Transcript Physics - Allen Hunley

College Physics
Chapter 1
Introduction
Physics 2010/2011
Instructor:
Telephone:
Allen Hunley
(931) 221-6116 (office)
E-Mail: [email protected]
Office Hours:
By appointment. (I am an adjunct member so I do not have an
office at APSU.)
Textbook:
College Physics (7th Edition)
by Serway & Faughn
Thomson Books/Cole (2006)
World Wide Web
Course
Web Address:
Textbook
Web Address:
http://teacherweb.com/KY/MSHS/AllenHunley/
www.cp7e.com
(Physics Now Web Site, free if you purchased a new edition
textbook)
Study
Suggested Study Procedure
1.
Read the assigned topics/materials before coming to the class/lab.
2.
Attend the class, take good notes, and actively participate in all the
activities in the class.
3.
Reread the topics/materials.
4.
Work the assigned problems starting the first day that they are
assigned - you will require time for this material to "sink in"!
5.
Ask questions in the interim.
6.
Use a three-hole binder for the course so that you can keep all the
materials (notes, homework assignments, answer sheets, exams, labs,
etc.) in it. This will help you to find all the necessary materials when
you prepare for your exams.
Evaluation
Lecture and lab grades are combined. You will receive the same letter
grade for the lecture course as for the lab course.
In summary, the distribution of credits among the various assignments is as
following:
Guide to letter grades is:
Homework Assignments 15 points
A = 90 - 100
Lab Activities
20 points
B = 80 – 89
Exams
50 points
C = 70 – 79
Final Exam
15 points
D = 60 – 69
Total
100 points
F = 0 - 59
Laboratory
Laboratory activities are highly valued in physics
and are incorporated into our classes. These
activities may consist of traditional hands-on
experiments or computer simulations. You will be
working in groups with 2-3 students in each group.
The grade is based entirely on the lab write-ups you
turn in. These activities contribute 20% of your
grade.
The aims of the class
•
•
•
On of the aims of this class is to teach you to think in a
physics way.
• As you see each concept, try to get a mental picture of
how it works.
• You will learn as much about how to solve problems as
you do about the laws of physics themselves.
So you will need to approach this class differently from
many of the other classes you are taking. Simply
memorizing solutions will not help.
Doing lots of homework problems is the best way to do
well in the class. As you do each problem, think of what
strategy you are using to solve the problem.
The Branches of Physics
Physics



Physics attempts to use a small number of basic
concepts, equations, and assumptions to describe
the physical world.
These physics principles can then be used to make
predictions about a broad range of phenomena.
Physics discoveries often turn out to have unexpected
practical applications, and advances in technology can in
turn lead to new physics discoveries.
Theories and Experiments





The goal of physics is to develop theories
based on experiments
A theory is a “guess,” expressed
mathematically, about how a system works
The theory makes predictions about how a
system should work
Experiments check the theories’ predictions
Every theory is a work in progress
Chapter 1
The Scientific Method


There is no single
procedure that scientists
follow in their work.
However, there are certain
steps common to all good
scientific investigations.
These steps are called the
scientific method.
Chapter 1
Models



Physics uses models that describe phenomena.
A model is a pattern, plan, representation, or
description designed to show the structure or
workings of an object, system, or concept.
A set of particles or interacting components
considered to be a distinct physical entity for the
purpose of study is called a system.
Chapter 1
Hypotheses



Models help scientists develop hypotheses.
A hypothesis is an explanation that is based on
prior scientific research or observations and that can
be tested.
The process of simplifying and modeling a situation
can help you determine the relevant variables and
identify a hypothesis for testing.
Chapter 1
Hypotheses, continued
Galileo modeled the behavior of falling
objects in order to develop a hypothesis
about how objects fall.
If heavier objects fell
faster than slower
ones,would two bricks of
different masses tied
together fall slower (b) or
faster (c) than the heavy
brick alone (a)? Because of
this contradiction, Galileo
hypothesized instead that all
objects fall at the same
rate, as in (d).
Chapter 1
Controlled Experiments


A hypothesis must be tested in a
controlled experiment.
A controlled experiment tests only one
factor at a time by using a comparison
of a control group with an
experimental group.
Units


To communicate the result of a
measurement for a quantity, a unit
must be defined
Defining units allows everyone to relate
to the same fundamental amount
Chapter 1
Numbers as Measurements




In SI, the standard measurement system for science,
there are seven base units.
Each base unit describes a single dimension, such
as length, mass, or time.
The units of length, mass, and time are the meter
(m), kilogram (kg), and second (s), respectively.
Derived units are formed by combining the seven
base units with multiplication or division. For
example, speeds are typically expressed in units of
meters per second (m/s).
Systems of Measurement

Standardized systems


agreed upon by some authority, usually a
governmental body
SI -- Systéme International



agreed to in 1960 by an international committee
main system used in this text
also called mks for the first letters in the units of
the fundamental quantities
Systems of Measurements,
cont

cgs – Gaussian system


named for the first letters of the units it
uses for fundamental quantities
US Customary


everyday units
often uses weight, in pounds, instead of
mass as a fundamental quantity
Length

Units

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
SI – meter, m
cgs – centimeter, cm
US Customary – foot, ft
Defined in terms of a meter – the
distance traveled by light in a vacuum
during a given time
Mass

Units




SI – kilogram, kg
cgs – gram, g
USC – slug, slug
Defined in terms of kilogram, based on
a specific cylinder kept at the
International Bureau of Weights and
Measures
Mass
The SI unit for mass is the
kilogram.
A kilogram is defined as the
mass of a special platinumiridium alloy cylinder kept at the
International Bureau of Weights
and Measures in France.
Time

Units


seconds, s in all three systems
9,192,631,700 times the period of
oscillation of radiation from the cesium
atom.
Fundamental Quantities and
Their Dimension



Length [L]
Mass [M]
Time [T]

other physical quantities can be
constructed from these three
Chapter 1
Dimensions and Units


Measurements of physical quantities must be
expressed in units that match the dimensions of
that quantity.
In addition to having the correct dimension,
measurements used in calculations should also have
the same units.
For example, when
determining area by
multiplying length and width,
be sure the measurements
are expressed in the same
units.
Dimensional Analysis


Technique to check the correctness of
an equation
Dimensions (length, mass, time,
combinations) can be treated as
algebraic quantities


add, subtract, multiply, divide
Both sides of equation must have the
same dimensions
Dimensional Analysis, cont.


Cannot give numerical factors: this is its
limitation
Dimensions of some common quantities
are listed in Table 1.5
Example 1
The following equation was given by a student during an
examination:
v  v0  at
2
Do a dimensional analysis and explain why the equation
can’t be correct.
ν has dimensions
L
T
a has dimensions
L
T2
t has dimension
T
Example 2
Newton’s law of universal gravitation is
represented by
Mm
F G
2
r
where F is the gravitational force, M and m are
masses, and r is a length. Force has the SI
units kg ∙ m/s2. What are the SI units of the
proportionality constant G?
Prefixes

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Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
See table 1.4
Chapter 1
SI Prefixes
In SI, units are
combined with
prefixes that
symbolize
certain powers
of 10. The most
common
prefixes and
their symbols
are shown in the
table.
Conversions

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When units are not consistent, you may need
to convert to appropriate ones
Units can be treated like algebraic quantities
that can “cancel” each other
See the inside of the front cover for an
extensive list of conversion factors
Example:
2.54 cm
15.0 in 
 38.1 cm
1 in
Chapter 1
Sample Problem
A typical bacterium has a mass of about 2.0 fg. Express
this measurement in terms of grams and kilograms.
Given:
mass = 2.0 fg
Unknown:
mass = ? g
mass = ? kg
Chapter 1
Sample Problem, continued
Build conversion factors from the relationships given in
Table 3 of the textbook. Two possibilities are:
1 10–15 g
1 fg
and
1 fg
1 10–15 g
Only the first one will cancel the units of femtograms
to
give units of grams.
 1  10–15 g 
–15
(2.0 fg) 
=
2.0

10
g

 1 fg 
Chapter 1
Sample Problem, continued
Take the previous answer, and use a similar process to
cancel the units of grams to give units of kilograms.
(2.0  10
–15
 1 kg 
–18
g) 
=
2.0

10
kg

3
 1  10 g 
Converting Units
Example 3
Convert the following:
a. 25m to cm
b. 345m to Km
c. 550cm to Km
d. 0.3 m/s to Km/hr
Chapter 1
Mathematics and Physics


Tables, graphs, and equations can make data
easier to understand.
For example, consider an experiment to test Galileo’s
hypothesis that all objects fall at the same rate in the
absence of air resistance.



In this experiment, a table-tennis ball and a golf ball are
dropped in a vacuum.
The results are recorded as a set of numbers corresponding
to the times of the fall and the distance each ball falls.
A convenient way to organize the data is to form a table,
as shown on the next slide.
Data from Dropped-Ball
Experiment
Chapter 1
A clear trend can be seen in the data. The more time that
passes after each ball is dropped, the farther the ball falls.
Graph from Dropped-Ball
Experiment
Chapter 1
One method for analyzing the data is to construct a
graph of the distance the balls have fallen versus the
elapsed time since they were released. a
The shape of the
graph provides
information about
the relationship
between time and
distance.
Equation from Dropped-Ball
Experiment
Chapter 1

We can use the following equation to describe the
relationship between the variables in the dropped-ball
experiment:
(change in position in meters) = 4.9  (time in
seconds)2


With symbols, the word equation above can be written as
follows:
Dy = 4.9(Dt)2
The Greek letter D (delta) means “change in.” The
abbreviation Dy indicates the vertical change in a ball’s
position from its starting point, and Dt indicates the time
elapsed.
Coordinate Systems

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Used to describe the position of a point in
space
Coordinate system consists of

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a fixed reference point called the origin
specific axes with scales and labels
instructions on how to label a point relative to the
origin and the axes
Cartesian
Plane polar
Cartesian coordinate system

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
Also called
rectangular
coordinate system
x- and y- axes
Points are labeled
(x,y)
Plane polar coordinate system

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
Origin and reference
line are noted
Point is distance r
from the origin in
the direction of
angle , ccw from
reference line
Points are labeled
(r,)
Trigonometry Review
opposite side
sin  
hypotenuse
adjacent side
cos  
hypotenuse
opposite side
tan  
adjacent side
More Trigonometry
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Pythagorean Theorem
2
2
2
r  x y
To find an angle, you need the inverse
trig function
1
  sin 0.707  45
 for example,
Be sure your calculator is set
appropriately for degrees or radians
Problem Solving Strategy
Problem Solving Strategy

Read the problem

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Identify the nature of the problem
Draw a diagram

Some types of problems require very
specific types of diagrams
Problem Solving cont.

Label the physical quantities


Can label on the diagram
Use letters that remind you of the quantity

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Many quantities have specific letters
Choose a coordinate system and label it
Identify principles and list data

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
Identify the principle involved
List the data (given information)
Indicate the unknown (what you are looking for)
Problem Solving, cont.

Choose equation(s)


Based on the principle, choose an equation
or set of equations to apply to the problem
Substitute into the equation(s)

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Solve for the unknown quantity
Substitute the data into the equation
Obtain a result
Include units
Problem Solving, final

Check the answer

Do the units match?

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Does the answer seem reasonable?


Are the units correct for the quantity being
found?
Check order of magnitude
Are signs appropriate and meaningful?
Problem Solving Summary
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Equations are the tools of physics


Carry through the algebra as far as
possible


Understand what the equations mean and
how to use them
Substitute numbers at the end
Be organized
Example 4
A certain corner of a room is selected as
the origin of a rectangular coordinate
system. If a fly is crawling on an adjacent
wall at a point having coordinates (2.0,
1.0), where the units are meters, what is
the distance of the fly from the corner of
the room?
Example 5
For the triangle shown in Figure P1.39, what are (a)
the length of the unknown side, (b) the tangent of
θ, and (c) the sine of φ?
Example 6
A high fountain of water is located at the center of a circular
pool as shown in Figure P1.41. Not wishing to get his feet
wet, a student walks around the pool and measures its
circumference to be 15.0 m. Next, the student stands at the
edge of the pool and uses a protractor to gauge the angle of
elevation at the bottom of the fountain to be 55.0°. How high
is the fountain?
Example 7
A surveyor measures the distance across a
straight river by the following method:
Starting directly across from a tree on the
opposite bank, he walks 100 m along the
riverbank to establish a baseline. Then he
sights across to the tree. The angle from his
baseline to the tree is 35.0°. How wide is
the river?
Chapter 1
Accuracy and Precision



Accuracy is a description of how close a
measurement is to the correct or accepted value of
the quantity measured.
Precision is the degree of exactness of a
measurement.
A numeric measure of confidence in a measurement
or result is known as uncertainty. A lower
uncertainty indicates greater confidence.
Uncertainty in Measurements

There is uncertainty in every measurement,
this uncertainty carries over through the
calculations


need a technique to account for this uncertainty
We will use rules for significant figures to
approximate the uncertainty in results of
calculations
Significant Figures



A significant figure is one that is reliably
known
All non-zero digits are significant
Zeros are significant when



between other non-zero digits
after the decimal point and another significant
figure
can be clarified by using scientific notation
Rules for Determining
Significant Zeros
Chapter 1
Example 8
How many significant digits are in each of
the following:
a.) 0.007
b.) 1.09
c.) 100
d.) 0.8090
Operations with Significant
Figures
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When adding or subtracting, round the result
to the smallest number of decimal places of
any term in the sum
If the last digit to be dropped is less than 5,
drop the digit
If the last digit dropped is greater than or
equal to 5, raise the last retained digit by 1
Operations with Significant
Figures, cont.

When multiplying or dividing two or more
quantities, the number of significant figures in
the final result is the same as the number of
significant figures in the least accurate of the
factors being combined
Rules for Calculating with
Significant Figures
Example 9
A fisherman catches two striped bass. The smaller
of the two has a measured length of 93.46 cm (two
decimal places, four significant figures), and the
larger fish has a measured length of 135.3 cm (one
decimal place, four significant figures). What is the
total length of fish caught for the day?
Example 10
Using your calculator, find, in scientific notation with
appropriate rounding,
(a) the value of (2.437 × 104)(6.5211 × 109)/(5.37 × 104)
and
(b) (3.14159 × 102)(27.01 × 104)/(1 234 × 106).
Derived Units




Derived units are combinations of the
base units (mks).
Area is measured in m2
Volume is measured in m3
Speed is measured in m/s