What is physics

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Physics
? What is physics?

• Measurements in physics

- SI Standards (fundamental units) - Accuracy
and Precision - Significant Figures

• Language of physics

- Mathematical Expressions and Validity -
Graphs (recognizing functions)
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? What is physics?

• A way of describing the physical world

6th Century B.C. in the Greek city of Miletus
(now in Turkey) a group of men called
physikoi tried to answer questions about the
natural world. Physics comes from the Greek
physis meaning nature and the Latin
physica meaning natural things

• Physics is understanding the behavior and
  structure of matter

- It deals with how and why matter and energy act
as they do
- Energy is the conceptual system for explaining
how the universe works and accounting for changes
in matter
- The word energy comes from the Greek en,
meaning in and ergon, meaning work.
Energy is thus the power to do work. Sounds
weird!!
- Although energy is not a thing three ideas
about energy are important

• It is changed from one form to another
  (transformed) by physical events
• It cannot be created nor destroyed (conservation)
• 3. When it is transformed some of it usually
  goes into heat

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• Areas within physics studied this year

Mechanics Motion and its causes Thermodynamics
Heat and temperature Vibrations and Waves
Periodic motion Optics Behavior of
light Electromagnetism Electricity, magnetism
and EM waves Atomic Structure of the atom,
energy associated with atomic changes Nuclear
Structure of the nucleus, energy associated with
nuclear changes
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? What is physics?
- Investigations in physics generally follow the
scientific method
Observations initial data collection leading to
a question, hypothesis formulation and testing,
interpret results revise hypothesis if
necessary, state conclusions
- Physics uses models to simplify a physical
phenomenon
They explain the most fundamental features of a
phenomenon. Focus is usually on a single object
and the things that immediately affect it. This
is called the system

• Models help

identify relevant variables and a hypothesis
worth testing guide experimental design
(controlled experiment) make predictions for new
situations
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Measurements in physics - SI
Standards (fundamental units)
Fundamental units distance meter (m)
time second (s)
mass - kilogram (kg)
temperature - kelvin (K)
current ampere (A)
luminous Intensity -
candela (cd)
Amount of substance mole (mol) 6.02 x 1023
Derived units combinations of
fundamental units
speed (v) distance/time acceleration (a)
velocity / time force (F) mass x
acceleration energy (E) force x
distance charge (Q) current x time
units m/s
units m/s/s m/s2
units kgm/s2 N (Newton)
units kgm2/s2 Nm J (Joule)
units As C (Coulomb)
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Measurements in physics - Precision
and Accuracy
Its better to be roughly right than precisely
wrong Allan Greenspan, U.S. Federal Reserve
Chairman (retired)
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Measurements in physics - Precision
The precision of a series of measurements is an
indication of the agreement among repetitive
measurements. A high precision measurement
expresses high confidence that the measurement
lies within a narrow range of values.
Precision depends on the instrument used to make
the measurement. The precision of a measurement
is one half the smallest division of the
instrument.
The precision of a measurement is effected by
random errors that are not constant but cause
data to be scattered around a mean value. We say
that they occur as statistical deviations from a
normalized value.
Random variations can be caused by slight changes
in pressure, room temperature, supply voltage,
friction or pulling force over a distance. Human
interpretation is also a source of random error
such as how the instrument scale is read between
divisions.
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• Measurements in physics
• - Significant Figures

Significant figures reflect precision. Two
students may have calculated the free-fall
acceleration due to gravity as 9.625 ms-2 and 9.8
ms-2 respectively. The former is more precise
there are more significant figures but the
latter value is more accurate it is closer to
the correct answer.
General Rules
1. The leftmost non-zero digit is the most
significant figure.
2. If there is no decimal point, the rightmost
non-zero digit is the least significant.
3. If there is a decimal point, the rightmost
digit is the least significant digit, even if it
is a zero.

• All digits between the most significant digit and
  the least significant digit are significant
  figures.

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• Measurements in physics
• - Arithmetic with Significant Figures

When adding or subtracting measured quantities
the recorded answer cannot be more precise than
the least precise measurement.
Add 24.686 m 2.343 m 3.21 m
Answer 30.24 m 3.21m has the least dps
When multiplying or dividing measurements the
factor with the least number of significant
figures determines the recorded answer
Answer 6.8 cm2 2.1 cm has only 2sf
Multiply 3.22 cm x 2.1 cm
Note significant digits are only considered when
calculating with measurements there is no
uncertainty associated with counting. If you
counted the time for ten back and forth swings of
a pendulum and you wanted to find the time for
one swing, the measured time has the uncertainty
but the number of swings does not.
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• Measurements in physics
• - Repeated Measurements

Random errors influence the precision of
measurements taken during an experiment. Repeated
measurements help reduce the effects of random
uncertainties. When a series of measurements is
taken for a measurement, then the arithmetic mean
of a reading is taken as the most probable
answer. This is the same as saying, take the
average.
For example suppose we have the following
repeated measurements
l1 140 cm , l2 136 cm , l3 142 cm, l4
144 cm
lmean l1 l2 l3 l4 140cm 136cm
142cm 144cm 140.5 cm n
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The measurement is therefore l 141 cm (3sf)
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• Measurements in physics
• - Accuracy and systematic uncertainty

The accuracy of a measurement is its relation to
the true, nominal, or accepted value. It is
sometimes expressed as a percentage deviation
from the known value. The known or true value is
often based upon reproducible measurements.
Instruments might not be accurate. A two-point
calibration can be used to check. Does the
instrument read zero when it should and does it
give a correct value when it is measuring an
accepted value
Systematic uncertainty effects the accuracy of a
measurement because it comes from a source of
error that is constant throughout a set of
measurements. The measurements are consistently
shifted in one direction.
A common source of systematic error is not
zeroing your measuring instrument correctly so
that all data is constantly shifted away from the
true value. This can give high precision but poor
accuracy.
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• Measurements in physics
• - Accuracy and systematic uncertainty
• - Percentage Deviation

The accuracy of a measurement is sometimes
expressed as a percentage deviation from the
known value. The known or true value is often
based upon reproducible measurements.
For example, if a student determines
experimentally the acceleration due to gravity is
9.5 m/s2 but the known value is taken as 9.8 m/s2
then ..
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• Measurements in physics
• - Mistakes

Mistakes on the part of the individual such as..

• Misreading scales (using equipment incorrectly)

• Poor arithmetic and computational skills

• Wrongly transferring raw data to the final
  report

• Using the wrong theory and equations

These are a source of error but ARE NOT
considered a source of experimental error
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• Language of physics
• - Mathematical Expressions and Validity

Physicists use the tools of mathematics to
describe measured or predicted relationships
between physical quantities in a situation.
A physical equation is a compact statement based
on a model of the situation
Like most models, physics equations are only
valid if they can be used to make predictions
about situations. Physical expressions can be
checked for validity a number of ways

• 1. through an experiment
• through dimensional analysis
• by order of magnitude estimation

Lets say that you are trying to find the mass of
an object using, M V / ?
Dimensionally m3 / kg/m3 m3 m3 / kg m6 /
kg not kg So the variables are in the incorrect
order! (M V ?)
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• Language of physics
• - Tables (recording data)

Data should be organized and legible

• Give your table a specific title

• Record constants above the table

• Use Column headings and include units

• Record data to the appropriate number of
  significant figures.

Identifying, specific title Multiple tables must
be numbered
Table 1. Length vs. Period For a Pendulum Mass
of the pendulum bob is 103 g The angle of swing
is 4 degrees
Constants are listed above the table
Units given per measured quantity
Answer limited to 2 SF plus reaction time of stop
watch is about 0.2 s which limits answer to 1 dp
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• Language of physics
• - Graphs (recognizing functions)

So youve found a question that needs to be
answered, identified variables, restricted them,
produced a mathematical model and devised an
experiment that will collect data. How do you
know that your data supports or refutes your
model?
The answer lies in graphs It is important to be
able to recognize the shape of a graph and be
able to relate that shape to a mathematical
function. You can then compare this function to
your model. Some functions found in physics are
shown on the next two slides!
Direct
y? x y  kx k
slope of the line y is directly
proportional to x Note If the line does not go
through (o,o) it is linear y kx
b b y intercept
Independent y  k y does not
depend on x
b
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• Language of physics
• - Graphs (recognizing functions)

Inverse Proportional y ? 1/x
y  k/x y k x-1 y
is inversely proportional to x
Square y  ?  x2 y  kx2 y is proportional to the
square of x
Square root y  ?  vx y  k v x Y k x1/2 Y is
proportional to the square root of x
Note all these functions are all power
functions as they fit the general expression, y
A xB where A and B are constants
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• Language of physics
• - Graphs (recognizing functions)

Exponential Growth y  anbx y increases
exponentially with x
Exponential Decay y  an-bx Y decreases
exponentially with x
Periodic y  A sin (Bx  C) Y varies
periodically with x
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• Language of physics
• - Graphs (recognizing functions)

Lets say that you are investigating how the
period (T) of a pendulum (time for one swing)
depends on the length (l) of the pendulum and you
have come up with a mathematical model that says,
T 2? ? ( l/ g). You then test this model
experimentally and plot a graph of T vs. l (shown
below). Which function best describes your data?
The curve through the data cant be a straight
line because as the length decreases, the period
decreases so at zero length we would expect the
pendulum to take no time to swing back and forth.
The model says that T ? ? l or T ?
l1/2 This suggests that we should look at a power
function and in particular a square root function
(ykx1/2)
You can see that the computer generated power
function fit is a good fit to our model as the
data fits T (2.06) l0.46 The power 0.46 is
very close to 0.5 (1/2) We can also use our data
to verify the constant g because Comparing our
model with the fit equation we find 2? /
?g 2.06 so g (2? / 2.06)2 9.3
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• Language of physics
• - Graphs (turning a curve into a
  straight line)

Sometimes its nicer to see a relationship from a
straight line graph rather than a curved graph,
especially when we use uncertainty bars (next
slide). To turn a curve into a straight line you
look at the proportional statement. If you wanted
to turn the pendulum curved graph into a straight
line graph what would you plot on each axis?
Now T ? ? l so our data should fit a straight
line if we plot T vs. ? l instead of T vs. l
You can see that the data now fits a nice
straight line which goes very close to the
origin.
The slope (1.84) can be related back to the
proportionality constant which is 2? / ?g