Physics 1A
Lecture 1B
"I imagine good teaching as a circle of earnest
people sitting down to ask each other meaningful
questions. I don't see it as the handing down of
answers. So much of what passes for teaching is
merely a pointing out of what items to want."
--Alice Walker
Standards/Units
Last time we said that Physicists study objects
that range from enormous (galaxies) to
microscopic (quarks).
In order to measure objects you need to have a
standard to compare things.
There are three basic quantitative measurements:
Time, Length, and Mass
Every measurement we will make in this class can
be broken up into these base quantities.
For example, velocity can be broken up into Length
over Time.
Standards/Units
The most prevalent standard of units in the
world is the SI unit.
Here:
Length [L] => meters (m)
Mass [M] => kilograms (kg)
Time
[T] => seconds (s)
Other unit systems?
English
=> [feet, slugs, seconds]
Gaussian => [centimeter, grams, seconds]
Standards/Units
The obvious advantage of using the SI units is
that different units increase by power of tens.
It is much easier to remember that there are
1,000 mL in 1 L instead of 4 gills in 1 pint.
Become familiar with common prefixes, such
as:
micro => 10-6
milli
=> 10-3
centi => 10-2
kilo
=> 103
Mega => 106
Combining Measurements
Each measurement is a number multiplying a
unit.
=> To add two measurements both have to
have the same units !!
=> To multiply or divide measurements means
the result has the product or division of the
units. (see “dimensional analysis”)
Unit Conversions
Sometimes you will need to switch between
units. E.g., in order to add measurements.
Conversion factors with unit value allow you to
change the units of a quantity without
changing its physical value.
For example, changing 4.50 g/cm3 to ?? kg/m3
Unit Conversions
How important are unit conversions?
In 1999, $125 millon Mars Climate Orbiter was
approaching Mars. Contact was lost as it
reached Mars.
The Orbiter passed 57 km above the Mars
surface, instead of the intended 147 km.
Lockheed-Martin Astronautics (spacecraft
builders) programmed in conversion information
for telemetry data with English units.
NASA’s JPL (navigation) used SI units. Mix up
caused crash.
Dimensional Analysis
A useful tool is dimensional analysis.
With dimensional analysis you examine an
equation by only looking at the dimensions
and ignoring numerical values.
Everything in this class can be written in
terms of the base dimensions [L], [M], [T]
You can multiply, add, subtract, divide
dimensions like a typical algebra problem.
Dimensional Analysis
For example, let’s say that we were looking
at dimensions of the equation:
KE = (1/2)mv2
(1/2) has a dimension of [1]
m has a dimension of [M]
v has a dimension of [L/T]
So the dimensions of KE are: [1][M][L/T]2
Dimensional Analysis
In any given equation, you can only add like
dimensions.
Suppose you are taking an exam and you
derive the following equation:
v = vo + (1/2)at2
Use dimensional analysis to perform a quick
check for validity.
Not dimensionally
correct ->
Significant Figures
We will follow the general rules of
significant figures in this class.
How many significant figures does the value
500m have?
1.
How many significant figures does the value
0.005m have?
1.
How many significant figures does the value
0.0050m have?
2.
Scientific Notation
Be familiar with scientific notation.
It helps you to also better establish the
significant figures for a given value.
From the last slide we could have written
500m as 5x102m.
If we had a little more accuracy we could
rewrite as 5.0x102m.
One last warning for significant figures,
definitions are exact and thus have infinite
significant figures.
3ft = 1yd or 2.54cm = 1in.
Trigonometry
Estimation
Sometimes there will not be an easily found, exact
answer available for a given problem. Or you are
uncertain about your exact answer, and want a “sanity
check”.
In this case, “crude” estimates are extremely valuable.
For example, what if you were asked to find the
number of jelly beans in a container?
Estimates are designed to get you close to the answer
with ease (say within a power of ten).
Example
Estimation
Physicist Enrico Fermi was known for his
estimation prowess. At a party (in the late
60’s), he was approached by someone and asked
“How many piano tuners are there in Chicago?”
Answer
For estimation, the best thing is to be as
complete as possible.
First we should find out how many pianos there
were in Chicago.
Estimation
Answer
Fermi first estimated how many people lived
in Chicago, at the time it was 700,000.
He then guessed that 1 out of 3 families
owns a piano.
Assuming a family is about 4 people this
means 1 out of 12 people have a piano. We
round this to 1 out of 10 for ease.
This means that there were about 70,000
pianos in Chicago at that time.
Answer
Estimation
Next, Fermi turned to how many piano tuners
could get work for 70,000 pianos.
He first determined that it took 1 to 2 hours
to tune a piano.
Thus, a piano tuner could service about four
pianos a day.
Assume a typical work schedule, 5 days per
week and 50 weeks per year.
So, in a year a piano tuner will tune:
(4 pianos/day)x(5 days/week)x(50 weeks/year)
=1,000 pianos/year
Estimation
Answer
A piano should be tuned about once a year.
(1,000 pianos/year) x (1 year/tuner)
= 1,000 pianos/tuner
Thus,
Actual listing in the phone book:
50 piano tuners
Estimation
Start by decomposing the problem into
factors that you think you can guess
reasonably reliably, or know outright.
Round off all numbers to 1 digit significance,
so make algebra easy.
Do the algebra to get your answer.
For Next Time (FNT)
Start reading Chapter 2
Keep on working on the homework
for Chapter 1
California birth estimation