College Physics
Chapter 1
Introduction

Theories and Experiments
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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

Fundamental Quantities and Their Dimension

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Length [L]
Mass [M]
Time [T]
 other physical quantities can be constructed from these three

Units
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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

Systems of Measurement

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Standardized systems
 agreed upon by some authority, usually a governmental body
SI -- Systéme International

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 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

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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 10 8 m/s.

Mass
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Units
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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.

Standard Kilogram

Time

Units
 seconds, s in all three systems

9192631700 times the period of oscillation of radiation from a cesium atom

Approximate Values
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Various tables in the text show approximate values for length, mass, and time: See Page 3
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Note the wide range of values
Lengths – Table 1.1
Masses – Table 1.2
Time intervals – Table 1.3

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 found on page 4
Common prefixes to remember:
10 9 giga, G
10 1 deka, da
10 -3 milli, m
10
10
10
6
-1
-6 mega, M deci, d micro, 
10 3 kilo, k
10 -2 centi, c
10 -9 nano, n

Structure of Matter
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Matter is made up of molecules
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 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

More structure of matter
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Atoms are made up of
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 nucleus, very dense, contains
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 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

Structure of Matter

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.

Dimensional Analysis
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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.
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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}/{t 2 }
T x = at 2

Uncertainty in
Measurements
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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
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A significant figure is one that is reliably known
All non-zero digits are significant
Zeros are significant when
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 between other non-zero digits after the decimal point and another significant figure can be clarified by using scientific notation

Operations with Significant
Figures
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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

Operations with Significant
Figures, cont.
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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

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:
15.0
in

2.54
cm
1 in

38.1
cm

Examples of various units measuring a quantity

Order of Magnitude
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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
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Examples: 27~30, 1006950~1000000

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

y
Types of Coordinate
Systems
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Cartesian – (x,y) or (x,y,z)
Plane polar - (r,  ) s r
 x

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 sin
  opposite side hypotenuse cos
  adjacent side hypotenuse tan
  opposite side adjacent side

More Trigonometry
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Pythagorean Theorem r 2  x 2  y 2
To find an angle, you need the inverse trig function
 for example,   sin 0.707

45

Be sure your calculator is set appropriately for degrees or radians

Problem Solving Strategy

Problem Solving Strategy
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Read the problem
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Identify the nature of the problem
Draw a diagram
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Some types of problems require very specific types of diagrams

Problem Solving cont.
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Label the physical quantities
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Can label on the diagram
Use letters that remind you of the quantity
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Many quantities have specific letters
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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.
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Choose equation(s)
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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
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Check the answer
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Do the units match?
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Are the units correct for the quantity being found?
Does the answer seem reasonable?
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Check order of magnitude
Are signs appropriate and meaningful?

Problem Solving Summary
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Equations are the tools of physics
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Understand what the equations mean and how to use them
Carry through the algebra as far as possible
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Substitute numbers at the end
Be organized

Sample Problems
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
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)
+ (.1)(.2) =
 (21.1)(.2)  (25.5)(.1)
580.  (4.22 + 2.55) = (580  7) cm 2
% error = (603 – 580) x 100 = 3.8%
603

Sample Problems
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 v f
2 = v o
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.