Transcript CGS units of vol.

Unit I - notes
Significant Digits also called
Significant Figures
Significance is about precision of measurement.
Non-zero #s are always significant.
Zeros: initial – never; internal – always;
final – sometimes – if zero is not there as a place holder
then it is measured & significant.
Measure to uncertainty – that is, the first digit you must
estimate.
Mini lab
Ex. 1 – measure the width of a block of wood & give the
answer in an appropriate # of sign. dig. ( in cm)
Ex. 2 – measure the mass of a nickel. ( in g)
Precision vs. Accuracy
Mini lab
Measure the width of the block of wood provided a) from the
end of the ruler; b) from the beginning of the scale. Which
measurement is more accurate? Which is more precise?
Math & sign. Dig.
• When doing math & sign. dig - weakest link. Least precise
measure. Explain.
• For + & - it is the # of dec. pl. of the least precise meas. that
determines the precision of the ans.
• For x & ÷ determined by # of S.D. of least precise. that
determines the precision of the ans.
Dimensional Analysis
Algebra is doing the same things with letters
you did with #s.
Dimensional analysis is doing the same
things with units (dimensions) you did
with #s & letters.
Dimensional analysis is analyzing dimensions
(units) to determine what mathematical
operation should be done with the #s.
D.A. is only used when no formula is available
– formulas trump D.A.
MKS/CGS
2 systems of measurement in physics
MKS = meter kilogram second
CGS = centimeter gram second
Never hybridize the 2 – opportunity will be given from time to time for
you to make that mistake so be on guard.
You text does not deal w/ this issue but I will.
MKS most frequently used
CGS useful mainly for very small objects – ex. bugs or
spiders or germs, oh my!
Lab Report Format
Purpose: Corresponds to ”Problem” in the scientific
method. What are we attempting to determine in the
investigation. Should address independent & dependent
variables.
Data table - discussed on the next slide. We will do most
data tables on ExCel spreadsheets.
Calculations - when we do labs we will attempt to get
the computer to do most of the calculations. However,
you will be required to show 1 calculation of each type in
a lab report.
Conclusion - interpretation of the data. Generally you
will be given questions to answer as well.
Data tables
1.
2.
3.
4.
Stand alone – thus a title & that title should help make it stand
alone.
Should contain all data – known, measured, & calculated. Ex. 1.
What data would be collected for determining the density of 10
ml (would it matter what volume we chose?) of HCl? Get with
your study buddy & write a procedure. Talk it out.
Data should be organized based on math principles not
chronology. How would one organize the data for Ex. 1 above?
Get with your study buddy & prepare a data table for these data.
In the case of data to be graphed, data should be in x,y format as
you have learned in math. What is the dep. variable in Table 1-4
p. 18? Problem 25 p. 19? I believe data tables for graphed data
always ought to be vertically oriented! (& since I so believe that is
the way we will do it – ziiinngggggg!)
Should include units & the units should be in the headers not with
the individual data. Rationale.
Order of Magnitude - estimations
Order of magnitude is the rounded power of
10 of a # expressed in scientific notation.
Useful in making quick estimates.
What is the order of mag. of each of the
following:
# of inches in foot?
# of molecules in a mole?
Mass of a proton?
Mass of an e-? (in kg)
Volume of a block of wood? CGS units of vol.
Ways things can be related
?
Direct = linear: annotated in science as y a x (a = proportional)
Inverse: y a 1/x
Quadratic: y a x2
Inverse square: y a 1/x2
In physics, @ our level @ least, we can write equations for linear or
direct relationships only – therefore, we will endeavor to get
equations in linear form. Handout problem & can lab which will
follow will establish this point.
When we write these equations we write them in terms variables
given not x & y. See p. 19 + 16 fig. 1-16. The equations should be
written L = .08 cm/gxm + 13.7 cm not
y = .08 cm/g.xm + 13.7 cm
Functions
What does it mean to say that a variable is a
function of another variable?
= physically dependent upon.
Thus the terms independent variable (the x
variable) & dependent variable (the y variable).
In math, f(x) = x; b/c y is a function of x, that is,
y is physically dependent upon x.
y vs. x follows from this. This annotation seems
to be a science thing not a math thing. Have you
seen the annotation “y vs. x” before?
Graphing
See rules of graphing p.16
Add to those rules – draw plotted point within an open geometric figure. Use a
different figure for each line if you are plotting more than one line on the same
graph.
Legend
Interpretation of rule 4 - use as much of the page of graph paper as possible more than half in each direction.
Origin of all graphs is 0,0 but see jagged line fig. 1-15. Effectively some of the #s
can be omitted along 1 or both axes. What are the increments along each axes
on fig. 1-15? Notice that the #s .5 through 13 are omitted along the y axis.
Graphs may be oriented portrait or landscape.
Best fit/principle of uniformitarianism – rule # 8 graphing procedure p. 16.
Slope has dimensions (or not) – see p. 19.
slope = .08 cm/g not just .08
There is more to learn about slope – stay tuned!
Post lab – C vs d
In physics & (math as it turns out)
slope is often a meaningful. In this
case slope is p.
From the lab we also learn a
definition for p – what is it?
Metric Conversion
• km … m.dm.cm.mm…m…nm.Å
• square units – how many in2 in a ft2?
• cubic units
Post lab - Can lab
The point of this lab is using what we know
about how various relationships graph to get
data in a form we can write an equation, that is
in linear form. From the original graph we could
see we had an inverse relationship. Reason told
us that we had a quadratic relationship b/c drain
time was really a function of area (A=pr2).
Putting these 2 together led us to graphing t vs
1/d2. This, in turn, gave us a linear relationship
which allowed us to write an equation in the y =
mx + b format.
Physics
What is your current view of what physics is?
The study of matter & motion.
Notice the 2 aspects matter & motion.
What is matter?
Anything that has mass.
Therefore, physics is the study of objects & their motion
(or perhaps lack of it).
The Realm of Physics
c
v
?
Relativistic
Quantum
Mechanics
Relativistic Physics
Quantum
Mechanics
Classical Physics
10-14 m
10-10 m
Size
Classical Physics
Ordinary sized objects
Ordinary speeds
atoms --- celestial bodies
Foundational to understanding modern physics.
Modern Physics
Quantum Mechanics
extremely small objects
ordinary speeds
Relativistic Physics
ordinary sized objects
speeds approaching “c”
Relativistic Quantum Mechanics
extremely small objects
speeds approaching “c”
Topics studied in Physics
Vectors
Displacement
Velocity
Acceleration
Force
gravitational
electrical
nuclear
Momentum
Energy
Electricity & magnetism
Waves & optics
Heat & behavior of
gases