college physics chapter 1 introduction. theories and experiments the goal of physics is to develop...
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College Physics
Chapter 1Introduction
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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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Fundamental Quantities and Their Dimension Length [L] Mass [M] Time [T]
other physical quantities can be constructed from these three
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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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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 of 1/299792458 second. This establishes the speed of light at 299792458 m/sec or its accepted value of 3.00 x 108 m/s.
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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 of platinum and iridium alloy kept at the International Bureau of Weights and Measures located in Sevres, France.
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Standard Kilogram
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Time Units
seconds, s in all three systems
9192631700 times the period of oscillation of radiation from a cesium atom
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Approximate Values Various tables in the text show
approximate values for length, mass, and time: See Page 3 Note the wide range of values Lengths – Table 1.1 Masses – Table 1.2 Time intervals – Table 1.3
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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 found on page 4
Common prefixes to remember:
109 giga, G 106 mega, M 103 kilo, k101 deka, da 10-1 deci, d 10-2 centi, c10-3 milli, m 10-6 micro, 10-9 nano, n
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Structure of Matter Matter is made up of molecules
the smallest division that is identifiable as a substance
Bodies of mass smaller than the molecule will not have characteristics of a unique substance
Molecules are made up of atoms correspond to elements
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More structure of matter Atoms are made up of
nucleus, very dense, contains protons, positively charged, “heavy” neutrons, no charge, about same mass as
protons protons and neutrons are made up of quarks
orbited by electrons, negatively charges, “light”
fundamental particle, no structure
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Structure of Matter
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Structure of Matter
Quarks – up, down, strange, charm, bottom, and top.
Up, Charm, and Top have a charge of + that of a proton.
Down, Strange, and Bottom have a charge of - that of a proton.
The proton has two up quarks and one down quark. + - = + 1.
The neutron has two down quarks and one up quark. - - + = 0.
The other quarks are indirectly observed and not well understood.
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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 on page 5. Example: [a] = [v]/[t]; L/T = {x}/{t2}
T x = at2
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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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Operations with Significant Figures Accuracy – number of significant figures 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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Operations with Significant Figures, cont. 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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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 38.1
1
cmin cm
in
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Examples of various units measuring a quantity
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Order of Magnitude Approximation based on a number of
assumptions may need to modify assumptions if more
precise results are needed Order of magnitude is the power of 10
that applies Examples: 27~30, 1006950~1000000
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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
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Types of Coordinate Systems Cartesian – (x,y) or (x,y,z) Plane polar - (r,)
x
yr
s
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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 side
hypotenuse
adjacent side
hypotenuse
opposite side
adjacent 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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What is the % uncertainty in the measurement 3.76 0.25?
Answer: 0.25/3.76 x 100% = 6.6%
What is the % uncertainty in the measurement 11.3 0.9?.
Answer: 0.9/11.3 x 100% = 8%
Sample Problems
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In calculating the area of a piece of notebook paper you get measurements of (21.1 .1) cm for the width and (27.5 .2) cm for the length. Determine the area and the uncertainty. If the actual value of the area is 603 cm 2, determine the percent error from your calculation.
Answer: (21.1)(27.5) (21.1)(.2) (25.5)(.1) + (.1)(.2) =
580. (4.22 + 2.55) = (580 7) cm 2
% error = (603 – 580) x 100 = 3.8%
603
Sample Problems
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An airplane travels at 950 km/h. How long in seconds does it take to travel 1 km?
Answer: (950 km/h)(1h/3600sec) = .26sec
Use dimensional analysis to determine if the equation vf
2 = vo 2 + 2as is consistent.
Answer: [L] 2 = [L] 2 + [L][L]
[T] 2 [T] 2 [T] 2
[L] 2 = [L] 2
[T] 2 [T] 2 The equation is consistent.
Sample Problems