PHY300

1. Giambattista Physics
Chapter 1
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Chapter 1: Introduction
1.1 Why Study Physics?
1.2 Talking Physics
1.3 The Use of Mathematics
1.4 Scientific Notation and Significant Figures
1.5 Units
1.6 Dimensional Analysis
1.7 Problem-Solving Techniques
1.8 Approximation
1.9 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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More reasons…
Gain an appreciation for the “simplicity” (underlying
mathematical structure) of nature.
Physics encompasses all natural phenomena.

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1.2 Talking Physics
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 (velocity
includes direction); acceleration is a change of speed (including
speeding up or slowing down) or direction (even if the speed is
constant).
Basically, the language spoken by physicists is mathematics.

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Some terminology
y mx b
 
x is multiplied by the factor m.
The terms mx and b are added together.
Example:
y c
x
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.
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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Percentages Continued
The general rule is to multiply by
where the (+) is used if the quantity is increasing, and (-) is used
if the quantity is decreasing.
1
100
n
 

 
 

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Proportions
A B
 A is proportional to B. The value of A is
directly related to the value of B.
1
A
B

A is proportional to 1/B, or A is inversely
proportional to B. The value of A is
inversely related to the value of B.

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Proportions: Examples 1
Supposed that 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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Proportions: Examples 2
The area of a circle is
2
A r


The area is proportional to the radius squared:
2
A r

The proportionality constant is .

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Proportions: Examples 3
Suppose 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?
Because the area of a circle is proportional to radius squared,
2 2
1 1
2 2
2 2
(5 cm)
2.8
(3 cm)
A r
A r
  
The area of the first circle is 2.8 times larger than the second
circle.

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1.4 Scientific Notation and Significant Figures
This is a shorthand way of writing very large and/or very small
numbers.
Example: The radius of the sun is 700,000 km. In scientific
notation, this is written as
7.0105 km.
When properly written, the first
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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Rules for Identifying Significant Figures
1. Nonzero digits are always significant.
2. Final or ending zeros written to the right of the decimal point
are significant. (Example: 7.00)
3. Zeros written to the right of the decimal point for the purpose
of spacing are not significant. (Example: 0.0007)
4. Zeros written to the left of the decimal point may or may not
be significant. For example, 200 cm could have one, two, or
three significant figures; it’s not clear from the number alone.
Rewriting such a number in scientific notation is one way to
remove the ambiguity.
5. Zeros written between significant figures are significant.
(Example: 1001)

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Significant Figures in Calculations
1. When two or more quantities are added or subtracted, the
result is as precise as the least precise of the quantities (see
Example 1.4 in the text).
2. 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 (see Example 1.5 in the
text).
3. In a series of calculations, rounding to the correct number of
significant figures should be done only at the end, not at
each step. It’s a good idea to keep at least two extra
significant figures in calculations, then round at the end.

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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) 1012 centi (c) 10-2
giga (G) 109 milli (m) 10-3
mega (M) 106 micro () 10-6
kilo (k) 103 nano (n) 10-9

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Dimensions and Units
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 (e.g.,
meters, seconds, pounds, etc.). There is a need for a
standardized international system of units in physics. SI units will
be used throughout this class.

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SI Base Units
These units are based on an agreed upon international standard.

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Derived Units
A derived unit is composed of combinations of base units.
Example: The SI unit of energy is the joule:
1 joule = 1 kg m2/s2
The joule is a derived unit.
Kilograms (kg), meters (m),
and seconds (s) are base units.

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Converting Units
Units can be freely converted from one to another.
Examples: 12 inches = 1 foot
1 inch = 2.54 cm
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
1.3
kg
3
m
1 slug
14.59 kg
3
3 3
1 m
2.5 10 slugs/ft
3.28 feet

  
 
  
  

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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 refer to
dimensions, not particular units.

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Dimensional Analysis Example
Text problem 1.92: 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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Problem 1.92 Solution
This is essentially done by trial and error. Don’t be afraid of
making a mistake. The answer is the square root of [L]/[L/T^2]:
2
[L]
[T]
[L]/[T]
length of pendulum
period
acceleration due to gravity

 
We can only conclude that it is proportional. An unknown
(unitless) constant of proportionality may be present.

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1.7 Problem-Solving Techniques
General guidelines:
1. Read the problem thoroughly.
2. Draw a picture.
3. Write down the given information.
4. What is unknown?
5. What physical principles apply?
6. Are multiple steps needed?
7. Work symbolically! It is easier to catch mistakes.
8. Calculate the end result. Don’t forget units!
9. Check your answer for reasonableness.

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1.8 Approximation
All of the problems that we do in physics are 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.
Often, we can obtain a satisfactory answer by estimating.
Example (text problem 1.52): Estimate the number of times a
human heart beats during a lifetime. Say a typical heart beats
about 60 times per minute, and a lifetime is about 75 years.
60 beats
1 minute
60 minutes
 
 
  1 hour
s
24 hour
 
 
  1 day
s
36 day
5
 
 
  1 year
75 years
 
 
 
9
1 lifetime
2.4 10 beats/lifetime
 
 
 
 

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1.9 Graphs
Experimenters vary a quantity (the independent variable) and
measure another quantity (the dependent variable). One graphs
the dependent variable (vertical axis) vs. the independent
variable (horizontal axis).
Dependent variable
on vertical axis.
Independent variable on
horizontal axis.

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Label Axes
Always label the axes with both the quantity and its unit. For
example, in a graph of position versus time:
Position
(meters)
Time (seconds)

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Example Graphing Problem
(text problem 1.56) 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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Problem Solution Part 1
99.5
100
100.5
101
101.5
102
102.5
103
10 10.5 11 11.5 12 12.5 13
Temp
(F)
Time (hours)

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Problem Solution Part 2
a) Reading from the graph: 101.8 F.
b) 2 1
2 1
101.8 F 100.0 F
slope 0.9 F/hr
12.0 hr 10.0 hr
T T
t t
   
   
 
c) No. The patient would not survive such a large temperature
increase.