
– Sudbury’s airport is 333km from the Sault Airport
– The plane weighs 1642 lbs
– The air pressure was 101.9 kPa
• Vectors:
– Sudbury’s Airport is 285km [E 5o N] of the Sault Airport
– The plane’s “airspeed” was 132 kn [ 142o ]
– The car experienced a force of 1200N [NW]
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1-7 Scalars and Vectors
• Scalar:
– Sudbury’s airport is 358km from the Sault Airport
• Vector:
– Sudbury’s Airport is 285km [E 5o N] of the Sault Airport
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1-7 Scalars and Vectors
• Vectors: can be described in a number of different ways.
• 1-Dimensional Vectors
– Eg)
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N
1-7 Scalars and Vectors
40o
• 2-Dimensional Vectors
– Eg)
Options:
A) 400kn [ E 40o S ]
B) 400kn [ 40o S of E ]
C) 400kn [ @ 130o]
or
400 cos (40o) = 306 kn [E]
D) 306 kn [E] + 257 kn [S]
40o
400 sin (40o) = 257 kn [S]
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1-7 Scalars and Vectors
N
N
45o
15o
25o
N
N
165o
5000 N
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A review of trigonometry ratios:
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1-7 Scalars and Vectors
Some practice problems:
P1-1) From a start, you walk 4200ft in the direction [ E32oN]. How far
East and how far North did you end up walking?
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1-7 Scalars and Vectors
Some practice problems:
P1-2) You walk across a field by heading N15oW.
a) If you turn around and walk back, what heading did you take?
b) What are you headings (out and back) expressed in two alternate
ways?
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1-7 Scalars and Vectors
Some practice problems:
P1-3) A roof has a “4-12 pitch”, which is used to describe the “rise”
and “run” of the roof’s slope. If your house is 28ft wide with the peak in
the middle;
a) What is the height of the peak of the roof?
b) What is the distance along the roofline from the bottom to the top?
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1-7 Scalars and Vectors
Some practice problems:
P1-4) A roof has a “4-12 pitch”, which is used to describe the “rise”
and “run” of the roof’s slope. If your house is 28ft wide with the peak in
the middle;
a) What is the height of the peak of the roof?
b) What is the distance along the roofline from the bottom to the top?
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1-7 Scalars and Vectors
Some practice problems:
P1-5) Your plane descends at a slope of 7.5 degrees below
horizontal. If your plane flies 4.00 km horizontally during the decent,
how far down did your elevation drop, in feet, during this decent?
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1-8 Problem Solving in Physics
• No recipe or plug-and-chug works all the time, but here
are some guidelines:
1. Read the problem carefully
2. Sketch the system
3. Visualize the physical process
4. Strategize
5. Identify appropriate equations
6. Solve the equations
7. Check your answer
8. Explore limits and special cases
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1-8 Problem Solving in Physics
GRASP method of problem solving:
G = Given (list the variables you will be using and provide the
values that are given in the question.
R = Required (beside any variables that are not provided, but are
going to be needed, draw a box to show that this needs to be
answered.)
A = Analyze (choose the formulas needed for solving the problem,
and write the formulas).
S = Solve (do the math to find the answer)
P = Paraphrase ( the final “therefore” statement to summarize
your solution).
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Summary of Chapter 1 (1 of 2)
• Physics is based on a small number of laws and
principles
• SI Units of length are meters; of mass, kilograms; and of
time, seconds, but in your program, you will also
frequently be dealing with many non-SI units and you
may need to convert from one to the other.
• All terms in an equation must have the same dimensions
• The result of a calculation should have only as many
significant figures as the least accurate measurement
used in it
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Summary of Chapter 1 (2 of 2)
• Convert one unit to another by multiplying by their
conversion ratio
• Order-of-magnitude calculations are designed to be
accurate within a power of 10
• Scalars are numbers; vectors have both magnitude and
direction
• Problem solving: read, sketch, visualize, strategize,
identify equations, solve, check, explore limits
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