the science of physics chapter 1. 1-1: what is physics? main objectives: identify activities and...
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The Science of Physics
Chapter 1
1-1: What is Physics?
Main Objectives: Identify activities and fields that involve the
major areas within physicsDescribe the processes of the scientific
methodDescribe the role of models and diagrams in
physics
What is Physics?
The goal of physics is to describe and explain the physical world using basic concepts, equations, and assumptionsThese principles can then be used to make
predictions about a broad range of phenomena Example: The same principles that can be used to
explain the motion of planets can be used to explain the motion of a baseball being thrown into the air
Pure vs. Applied Science
Many physicists study the laws of nature to satisfy their own curiosity about the natural worldPure science is when scientists working to
increase knowledge in a certain field
Pure vs. Applied Science
Many current forms of technology were only made possible through the application of scientific principles → this is applied science.Advances by those practicing pure science
have an affect on those practicing applied science and vice versa.
Physics is Everywhere The Physics of Cars
The Scientific Method
Scientists seek to understand, describe, and explain the natural worldThis involves an organized process of inquiry
and investigation
The Scientific Method
The scientific method is not necessarily a single procedure that is followed by scientists It is a collection of core
steps that are utilized in good scientific investigations
The Scientific Method
Physicists use models to represent key features of natural phenomena
Simple models that describe part of system are developed first so that they can be combined to represent complex phenomena model – a pattern, plan, representation, or description
designed to show the structure or workings of an object, system, or concept
Examples: mathematical models, diagrams, computer simulations, etc.
The Scientific Method system – a set of particles of interacting
components considered to be a distinct physical entity for the purposes of study
The Scientific Method Models can help build hypotheses
hypothesis – an explanation that is based on prior scientific research or observations and that can be tested
Hypotheses must be testable through experimentationcontrolled experiment – an experiment that
only tests one factor (variable) at a time by using the comparison of a control group with an experimental group
Galileo’s Though Experiment
Galileo’s Hypothesis: All objects fall at the same rate in the absence of air resistance
The Scientific Method
The best models/hypotheses can be used to make predictionsHowever, at any time there is the possibility
that an experiment will produce results that invalidate a certain model or hypothesis
A conclusion is only valid if it can be verified by others through experimentation
1-2: Measurements in Experiments
Main Objectives: List basic SI units and the quantities they
describeConvert measurements into scientific notationDistinguish between accuracy and precisionUse significant figures in measurements and
calculations
Accuracy and Precision
Good measurements in the lab are both correct and reproducible accuracy – how close a single measurement
comes to the actual dimension or true value of the quantity being measured
precision – the degree of exactness of a measurement
Example: 1.25 cm is a more precise measurement than 1.2 cm
Accuracy and Precision
All measurements made with instruments are really approximations that depend on the quality of the instruments and the skill of the person doing the measurement
The precision of the instrument depends on the how small the scale is on the device. The finer the scale the more precise the
instrument
SI Units The International System of Units, SI, is a
revised version of the metric system Correct units along with numerical values are
critical when communicating measurements. The are seven base SI units of which other SI
units are derived (derived units). Sometimes non-SI units are preferred for
convenience or practical reasons
Common SI Prefixes Units larger than the base unit
Tera T 10-12 = 0.000000000001 terameter (Tm)
Giga G 10-9 = 0.000000001 gigameter (Gm)
Mega M 10-6 = 0.000001 megameter (Mm)
Kilo k 10-3 = 0.001 kilometer (km)
Hecto h 10-2 = 0.01 hectometer (hm)
Deka da 10-1 = 0.1 decameter (dam)
Base Unit
100 = 1 meter (m)
Common SI Prefixes Units smaller than the base unit
Base Unit
100 = 1 meter (m)
Deci d 101 = 10 decimeter (dm)
Centi c 102 = 100 centimeter (cm)
Milli m 103 = 1000 millimeter (mm)
Micro μ 106 = 1,000,000 micrometer (μm)
Nano n 109 = 1,000,000,000 nanometer (nm)
Pico p 1012 = 1,000,000,000,000 picometer (pm)
Conversion Factors The same quantity can usually be measured
or expressed in many different ways. Examples:
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
1 m = 10 dm = 100 cm = 1000 mm
Whenever two measurements are equal, a ratio of these measurements will equal one Ratios of these equivalent (equal) measurements
are called conversion factors.
Conversion Factors In a conversion factor, the measurement in
the numerator (on the top) is equivalent to the measurement in the denominator (on the bottom.Example: “one meter per 100
centimeters”
1 m1 m 100 100 cmcm
Conversion Factors Because conversion factors are equal to one,
when a measurement is multiplied by a conversion factor, the size of a measurement stays the same.
Example: How many meters are in 0.68 km?1. Unknown: 0.68 km in meters
2. Known:
- 0.68 km
- 1 km = 1000 m → Conversion Factor:
3/4. Solution-Calculation:
1000 m1000 m 1 km1 km
0.68 km0.68 km x x 1000 m1000 m = 680 m = 680 m 1 1 km1 1 km
Scientific Notation
scientific notation – a number is written as the product of two numbers: a coefficient and a power of ten
Example: 36,000 is written in scientific notation as 3.6 x 104 or 3.6e4Coefficient = 3.6 → a number greater than or
equal to 1 and less than 10.Power of ten / exponent = 4 3.6 x 104 = 3.6 x 10 x 10 x 10 x 10 = 36,000
Scientific Notation
When writing numbers greater than ten in scientific notation the exponent is positive and equal to the number of places that the decimal has been moved to the left.
Scientific Notation
Numbers less than one have a negative exponent when written in scientific notation. Example: 0.0081 is written in scientific notation as
8.1 x 10-3
8.1 x 10-3 = 8.1/(10 x 10 x 10) = 0.0081
When writing a number less than one in scientific notation, the value of the exponent equals the number of places you move the decimal to the right.
Measurement and Uncertainty
Accurate measurements are an important part of physics, but no measurement is absolutely precise There is an uncertainty associated with every
measurement Uncertainty arises from various sources
Individual errors → Example: misusing equipment The limited accuracy of every measuring
instrument
Measurement and Uncertainty
The number of reliably known digits in a number is called the number of significant figuresSignificant figures in a measurement include
all of the digits that are known precisely plus one last digit that is estimated
23.21 → 4 significant figures 0.062 → 2 significant figures
Significant Figures - Rules1. Every nonzero digit in a recorded
measurement is significant.
- Example: 24.7 m, 0.743 m, and 714 m all have three sig. figs.
2. Zeros appearing between nonzero digits are significant.
- Example: 7003 m, 40.79 m, and 1.503 m all have 4 sig. figs.
Significant Figures - Rules3. Zeros appearing in front of all nonzero digits are
not significant; they act as placeholders and cannot arbitrarily be dropped (you can get rid of them by writing the number in scientific notation).
- Example: 0.0071 m has two sig. figs. And can be written as 7.1 x 10-3
4. Zeros at the end of the number and to the right of a decimal point are always significant.
- Example: 43.00 m, 1.010 m, and 9.000 all have 4 sig. figs.
Significant Figures - Rules
5. Zeros at the end of a measurement and to the left of the decimal point are not significant unless they are measured values (then they are significant). Numbers can be written in scientific notation to remove ambiguity.- Example: 7000 m has 1 sig. fig.; if those zeros were measured it could be written as 7.000 x 103 m
Significant Figures - Rules
6. Measurements have an unlimited number of significant figures when they are counted or if they are exactly defined quantities.
- Example: 23 people or 60 minutes = 1 hour
* You must recognize exact values to round answers correctly in calculations involving measurements.
Significant Figures in Calculations
In calculations involving measurements, an answer cannot be more precise than the least precise measurement from which it was calculated.Example: The area of a room that measures
7.7 m (2 sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be 41.58 m2 (4 sig. figs.) – you must round the answer to 42 m2
Significant Figures in Calculations
The answer to an addition or subtraction problem should be rounded to have the same number of decimal places as the measurement with the least number of decimal places.Example: 34.61m – 17.3m = 17.31 → 17.3 (1
decimal place)
Significant Figures in Calculations
In calculations involving multiplication and division, the answer is rounded off to the number of significant figures in the least precise term (least number of sig. figs.) in the calculationsExample: 8.3m x 2.22m = 18.462 → 18mExample: 8432m ÷ 12.5 = 674.56 → 675m
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1-3: The Language of Physics
Main Objectives: Interpret data in tables and graphs, and
recognize equations that summarize dataCreate and identify different types of graphsManipulate algebraic equations to solve for
different variables
Organizing Data
Data can be organized in a variety of waysData is commonly organized in tables and
graphs which can be represented by equations that show the relationships between variables
Displaying Data - Graphing
An important step in analyzing data is to identify the independent variable (or manipulated variable) and the dependent variables (or responding variables). Independent variable – altered by the
experimenter; influence other variablesDependent variables – possibly change as a
result of changes in the independent variable.
Displaying Data - Graphing
See Figures 3.2 & 3.3 What is the independent variable? What
are the dependent variables?
What is the relationship between the independent variable and the dependent variables?
A Test of Galileo’s Hypothesis
Figure 3.2
A Test of Galileo’s Hypothesis
This graph can be summarized by the equation (change in position in m) = 4.9 x (time elapsed in s)2
or ∆y=4.9(∆t)2
Linear Relationships When there is a linear relationship
between two variables a graph of there relationship will be a straight line.
This relationship can be written as a linear equation → y = mx + bm is the slopeb is the y-intercept
Both are constants that can be found on the graph
Linear Relationships
Slope (m) – the ratio of vertical change (∆y) to horizontal change (∆x)
m = rise/run = ∆y / ∆x
y-intercept (b) – the point at which the line crosses the y-axis; it is the value of y when x is zero
Quadratic Relationships When a smooth line drawn through the data
points curves upward (not a straight line), the graphs are frequently parabolasThis indicates that the variables are related by
the equation: y = kxThis equation is one form of a quadratic
relationshipk is a constant that shows you how fast y
changes with x See Figure 3.3
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Inverse Relationships
Sometimes variables have an inverse relationship and form a hyperbola when graphed.
The general equation for an inverse relationship is xy = k or…
y = k(1/x) = kx-1
Manipulating Equations The way in which quantities/variables
relate to each other can be represented symbolically by an equation, as well as a graph.
Example: distance = speed x time
d = vt
You can use the rules of algebra to rearrange equations
Solve for v in the equation above
Solving Equations Using Algebra
When rearranging equations using algebra, any process that you do to one side of the equation you must do to the other side of the equationThe steps can be performed in any sequence,
but make sure you perform the same operations on both sides of the equation.
Solving Equations Using Algebra
Solve the following equations for x:ay/x = cb/s
y = mx + b
Units in Equations Most physical quantities have units and
numerical values When using quantities in equations you must
substitute the numerical value and the units Mathematical operations can be done on units
just as they can be done on numbers Make sure to use the same units for the same
type of measurement Example: If a problem involves length
measurements in meters (m) and centimeters (cm) convert them both to the same units
Units in Equations
Example: Solve for d using d = vt.
v = 11.0 m/s and t = 6.00 s