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Chapter One Lecture
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What Is Physics?
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Qualitative Description
 The goal of science is to understand and explain the physical universe.
Physicists observe the physical world, and try to categorize and understand the phenomena they observe. Many people think that science is something new - but scientific observation started before
recorded history when people first discovered reoccurring relationships in the environment. Through careful observation of these relationships they began to know nature, and because of nature's
dependability, they found they could make reliable predictions that would seem to give them some control over their surroundings. In fact, even before entering school, everyone is already an active
scientist, testing his or her surroundings, describing general relationships, and consistently modifying ideas to fit new observations and experiences.
Scientific Reasoning
Observation and measurement is the beginning of scientific inquiry.
However, simply tabulating a list of facts and numbers does not add up to an understanding of the natural world. In science, we don't just want a general idea or description of
 how things work; we want a precise
understanding of physical phenomena so that we can further build on the event and make more interesting predictions. To demonstrate that understanding (and to put it to use in your
everyday life), you need to know not only the factual information contained within a certain physical situation, but also be able to apply, use, and predict further behavior with reasonable
success using what you have learned and experienced. The goal of science is really to predict the future using past scientific observation and then to test that prediction. If given a known set
of circumstances, what will occur as a result of the applicable physical phenomena? A scientist will only say that she understands something if
she can make quantitative and qualitative predictions based on known laws and theories. The goal of science is not only the presence of observation but also the presentation of theoretical explanations that
lead to better understanding and further investigation.
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In physics, we don't just want a general idea or description of how
things work; we want a precise understanding of physical phenomena. To demonstrate that understanding, I need to be able to describe events
quantitatively. For instance, if I drop a ball from a certain height, the ball will hit the ground after a short period of time. Now I know that if I
drop the ball from a higher height, then the ball will take
 longer to hit the ground. But to demonstrate that I really understand the phenomena of the ball dropping, I have to be able to answer quantitative questions.
If I drop the ball from twice the height, how much longer will it take for the ball to hit the ground? The answer is found in an equation we will encounter in chapter 2.
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We will discuss this equation in detail in the coming weeks, but basically it says that if I
double the height, the ball will take about 1.4 times longer to reach the floor. Without the quantitative equation, I can't really make precise
statements about the physical phenomena. Goal of physics is to predict the future. That is given a known set of circumstances, what will occur
as a result of the applicable physical phenomena. As a physicist, I only will say that I understand something if I can make quantitative predictions based on known laws and theories.
The word "theory" comes from the Greek word that means "to see."
A scientific theory is a canvas of ideas that the scientist uses to paint an artistic model that unifies and explains observations of physical events.
Theories must always agree with the data collected and are not merely dubious guesswork. In fact, if a theory cannot be routinely tested with
further observation, then it is not a theory. If you cannot validate a theory's ideas about physical events, then it cannot tell you anything useful about the world you are trying to describe.
Interpreting Formulas
 Some students think physics is difficult
because of the mathematics used. Yet it is the mathematics itself that allows one to understand the world and make predictions about how things will behave. It is very important then, that you
understand not only how to use and manipulate equations but also what the equations physically mean. You must learn what each piece of a formula is measuring, the units of measure involved in the equation, and what
information is being sought using the equation. Equations and mathematical formulae have meaning. Equations apply to certain observations and events, they describe each detail of an event, and they
help you make predictions based on the measurements and observations. For instance, in chapter 2 we will encounter the equation Dx = vt. This equation has a meaning. It says that if I am moving at a constant velocity v, then the distance I move (Dx) is equal to the velocity times the time. Double time, double distance. Double velocity, double
distance. Cut time in half, cut distance in half. It is quantitative. If I double my speed from 30 miles/hour to 60 miles per hour, then it will
take 1/2 the time to go 20 miles. Also, the symbol means something. It doesn't matter which symbol I use if I know what it means. It makes sense to use "t" for time, but I could use anything.
Deriving Formulas
There are a few very fundamental laws in physics. Much of the rest
of physics can be derived from these few fundamental laws. Occasionally, the book or I will actually derive one equation from a set of other
equations. Why do we do this? - to show the relationships between the more fundamental laws and the derived laws.
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Units
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Every measurement or quantitative statement requires a unit. If I
say I am driving my car 30 that doesn't mean anything. Am I driving it 30 miles/hour, 30 km/hour, or 30 ft/sec. 30 only means something when I
attach a unit to it. What is the speed of light in a vacuum? 186,000 miles/sec or 3´108 m/sec. The number depends on the units.
SI Units
 Meter – (1889-1960) A platinum-iridium alloy
rod with two etched marks defined the standard "meter." The new Meter is defined as the length of path traveled by light in a vacuum during 1/(299,792,458)th of a second. Freaky, Huh?
(LENGTH) (Unit –m) Second – Old definition was 1/(86,400)th of a
mean solar day (time between noon one day until noon the next). Alternatively, the second is defined as 9,192,631,770 vibrations of a cesium atom. (TIME) (Unit – s) Kilogram – A hunk of metal. A precisely
turned hunk of platinum-iridium alloy cylinder kept under guard in Paris.(MASS) (Unit – kg) (Joe! Mention the Standards Bureau guy from
Wash. D.C.!!!)
We will most use the International System of Units (Système International (SI)) units. These consist of the meter (length), the second (time),
and the kilogram (mass). Each of these has prefixes and suffixes that you have encountered and should be familiar with. For instance, centi means 10-2. So a centimeter is 1´10-2 meters = 0.02 meters. A kilogram is 1´103 grams = 1000 grams. There is a table in the front cover of the book of suffixes and prefixes.
Changing Units
 Occasionally, you might have to change to a different set of units. For instance if I am
traveling 65 miles/hour, how fast am I traveling in ft/second? Units behave like any algebraic quantity and cancel when multiplication is performed.
How fast is this in meters/second?
Consistency of Units
When working with formulas and solving problem you must make sure that the units are always consistent.
For instance suppose I am traveling 30 meters/second. How far do I travel in one hour? I cannot say
(30 m/s) (1 hour) = ? because the units do not work out correctly.
I end up getting m-hour/second.
I must convert hours to seconds.
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Solving Problems in Physics
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Significant Figures
Notice in the above problem, I wrote 1.1´105 meters rather than 1.08´105 meters. Why did I do that? -- because I can only know my
answer to a specific accuracy. Every number has a number of significant figures. That is, what is the precision of the number? The number 25
has two significant figures. If a table is 25 inches wide, that means it is more than about 24.5 and less than about 25.5 inches. However, if the
table is 25.0 inches wide, then I now have 3 significant figures. The table is more than about 24.9 inches wide and less than about 25.1
inches wide. 310.0 has four significant digits, but what about 310, which has one or two significant digits (which is it?) which is one reason we use scientific notation. 3.1´102 has two significant digits while 3.10´105 has
three significant digits.
Suppose I have a rectangular garden that is 10.3 by 4.2 meters.
What is the area of the garden? My calculator says it is 43.26 square meters. But that is way too accurate. How could I know the area to .01 square meters when I only know the length to .1 meters?
The rules are as follows.
- When multiplying or dividing numbers, the answer has only as many digits as the number with the least number of significant digits. So 3.2´5.63 = 18. (Only two significant digits).
- When adding or subtracting, the number of decimal places in the answer should match the number with the smallest number of
decimal places. So 3.26 + 4.3 = 7.3.
Dimensional Analysis
This topic is covered in Appendix B of the textbook. Dimensional
analysis helps you solve problems as well as check whether your solution is correct. Since most values have some kind of units, we can use these
units to our advantage. Suppose you want to calculate how far a car will travel that is going a certain speed for a certain time. You can't remember if the equations for calculating this is x = (1/2)vt2 or x =
(1/2)vt. We write the dimensions of the quantities in square brackets.
This still doesn't guarantee that the relation is correct, only that it
is not incorrect. For instance, the constant 1/2 doesn't have any dimensions, so we don't really know what the constant is. (In fact, it is 1 here).
You can also use dimensional analysis to help check your answer.
For instance, speed should be [L]/[T]. If it is not, then there is a problem with your answer.
Rapid Estimating (Order of Magnitude)
Many times it is important to get an idea of what an answer may
be without actually working out the exact number. Often, the answer you get this way will be perfectly adequate for the question being asked.
Even if it is not, a rapid estimate will help you know if the exact answer you calculate is reasonable.
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 Problem: How long would it take to drive a car
around the world? The earth has a radius of 6.38´103 km around. (You can't really go straight
around, but remember we are estimating). You can drive maybe 50 miles/hour. (Sometime it will be more like 75, sometimes more like 30). You can drive
about 10 hours/day. So,
An "order of magnitude" estimate only uses one significant figure & powers of 10.
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Problem: How many quarters would it take to fill up a football stadium?
Each quarter is about 1 inch in diameter and .1 inch thick so it has a volume of:
Volume of One Quarter = pr2t
pr2t = (3)(5´10-1 in)2(0.1in) = (3)(5´10-1 in)2(1´10-1in) = 75´10-3in3
= 7.5´10-2 in3 » 10´10-2 in3
Volume of One Quarter = 1´10-1 in3.
The stadium has a field that is 100 yards by 50 yards long; its footprint
is probably about 4 fields large. Its stands are how high? 10ft, 100ft, 1000ft. Say 90ft. Or about 30 yards high.
So the Stadium has a volume of about:
4´(length)(width)(height) = 4(100yd)(50yd)(30yd) = 4(1´102yd)(5´101yd)(3´101yd)
= 60´104 yd3 = 6´105 yd3 = Stadium Volume
So we have the Volume of One Quarter and the Stadium. How do we figure out how many quarters fit into the stadium?
Hmmmm….
Units? (Inches? Yards?) What do we need to do? (Convert!)
3´1011 = 3´102´109= 300´109 or 300 billion quarters » 75 billion dollars.
This is not exactly right, but it is probably more that a 100 billion and less than 1000 billion (one trillion).
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 Problem: Estimate the number of Ping Pong
Balls that could fit into the volume of the classroom.
First, how do we calculate the number of ping pong balls? Conceptually, we are trying to
estimate how many "smaller" ping pong balls"fit into" a "larger" room. So we are talking about mathematical division, or
Room's dimensions are about 5.0 meters wide by 4.0 m high by 7.0 m long
Volume of Room = (Length)(Width)(Height) = (5.0m)(4.0m)(7.0m) = 140m3
After going to the sports section of Wal-Mart and staring at a typical
ping pong ball I estimate that it had a radius of about 1.5 centimeters.
We need to be consistent with the units of measure, so
Hmmmmm….., but do all the ping pong balls actually fit into a square
room? The ping pong balls don't completely pack into the room, so assuming that they are only about 80% efficient at packing into the
room's dimensions that would lead to the final estimate of;
1.0×107(.80) » 8×106 or 8 million Ping Pong Balls.
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