Chapter 1
Lecture
Outline
1
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Chapter 1: Introduction
•Why Study Physics?
•Mathematics and Physics Speak
•Scientific Notation and Significant Figures
•Units
•Dimensional Analysis
•Problem Solving Techniques
•Approximations
•Graphs
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§1.1 Why Study Physics?
Physics is the foundation of every science (astronomy,
biology, chemistry…).
Many pieces of technology and/or medical equipment and
procedures are developed with the help of physicists.
Studying physics will help you develop good thinking skills,
problem solving skills, and give you the background needed
to differentiate between science and pseudoscience.
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Gain an appreciation for the simplicity of nature.
Physics encompasses all natural phenomena.
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§1.2 Physics Speak
Be aware that physicists have their own precise definitions
of some words that are different from their common English
language definitions.
Examples: speed and velocity are no longer synonyms;
acceleration is a change of speed or direction.
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§1.3 Math
Galileo Wrote:
Philosophy is written in this grand book, the universe, which stands
continually open to our gaze. But the book cannot be understood unless
one first learns to comprehend the language and read the characters in
which it is written. It is written in the language of mathematics, and its
characters are triangles, circles, and other geometric figures without
which it is humanly impossible to understand a single word of it; without
these, one is wandering in a dark labyrinth.
From Opere Il Saggiatore p. 171 by Galileo Galilei (http://www-gap.dcs.stand.ac.uk/~history/Mathematicians/Galileo.html)
Basically, the language spoken by physicists is mathematics.
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Definitions:
y  m x b
x is multiplied by the factor m.
The terms mx and b are added together.
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Example:
x
y  c
a
x is multiplied by the factor 1/a or x is divided by the factor
a. The terms x/a and c are added together.
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Percentages:
Example: You put $10,000 in a CD for one year. The APY
is 3.05%. How much interest does the bank pay you at the
end of the year?
$10,0001.0305 $10,305
The bank pays you
$305 in interest.
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Example: You have $5,000 invested in stock XYZ. It loses
6.4% of its value today. How much is your investment now
worth?
$5,000 0.936  $4,680
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n 

The general rule is to multiply by 1 

 100
where the (+) is used if the quantity is increasing and (–) is
used if the quantity is decreasing.
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Proportions:
A B
1
A
B
A is proportional to B. The value of A is
directly dependent on the value of B.
A is proportional to 1/B. The value of A is
inversely dependent on the value of B.
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Example: For items at the grocery store:
cost  weight
The more you buy, the more you pay. This is just the
relationship between cost and weight.
To change from  to = we need to know the proportionality
constant.
cost  (cost per pound) (weight)
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Example: The area of a circle is
A  r .
2
The area is proportional to the radius squared.
A r
2
The proportionality constant is .
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Example: If you have one circle with a radius of 5.0 cm and
a second circle with a radius of 3.0 cm, by what factor is the
area of the first circle larger than the area of the second
circle?
The area of a circle is proportional to r2:

A1 r
5 cm
 
 2.8
2
A2 r
3 cm
2
1
2
2
2
The area of the first circle is 2.8 times larger than
the second circle.
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Example 1.1, p 4
• Effect of Increasing Radius on the Volume
of a Sphere
– The volume of a sphere is given by the
equation V = 4/3 r3, where V is the volume
and r is the radius of the sphere. If a
basketball has a radius of 12.4 cm and a
tennis ball has a radius of 3.20 cm, by what
factor is the volume of the basketball larger
that the tennis ball?
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Practice Problem 1.1 – Power
Dissipated by a Lightbulb
• The electric power P dissipated by a
lightbulb of resistance R is P = V2/R,
where V represents the line voltage.
During a brownout, the line voltage is
10.0% less than its normal value. How
much power is drawn by a lightbulb during
the brownout if it normally draws 100.0 W
(watts). Assume that the resistance
doesn’t change.
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19
Follow up problem
• A spherical balloon is partially blown up
and its surface area is measured. More
air is then added, increasing the volume of
the balloon. If the surface area of the
balloon expands be a factor of 2.0 during
this procedure, by what factor does the
radius of the balloon change?
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• Strategy Relate the surface area S to the radius r using
S  4 r 2 .
• Solution Find the ratio of the new radius to the old.
S1  4 r12 and S2  4 r22  2.0S1  2.0(4 r12 ).
4 r22  2.0(4 r12 )
r22  2.0r12
2
 r2 
   2.0
 r1 
r2
 2.0  1.4
r1
• The radius of the balloon increases by a factor of 1.4.
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Assignment #1
• p. 19 – 2, 5, 6, and 9.
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§1.4 Scientific Notation &
Significant Figures
This is a shorthand way of writing very large and/or very
small numbers.
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Example: The radius of the sun is 700,000 km.
Write as 7.0105 km.
When properly written this number
will be between 1.0 and 10.0
Example: The radius of a hydrogen atom is 0.0000000000529
m. This is more easily written as 5.2910-11 m.
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Significant figures:
From the box on page 5:
1. Nonzero digits are always significant.
2. Final ending zeroes written to the right of the
decimal are significant. (Example: 7.00.)
3. Zeroes that are placeholders are not significant.
(Example: 700,000 versus 700,000.0.)
4. Zeroes written between digits are significant.
(Example: 105,000; 150,000.)
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Example 1.2
• For each of these values, identify the
number of significant figures and rewrite
each in its standard scientific notation.
•
•
•
•
409.8 s
0.058700 cm
9500 g
950.0 x 101 mL
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Practice Problem 1.2
• State the number of significant figures in
each of these measurements and rewrite
them in standard scientific notation.
• 0.00010544 kg
• 0.005800 cm
• 60200 s
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• Significant Figures in Calculations
– When two or more quantities are added or subtracted, the result is as
precise as the least precise of the quantities. If the quantities are
written in scientific notation with different powers of ten, first rewrite
them with the same power of ten. After adding or subtracting, round the
result, keeping only as many decimal places as are significant in all of
the quantities that were added or subtracted.
– When quantities are multiplied or divided, the result has the same
number of significant figures as the quantity with the smallest number of
significant figures.
– In a series of calculations, rounding to the correct number of significant
figures should only be done at the end, not at each step. Rounding at
each step would increase the chance that roundoff error could snowball
and have an adverse effect on the accuracy of the final answer. It’s a
good idea to keep at least two extra significant figures in calculations,
then round at the end.
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Example and Practice Problem 1.3
• Significant Figures in Addition.
– Calculate the sum 44.56005 s + 0.0698 s +
1103.2 s.
• Significant Figures in Subtraction.
– Calculate the difference 568.42 m – 3.924 m
and write the result in scientific notation. How
many significant figures are in the result?
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Example and Practice Problem 1.4
• Significant Figures in Multiplication
– Find the product of 45.26 m/s and 2.41 s.
How many significant figures does the product
have?
• Significant Figures in Division
– Write the solution to 28.84 m divided by 6.2 s
with the correct number of significant figures.
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Follow-up Problems
• Perform these operations with the
appropriate number of significant figures.
• 3.783 x 106 kg + 1.25 x 108 kg
• (3.783 x 106 m) / (3.0 x 10-2 s)
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• (a) Strategy Rewrite the numbers so that the power of 10 is the
same for each. Then add and give the answer with the number of
significant figures determined by the less precise of the two
numbers.
Solution Perform the operation with the appropriate number of
significant figures.
3.783 106 kg  1.25 108 kg  0.03783 108 kg  1.25 108 kg  1.29  108 kg
• (b) Strategy Find the quotient and give the answer with the
number of significant figures determined by the number with the
fewest significant figures.
Solution Perform the operation with the appropriate number of
significant figures.
(3.783 106 m)  (3.0 102 s)  1.3 108 m s
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Follow-up Problem
• Solve the following problem and express
the answer in meters with the appropriate
number of significant figures and in
scientific notation:
3.08 x 10-1 km + 2.00 x 103 cm
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• Strategy Convert each length to meters. Then, rewrite
the numbers so that the power of 10 is the same for
each. Finally, add and give the answer with the number
of significant figures determined by the less precise of
the two numbers.
Solution Solve the problem.
3.08 101 km  2.00 103 cm  3.08 102 m  2.00 101 m  3.08 102 m  0.200  102 m  3.28  102 m
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Assignment #2
• p. 19 – 14, 16, and 18
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§1.5 Units
Some of the standard SI unit prefixes and their respective
powers of 10.
Prefix
Power of 10 Prefix
Power of 10
tera (T)
giga (G)
mega (M)
kilo (k)
1012
109
106
103
10-2
10-3
10-6
10-9
centi (c)
milli (m)
micro ()
nano (n)
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Dimensions are basic types of quantities that can be
measured or computed. Examples are length, time, mass,
electric current, and temperature.
A unit is a standard amount of a dimensional quantity.
There is a need for a system of units. SI units will be
used throughout this class.
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The quantities in this
column are based on an
agreed upon standard.
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A derived unit is composed of combinations of base units.
Example: The SI unit of energy is the joule.
1 joule = 1 kg m2/sec2
Derived unit
Base units
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Units can be freely converted from one to another.
Examples:
12 inches = 1 foot
1 inch = 2.54 cm
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Example: The density of air is 1.3 kg/m3. Change the units
to slugs/ft3.
1 slug = 14.59 kg
1 m = 3.28 feet
kg  1 slug  1 m 
3
3

1.3 3 

2
.
5

10
slugs/ft

m  14.59kg  3.28feet 
3
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Example 1.5 – Buying Clothes in a
Foreign Country
• Michel, an exchange student from France,
is studying in the United States. He
wishes to buy a new pair of jeans, but the
sizes are all in inches. He does remember
that 1 m = 3.28 ft and that 1 ft = 12 in. If
his waist is 82 cm, what is his waist size in
inches?
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Practice Problem 1.5 – Driving on
the Autobahn
• A BMW convertible travels on the German
autobahn at a speed of 128 km/h. What is
the speed of the car (a) in meters per
second? (b) in miles per hour?
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Example 1.6 – Conversion of
Volume
• A beaker of water contains 255 mL of
water. (1 mL – 1 milliliter; 1 L = 1000
cm3.) What is the volume of the water in
(a) cubic centimeters? (b) cubic meters?
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Practice Problem 1.6 – Surface
Area of Earth
• The radius of Earth is 6.4 x 103 km. Find
the surface area of Earth in square meters
and in square miles. (Surface are of a
sphere = 4r2.)
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Follow-up Problem
• A snail crawls at a pace of 5.0 cm/min.
Express the snail’s speed in (a) ft/s and (b)
mi/h.
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• (a) Strategy There are 12 inches in one foot, 2.54
centimeters in one inch, and 60 seconds in one minute.
Solution Express the snail’s speed in feet per second.
5.0 cm 1min
1 in
1 ft



 2.7 103 ft s
1 min 60 s 2.54 cm 12 in
• (b) Strategy There are 5280 feet in one mile, 12 inches
in one foot, 2.54 centimeters in one inch, and 60 minutes
in one hour.
Solution Express the snail’s speed in miles per hour.
5.0 cm 60 min
1 in
1 ft
1 mi




 1.9 103 mi h
1 min
1h
2.54 cm 12 in 5280 ft
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Assignment #3
• p. 20 – 23, 25, 26, 28, 29, and 31.
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§1.6 Dimensional Analysis
Dimensions are basic types of quantities such as length [L];
time [T]; or mass [M].
The square brackets are
referring to dimensions not
units.
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Example (text problem 1.84): Use dimensional analysis to
determine how the period of a pendulum depends on mass,
the length of the pendulum, and the acceleration due to
gravity (here the units are distance/time2).
Mass of the pendulum [M]
Length of the pendulum [L]
Acceleration of gravity [L/T2]
The period of a pendulum is how long it takes to complete 1
swing; the dimensions are time [T].
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§1.7 Problem Solving Techniques
Summary of the list on page 13:
•Read the problem thoroughly.
•Draw a picture.
•Label the picture with the given information.
•What is unknown?
•What physical principles apply?
•Are their multiple steps needed?
•Work symbolically! It is easier to catch mistakes.
•Calculate the end result. Don’t forget units!
•Check your answer for reasonableness.
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§1.8 Approximations
All of the problems that we will do this semester will be an
approximation of reality. We will use models of how things
work to compute our desired results. The more effects we
include, the more correct our results will be.
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Example (text problem 1.44): Estimate the number of
times a human heart beats during its lifetime.
Estimate that a typical heart beats ~60 times per minute:
 60 beats  60 minutes 24 hours 365days  75 years 






 1 minute 1 hour  1day  1 year  1 lifetime
 2.4 109 beats/lifetime
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Example 1.9 – Number of Cells in
the Human Body
• Averaged-sized cells in the human body
are about 10 m in length. How many
cells are in the human body? Make an
order-of-magnitude estimate.
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Practice Problem 1.9 – Drinking Water
Consumed in the United States
• How many liters of water are swallowed by
the people living in the United States in
one year? This is a type of problem made
famous by Enrico Fermi (1901-1954), who
was a master at this sort of back-of-theenvelope calculation. Such problems are
often called Fermi problems in his honor.
(1 liter = 10-3 m3 ≈ 1 quart.)
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Follow-up Problem
• What is the order of magnitude of the
number of seconds in a year?
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• Strategy Estimate the appropriate orders
of magnitude.
Solution Find the order of magnitude of
the number of seconds in one year.
seconds/minute ~ 102, minutes/hour ~ 102,
hours/day ~ 101, days/year ~ 102
2
10
2
10
1
2
10 10

7
10 s
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§1.9 Graphs
Experimenters vary a quantity (the independent variable) and
measure another quantity (the dependent variable).
Dependent
variable here
Independent variable here
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Be sure to label the axes with both the quantity and its unit.
For example:
Position
(meters)
Time (seconds)
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Example (text problem 1.49): A nurse recorded the values
shown in the table for a patient’s temperature. Plot a graph
of temperature versus time and find (a) the patient’s
temperature at noon, (b) the slope of the graph, and (c) if
you would expect the graph to follow the same trend over
the next 12 hours? Explain.
The given data:
Time
Decimal time
Temp (°F)
10:00 AM
10.0
100.00
10:30 AM
10.5
100.45
11:00 AM
11.0
100.90
11:30 AM
11.5
101.35
12:45 PM
12.75
102.48
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103
102.5
temp (F)
102
101.5
101
100.5
100
99.5
10
11
12
13
time (hours)
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(a)
Reading from the graph: 101.8 F.
(b)
T2  T1 101.8 F  100.0 F
slope 

 0.9 F/hour
t2  t1
12.0 hr  10.0 hr
(c)
No.
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Example 1.10 – Length of a Spring
• In an introductory physics laboratory experiment,
students are investigating how the length of a spring
varies with the weight hanging from it. Various weights
(accurately calibrated to 0.01 N) ranging up to 6.00 N
can be hung from the spring; then the length of the
spring is measured with a meterstick. The goal is to
see if the weight F and length L are related by F = kx
where x = (L – Lo), Lo is the length of the spring when
no weight in hanging from it, and k is called the spring
constant of the spring. Graph the data in the table and
calculate k for this spring.
F (N)
0
0.50
1.00
2.50
3.00
3.50
4.00
5.00
6.00
L (cm)
9.4
10.2
12.5
17.9
19.7
22.5
23.0
28.8
29.5
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Fig. 01.04
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Practice Problem 1.10 – Another
Weight of the Spring
• What is the length of the spring of
Example 1.10 when a weight of 8.00 N is
suspended? Assume that the relationship
found in Example 1.10 still holds for this
weight.
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Follow-up Problem
• An object is moving in the
x-direction. A graph of the
distance it has moved as a
function of time is shown.
(a) What are the slope and
vertical axis intercept? (b)
What physical significance
do the slope and intercept
on the vertical axis have for
this graph?
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• (a) Strategy Refer to the figure. Use the definition of the slope of
a line and the fact that the vertical axis intercept is the x-value
corresponding to t = 0.
Solution Compute the slope.
x 17.0 km  3.0 km

 1.6 km h .
t
9.0 h  0.0 h
When t = 0, x = 3.0 km; therefore, the vertical axis intercept is 3.0
km.
(b) Strategy and Solution The physical significance of the slope
of the graph is that it represents the speed of the object. The
physical significance of the vertical axis intercept is that it represents
the starting position of the object (position at time zero).
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Assignment #4
• p. 21 – 52 and 54
• p. 22 – 62, 68, 69 and 70
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Summary
•Math Skills
•The SI System of Units
•Dimensional Analysis
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