ReadingGuide2051/ReadingGuide_Ch1_Solution.html at master · jtaou/ReadingGuide2051 · GitHub

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<h1>Chapter 1 – Units and Measurements</h1>

<p>The following describes the topics to watch out for and skills to master as
you read through Chapter 1 and the Appendices.</p>

<p>Today, we will explore units and measurement covered in Chapter 1. Physics
and all of the other sciences are inextricably connected with the ability to
measure and quantify phenomena. This course will develop how we expect physical
quantities to be related, but all the understanding that we think we have
derives from experiments. The more accurately and precisely we can measure
distance, time or mass (and many other quantities) determines what we can
ultimately infer about the Universe.</p>

<h3>Introduction</h3>

<p>- What can be used to describe atoms as well as galaxies? <span
id="ans">Physics.</span></p>

<h3>1.1 The Scope and Scale of Physics</h3>

<p>- Physics is devoted to the understanding of what? <span id="ans">All
natural phenomena which means all natural things that occur</span></p>

<p>- What force acts on the Whirlpool galaxy as well as Earth? <span
id="ans">Gravity</span></p>

<p>- What law ties together food calories, batteries, heat, light, and watch
springs? What does it state? <span id="ans">Conservation of energy. Energy can
change form but is never lost.</span></p>

<p>- Describe the scope of physics. Describes the most basic understanding of
phenomena. <span id="ans">Describes the interactions of matter, space, and
time.</span></p>

<p>- Physics can be used to describe what aspects of smartphones? <span
id="ans">Electricity flow through circuits and GPS.</span></p>

<p>- What other disciplines use physics? <span id="ans">Chemistry, engineering,
architecture, geology, biophysics, geophysics, biological sciences, medical
diagnostics, medical therapy</span></p>

<p>- What is an order of magnitude? <span id="ans">The size of a quantity as it
related to a power of 10.</span></p>

<p>- What is the order of magnitude of 297,395? <span id="ans">Log10(297,395) =
5.47. So the order of magnitude is 10^6.</span></p>

<p>- Is an order of magnitude is designed to more like an exact quantity or a
ballpark estimate? <span id="ans">A ballpark estimate.</span></p>

<p>- READING EXERCISE : Use order of magnitude arguments and Figure 1.4 to
determine how many electrons are in a person.<span id="ans">m_elec = 10^-10 kg.
m_human = 10^2 kg. 10^2kg/10^-30 kg = 10^32 electrons/human</span></p>

<p>- Describe the relationships among models, theories, and laws. <span
id="ans">model - representation of something that is often too difficult to
display directly, justified by experimental tests, it is only accurate in
describing certain aspects of a physical system.theory - testable explanation
for patterns in nature supported by scientific evidence and verified multiple
times.All scientific laws and theories are valid until a counterexample is
observed. law - concise language that describes a generalized pattern in nature
supported by scientific evidence and repeated experiments.</span></p>

<p>- What determines the validity of a theory? <span id="ans">Experimental
tests produce results that confirm the theory.</span></p>

<p>- Can the validity of a model be limited or must it be universally valid?
How does this compare with the required validity of a theory or a law? <span
id="ans">Models only need be accurate in describing certain aspects of a
physical system. A theory or law must be valid in all situations.</span></p>

<h3>1.2 Units and Standards</h3>

<p>- How is a physical quantity defined? <span id="ans">Characteristic or
property of an object that can be measured or calculated from other
measurements.</span></p>

<p>- What is a unit? <span id="ans">Standards used for expressing and comparing
measurements.</span></p>

<p>- What is the difference between SI and English units? <span id="ans">Si
units – international system of units that scientists in most countries have
agreed to use (i.e. m, L, g). English units – system of units that is used
widely only in the US (i.e. ft, gal, lbs)</span></p>

<p>- What are base quantities <span id="ans">Base quantity - physical quantity
chosen by convention andpractical considerations such that all other physical
quantities can beexpressed as algebraic combinations of them.</span></p>

<p>- What are base units? <span id="ans">Base unit - standard forexpressing the
measurement of a base quantity within a particular system of units; defined by
a particular procedure used to measure the corresponding base
quantity</span></p>

<p>- How do base units and quantities differ from derived quantities and units?
<span id="ans">derived quantity - physical quantity defined using
algebraiccombinations of base quantities. Derived units - units that can be
calculatedusing algebraic combinations of the fundamental units.</span></p>

<p>- What are the SI base units of length, mass, time, and thermodynamic
temperature? <span id="ans">m kg, s, K.</span></p>

<p>- Is area a base or derived quantity? <span id="ans">Derived.</span></p>

<p>- How is the second defined in the metric system now? <span id="ans">time it
takes for certain number (~9B) vibrations of a Cesium atom</span></p>

<p>- How is the meter defined in the metric system now? <span id="ans">distance
light travels in 1/(light speed) of a second</span></p>

<p>- How is the kg defined in the metric system now? <span id="ans">based on
mass of a standard object at NIST</span></p>

<p>- Understand Table 1.2 and how to convert the unit prefixes into numbers
that you can plug into a calculator (e.g. converting mm to m)</p>

<p>- NOTE: You should be able to express a quantity given in scientific
notation to a more readable version that uses an SI unit prefix (e.g.
converting W to MW).</p>

<p>- Conversion factors are given in Appendix B.</p>

<p>- Go through example 1.1 (Using Metric Prefixes) to understand how to choose
metric prefixes.</p>

<h3>1.3 Unit Conversion</h3>

<p>- What ratio (what divided by what?) is a conversion factor? <span
id="ans">a ratio how many of one unit are equal to another unit: for example
the first unit divided by the equal number of the other</span></p>

<p>- How should the conversion factor be chosen/mathematically arranged ? <span
id="ans">so the old unit cancels out</span></p>

<p>- READING EXERCISE: Use conversion factors to express the value of a given
quantity in different units by going through the examples.</p>

<p>- Common conversion factors are given in Appendix B.</p>

<p>- Be sure to cancel units correctly when doing conversions and be certain
that the final answer is in the right units.</p>

<h3>1.4 Dimensional Analysis</h3>

<p>- What are some examples of dimensions? <span id="ans">time, mass, mass
squared (M^2), 1/length (1/L) ...</span></p>

<p>- If a quantity is dimensionless, what are its units? <span id="ans">The
quantity has no units.</span></p>

<p>- What does it mean for an equation to be dimensionally consistent? <span
id="ans">every term has the same dimensions</span></p>

<p>- NOTE: Dimensional analysis can help you remember the correct form of an
equation.</p>

<p>- Is the equation v=a*t dimensionally consistent? <span id="ans">Yes. [v] =
[L]/[T] = [L]/[T^2] * [T] = [L]/[T].</span></p>

<h3>1.5 Estimates and Fermi Calculations</h3>

<p>- What is a Fermi calculation? (This section of the book will not be covered
in class) <span id="ans">An estimation.</span></p>

<h3>1.6 Significant Figures</h3>

<p>- What is the difference between accuracy and precision? <span
id="ans">Accuracy - how close a measurement is to the accepted reference value
for that measurement. Precision - how close the agreement is between repeated
independent measurements</span></p>

<p>- <span id="comm">Compared to the book definition, uncertainty is better
defined as an estimate of how much measured values may deviate from the true
value; Thus the proper definition of uncertainty could include some estimate of
possible discrepancy as well as an estimate of how much measurements may
deviate from one another</span></p>

<p>- What is discrepancy or measurement error ? <span id="ans">Difference
between the measured value and an expected value.</span></p>

<p>- Understand how to calculate percent uncertainty by understanding Example
1.7 (calculating percent uncertainty: a bag of apples).</p>

<p>- Why are significant figures useful? <span id="ans">They are used to
express the precision of a measuring tool used to measure a value</span></p>

<p>- We assume that you already have some familiarity with methods of using
significant figures, and that you will be able to apply those rules. However,
the rules are not always used in this class. Except on LON-CAPA it is safest to
give answers using those rules; it may not always be required though, so it's a
good idea to ask if in doubt.</p>

<p>- Our LON-CAPA homework assignments will usually ask you to enter 3
significant figures for your answers. You need to understand how to do this
correctly. A number like 0.001 has only 1 significant figure, not 3 or 4
because the leading zeros are not significant. The way to see this is to write
it in Scientific Notation (0.001 = 1 x 10^-3 -- there is only 1 significant
figure in that). Significant figures arise because our knowledge is limited by
what we can measure and in real life, we can only measure quantities to a
certain level of precision (that depends on the measuring tools we have). Some
physical quantities have been measured to many decimal places, but only by
means of exquisitely careful measurement with the absolutely best tools. With
the tools you'll have in lab you'll rarely be able to measure quantities to
better than 3 significant figures, so giving lots and lots of digits after a
decimal place is nonsense from an epistemological point of view.</p>

<h3>1.7 Solving Problems in Physics</h3>

<p>- What are the three stages recommended in the book for problem solving?
<span id="ans">Strategy, Solution, Significance.</span></p>

<p>- What is the problem solving strategy? <span id="ans">Make a list of what
is given or can be inferred from the problem as stated (identify the
“knowns”) Identify exactly what needs to be determined in the problem
(identify the unknowns). Determine which physical principles can help you solve
the problem.</span></p>

<p>- NOTE: Making a sketch is almost always an essential part of problem
solving</p>

<p>- How do you find the numerical solution to a problem? <span
id="ans">Substitute the knowns (along with their units) into the appropriate
equation and obtain numerical solutions complete with units.</span></p>

<p>- What do you do to check the significance of the answer? <span
id="ans">Check your units. Check the answer to see whether it is reasonable.
Check to see whether the answer tells you something interesting.</span></p>

<h3>Appendix E</h3>

<p>- Memorize the formulas for areas of circles, triangles and rectangles and
areas and volumes of spheres, boxes and cylinders.</p>

<p>- Know the General Quadratic Formula</p>

<p>- Remember trigonometry (SOH CAH TOA). Note the trig identities and the
expansions that can be used to find approximate solutions for limiting
cases.</p>

<p>- Note the table of derivatives and integrals.</p>

<p>- Not included in any Appendix in this book are a review of the rules for
powers and logarithms. For the following, we use the LON-CAPA conventions that
are also common to many computer programming languages): "^" means
exponentiation (e.g. x^2 is x squared), "/" means "divide by", "*" means
"multiply by", and "&lt;&gt;" means "not equal to".</p>

<p>- For exponents, you should remember that:</p>

<p>x^(-a) = 1/(x^a)</p>

<p>x^0 = 1 (for x &lt;&gt; 0)</p>

<p>x^(a+b) = (x^a)*(x^b)</p>

<p>x^(1/n) = nth root of x.</p>

<p>•For logarithms, you should remember that:</p>

<p>log(a^b) = b * log(a)</p>

<p>log(ab) = log(a) + log(b)</p>

<p>- Note that log(a + b) &lt;&gt; log(a) + log(b). If you get log(a+b), you
are stuck unless you can use an expansion to get an approximate formula.</p>

<p></p>
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