chapter 1 introduction to physics
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Classroom introduction to physics, Physics is an experimental science Measurements unitsTRANSCRIPT
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College Physics
Chapter 1Introduction
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Physics 2010/2011Instructor: Allen Hunley
Telephone: (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)
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World Wide WebCourseWeb Address: http://teacherweb.com/KY/MSHS/AllenHunley/
TextbookWeb Address: www.cp7e.com
(Physics Now Web Site, free if you purchased a new edition textbook)
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Study Suggested Study Procedure1. 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.
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EvaluationLecture 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 - 100Lab Activities 20 points B = 80 – 89Exams 50 points C = 70 – 79Final Exam 15 points D = 60 – 69Total 100 points F = 0 - 59
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LaboratoryLaboratory 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.
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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.
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The Branches of Physics
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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.
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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
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Chapter 1The 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.
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Chapter 1Models 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.
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Chapter 1Hypotheses 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.
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Chapter 1Hypotheses, 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).
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Chapter 1Controlled 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.
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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
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Chapter 1Numbers 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).
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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
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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
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Length Units
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
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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
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MassThe SI unit for mass is the
kilogram. A kilogram is defined as the mass of a special platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures in France.
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Time Units
seconds, s in all three systems 9,192,631,700 times the period of
oscillation of radiation from the cesium atom.
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Fundamental Quantities and Their Dimension Length [L] Mass [M] Time [T]
other physical quantities can be constructed from these three
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Chapter 1Dimensions 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.
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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
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Dimensional Analysis, cont. Cannot give numerical factors: this
is its limitation Dimensions of some common
quantities are listed in Table 1.5
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Example 1
TL T
The following equation was given by a student during an examination:
Do a dimensional analysis and explain why the equation can’t be correct.
20 atvv
ν has dimensions a has dimensions t has dimension
2TL
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Example 2Newton’s law of universal gravitation is represented by
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?
2rMmGF
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Prefixes Prefixes correspond to powers of
10 Each prefix has a specific name Each prefix has a specific
abbreviation See table 1.4
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Chapter 1SI 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.
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Conversions 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:
2.5415.0 38.11
cmin cmin
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Chapter 1
Sample ProblemA typical bacterium has a mass of about 2.0 fg.
Expressthis measurement in terms of grams and
kilograms.Given: mass = 2.0 fg
Unknown: mass = ? g mass = ? kg
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Chapter 1Sample Problem, continued
Build conversion factors from the relationships given in
Table 3 of the textbook. Two possibilities are:
Only the first one will cancel the units of femtograms to
give units of grams.
–15
–15
1 10 g 1 fg and 1 fg 1 10 g
–15–151 10 g(2.0 fg) = 2.0 10 g
1 fg
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Chapter 1Sample Problem, continued
Take the previous answer, and use a similar process to
cancel the units of grams to give units of kilograms. –15 –18
3
1 kg(2.0 10 g) = 2.0 10 kg1 10 g
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Converting UnitsExample 3
Convert the following:a. 25m to cmb. 345m to Kmc. 550cm to Kmd. 0.3 m/s to Km/hr
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Chapter 1Mathematics 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.
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Chapter 1Data from Dropped-Ball Experiment
A clear trend can be seen in the data. The more time that passes after each ball is dropped, the farther the ball falls.
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Chapter 1Graph from Dropped-Ball Experiment
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.
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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:y = 4.9(t)2
The Greek letter (delta) means “change in.” The abbreviation y indicates the vertical change in a ball’s position from its starting point, and t indicates the time elapsed.
This equation allows you to reproduce the graph and make predictions about the change in position for any time.
Chapter 1Equation from Dropped-Ball Experiment
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Coordinate Systems Used to describe the position of a point
in space Coordinate system consists of
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
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Cartesian coordinate system
Also called rectangular coordinate system
x- and y- axes Points are labeled
(x,y)
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Plane polar coordinate system 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,)
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Trigonometry Review
sin
cos
tan
opposite sidehypotenuseadjacent sidehypotenuse
opposite sideadjacent side
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More Trigonometry Pythagorean Theorem
To find an angle, you need the inverse trig function for example,
Be sure your calculator is set appropriately for degrees or radians
2 2 2r x y
1sin 0.707 45
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Problem Solving Strategy
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Problem Solving Strategy Read the problem
Identify the nature of the problem Draw a diagram
Some types of problems require very specific types of diagrams
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Problem Solving cont. Label the physical quantities
Can label on the diagram Use letters that remind you of the quantity
Many quantities have specific letters Choose a coordinate system and label it
Identify principles and list data Identify the principle involved List the data (given information) Indicate the unknown (what you are looking
for)
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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) Solve for the unknown quantity Substitute the data into the equation Obtain a result Include units
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Problem Solving, final Check the answer
Do the units match? Are the units correct for the quantity
being found? Does the answer seem reasonable?
Check order of magnitude Are signs appropriate and
meaningful?
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Problem Solving Summary Equations are the tools of physics
Understand what the equations mean and how to use them
Carry through the algebra as far as possible Substitute numbers at the end
Be organized
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Example 4A 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?
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Example 5For 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?
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Example 6A 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?
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Example 7A 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?
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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.
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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
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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
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Chapter 1Rules for Determining Significant Zeros
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Example 8How many significant digits are in each
of the following:a.) 0.007b.) 1.09c.) 100d.) 0.8090
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Operations with Significant Figures 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
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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
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Rules for Calculating with Significant Figures
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Example 9A 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?
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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).
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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
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