Transcript ohm symbol microsoft word

Physics: the science of matter and energy and interactions between the two,
grouped in traditional field like acoustics, optics, mechanics, thermodynamics,
and electromagnetism, etc.
Mechanics: motion and its causes, interactions between objects
Thermodynamics: heat and temperature
Vibrations and wave phenomena: specific types of repetitive motions
Optics: light
Electromagnetism: electricity, magnetism and light
Relativity: particles moving at any speed and includes very high speeds
Quantum mechanics: behavior of submicroscopic particles
Nature of Measurement
• Measurement - quantitative observation consisting of 2 parts
• Part 1 – number
• Part 2 – scale (unit)
A number without a unit is NOT a measurement!
• Examples:
• 20 grams
What quantity is this a measurement of?
• 6.63 × 104 meters per second (m/s)
What quantity is this a
measurement of?
When making a measurement, we compare something to a standard.
When you use a ruler, the ruler is the standard that you compare the length of
an objet to.
When you use a balance, the gram is the standard that we usually compare to.
The 7 Fundamental SI Units (Base Units)
Quantity (symbol)
Mass
(symbol is “m”)
Name of Unit
Abbreviation
kilogram
kg
Length (symbol is “l”)
meter
m
Time
second
s
Temperature (symbol is “T”)
kelvin
K
Amount of
substance
mole
mol
Electric current (symbol is “I”)
ampere
A
Luminous
intensity
candela
cd
(symbol is “t”)
(symbol is “n”)
(symbol is “IV”)
Why is volume not listed as a quantity?
Volume is a derived unit (length x length x length = volume)!
Any unit not listed above is a derived unit.
Derived Units
Derived units are units that are defined by a combination of
two or more base units.
Volume = (length x width x height)
If distances are in meters, what would the units for
volume be? (m)x(m)x(m) = m3
(cubic meters)
A definition: 1 cm3 = 1 mL
(one cubic centimeter is one milliliter)
Density = mass ÷ volume = m/V
If mass is in grams and volume is in mL, what
would the units for density be?
(g)÷(mL) = g/mL
(gram per milliliter)
Definitions of SI Prefixes:
Big
terra (T)
giga (G)
mega (M)
kilo (k)
hecto (h)
deka (da)
means
means
means
means
means
means
Middle
Small
deci (d)
centi (c)
milli (m)
micro (m)
nano (n)
pico (p)
femto (f)
atto (a)
means
means
means
means
means
means
means
means
1X1012
1X109
1X106
1X103
1X102
1X101
1000 000 000 000
1000 000 000
1000 000
1000
100
10
1X100
1
1X10-1
1X10-2
1X10-3
1X10-6
1X10-9
1X10-12
1X10-15
1X10-18
0.1
0.01
0.001
0.000001
0.000000001
0.000000000001
0.000000000000001
0.000000000000000001
SI Prefixes written in Equivalence Statement format
1 TL
1 Gs
1 Mg
1 km
=
=
=
=
1X1012 L
1X109 s
1X106 g
1X103 m
Notice the 3, 6, 9, 12 pattern!
1g
1L
1m
1s
=
=
=
=
1X103 mg
1X106 mL
1X109 nm
1X1012 ps
Notice that if we write 1 large unit on the left side of the equal sign, then there
must be a larger number of the smaller units on the right side to be equal.
Uncertainty in Measurement
• A digit that must be estimated is called an
uncertain digit.
• All measurements include all the digits we are
certain of plus one guess digit.
• A measurement always has some degree of
uncertainty because we can always make a
guess about the last digit.
Generally, the more digits a measurement has, the more
precise it is considered to be. Between two numbers,
the number with uncertainty in the smallest decimal
place is the more precise number.
3.28 g
3.2764 g
5 cm
6 cm
7 cm
8 cm
Significant Figures are those digits in a measurement that we are
certain of plus one guess digit at the end.
All non-digital devices have precisions that are one place smaller than the
smallest marking on the device. In the case of the ruler above, the smallest
marks are at the 0.1 cm scale. Therefore, the precision would be at the 0.01 cm
scale.
We would say the measurement was 6.36 cm +/- 0.01 cm (or +/- 0.05 cm
depending upon how well we can estimate our guess). This measurement
would have 3 significant figures!
However, if you are not making the measurement, and the measurement is
given to you, you must use different rules to determine significant figures.
Rules for Significant Figures in Measurements given to you by an
outside source
• Nonzero integers always count as significant figures.
– 3456 has 4 sig figs.
• Leading zeros do not count as significant figures.
– 0.048 has 2 sig figs.
• Captive zeros always count as significant figures.
– 16.07 has 4 sig figs.
• Trailing zeros are significant only if the number contains a decimal point.
– 9.300 has 4 sig figs
– 150 has 2 sig figs.
• Exact numbers have an infinite number of significant figures.
– 1 inch = 2.54 cm, exactly
Exact numbers are definitions or simple counting: 12 is 1 dozen and 4 cars
How many significant figures are in each of the following numbers?
These measurements are given to you by someone else-they are not
numbers that you obtained from a measurement. This means that we
must apply the arbitrary rules for significant figures.
450 g
0.029 m
20.3 s
0.00300 g
$45,700,000
13 people
6.2X10-2 mL
1.300X108 m
Significant Figure Rules for Mathematical Operations:
Multiplication and Division: the number with the fewest
significant figures in the calculation determines how many
significant figures the answer will have.
Examples:
(4.53 m)*(0.28 m)*(1.342 m) = 1.7021928 m3
(from the calculator)
1.7 m3
(correct answer)
(678.3 m)÷(18.4 s) =
36.86413043 m/s
(from the calculator)
36.9 m/s
(correct)
Significant Figure Rules for Mathematical Operations:
Addition and Subtraction: The number with the least
precision determine where the answer ends.
a)
4,300
+ 298
4,598
4,600
b)
the “3” in 4,300 is a guess number and is in the hundred’s position
m
the “8” in 298 is a guess number and is in the one’s position
m
m (calculator answer)
m (correct answer)
Since the hundred’s position is less
precise than the one’s position, the
answer must have its last significant
digit in the hundreds position.
321.4 m
- 298 m
23.4 m (calculator answer)
23 m (correct answer)
Scientific Method: review (discussion)
a) Not Precise and not Accurate
b) Not Accurate but Precise
c) Accurate and Precise
The Difference Between Precision and Accuracy can be more
difficult to see when numbers are given instead of the darts.
Trial
Volume (mL)
1
3.6
2
3.5
3
3.7
Average
3.6
The values are only changing in the last
decimal place, so they are precise.
If the TRUE value for the volume is 3.6, then
the data is also accurate.
However, if the TRUE value for the volume
was 4.2, then the data would only be precise
and would not be accurate.
The Difference Between Precision and Accuracy can be more
difficult to see when numbers are given instead of the darts.
Trial
Volume (mL)
1
3.8
2
2.8
3
4.2
Average
3.6
The values are changing both decimal place,
so they are not precise.
If the TRUE value for the volume was 4.2,
then the data would not be precise and would
not be accurate.
However, if the TRUE value for the volume is
3.6, then the data is accurate by accident.
Problem Solving Strategy Illustration
A solid object is found to have a mass of 84.241 g and a volume of 28.53 mL.
What is the density of the object?
First Step: Highlight key concepts or quantities in the word problem
Second Step: Assign an appropriate symbol for all key quantities
mass = m = 84.241 g
volume = V = 28.53 mL
density = d = ?
Third Step: Use the list of symbols to identify any useful equations
d =
m
V
m = 84.241 g
V = 28.53 mL
d =
d=?
m
V
Fourth and Fifth Steps: Arrange the symbols in the equation so that the
unknown variable is by itself on one side and then substitute quantities into
the mathematical equation and complete the indicated mathematics
d =
84.241 g
28.53 mL
Sixth Step: Check significant figures and units and write the correct answer
You have 14.3 mL of an object that has a density of 7.932 g/mL.
What is the mass of the object?
You have 435.3 g of a liquid that has a density of 0.8325 g/mL.
What is the volume of the liquid?
Problem Solving Strategy Illustration 2
See Example Problem 1 on page 4
What is the resistance of a light bulb that has a current of 0.75 amp and a voltage
of 120 v?
From the book the key equation is:
V = IR
Where V is voltage in volts (v)
I is current in amperes (amp)
R is resistance in ohms (ohm)
Use the approach outlined in the 1st Problem Solving Strategy Illustration and
the information on page 4 to complete the problem above.
Mathematics with Scientific Notation:
Let your calculator handle the exponents!
Let’s do an example: 3.4X106
2.8X105
+
On your calculator (Texas Instruments), type the following in order:
3.4
2nd
EE
6
+
2.8
2nd
EE
5
On your calculator (Casio), type the following in order:
3.4
exp
6
+
2.8
exp
5
=
When you let the calculator handle the math, you job is to take care of the
significant figures-calculators do not understand significant figures!
=
Unit Conversion Problems: the quantity given and the answer are
representing the same concept, but the units have changed.
How many Gm are in 1.5X1013 meters?
For example:
We need the following equivalence statement:
1 Gm
=
1X109 m
Now we use the equivalence statement so that the “m” units cancel out
and are replaced by the units “Gm”.
(
1.5X1013
m
)(
)
1 Gm
1X109 m
= 1.5X104 Gm
How many mg are in 3.42X10-4 g?
(
3.42X10-4 g
)(
)
Equivalence Statements and Conversion Factors
Any statement that says that one quantity is equal to another
is an equivalence statement.
12 things = 1 dozen
1 inch = 2.54 cm
1 km = 1000 m
Each of these equivalence statements can be used to create
conversion factors.
Example:
1 inch
1 inch
2.54 cm
=
2.54 cm
2.54 cm
1 inch
1 inch
=
2.54 cm
This is a conversion factor that converts
from “in” into “cm”
This is a conversion factor that converts
from “cm” into “in”
How many dozen apples do you have if you have 270 apples?
We need the following equivalence statement: 12 apples = 1 dozen apples
(
)(
270 apples
1 dozen apples
12 apples
)
= 22.5 dozen apples
Conversion Factor
(created from the equivalence statement)
We could have tried to remember that 1/12 is 0.0833 and then used the
value 0.0833 as a conversion factor. However, in the long run it is more
efficient to learn the equivalence statements and then use them to create
conversion factors as needed.
How many apples do you have if you have 13.5 dozen apples?
Dimensional Analysis
Using units to guide your use of conversion factors to solve problems.
If you know that your car has a mileage rating of 23.5 miles per gallon and you
assume that gas costs $3.60 per gallon, how much will it cost you to travel
545 miles?
What were you given?
Important Equivalence statements:
1 gal = 23.5 miles
Travel 545 miles
What were you asked to find?
$3.60 = 1 gal
Cost for traveling 545 miles
Start with what you were given and convert the units into what you were asked
to find (using the equivalence statements you know).
(545 miles)(
1 gal
23.5 miles
= $ 83.5
)(
$ 3.60
1 gal
)
Error (or absolute error) is the difference between the accepted value for a
measurement and the experimental value for a measurement.
Error = Experimental Value – Accepted Value
Example: The accepted density for chloroform is 2.97 g/mL;
In an experiment, a student obtained a value of 2.85 g/mL.
The Error in her measurement is:
Error = 2.85 g/mL – 2.97 g/mL = - 0.12 g/mL
Percent Error is the error expressed as a percentage!
% Error =
(
)
* 100
% Error = [(2.85 – 2.97)/2.97]*100 = 4.0%
Notice that the error was negative, but the percent error was not. Percent error is always positive.
Independent Variable: the variable that a scientist chooses to change during an
experiment is called the independent variable
Dependent Variable: the variable that responds to changes in made to the
independent variable is called the dependent variable
When making a graph, we plot the independent variable on the x-axis (horizontal)
and the dependent variable on the y-axis.
If this type of graph forms a line, then the dependent and independent variable have
a linear relationship which can be described by the general equation for a line:
y = mx + b
where m is the slope and b is the y intercept
Slope =
(
y2 – y1
x2 – x1
)
Non-linear Relationships
Non-linear relationships fall into two categories:
Quadratic Relationships and Inverse Relationships
If the best fit for the data is an equation like this: y = ax2 + bx + c
then the data has a quadratic relationship and the shape of the graph is called a
parabola.
If the best fit for the data is an equation like this: y = a/x then the data has an
inverse relationship and the shape of the graph is called a hyperbola
Note: if the data does not form any type of discernible pattern then the variables are
not related to each other (in other words, changing one does not do anything
particular to the other.
What is the relationship between the variables in this graph?
45
40
35
30
25
20
15
10
5
0
0
20
40
60
80
100
120
What is the relationship between the variables in this graph?
600
500
400
300
200
100
0
0
100
200
300
400
500
What is the relationship between the variables in this graph?
100
90
y = x2 + 2E-14x - 2E-14
80
70
60
50
40
30
20
10
0
0
2
4
6
8
10
Note: spreadsheet programs like Microsoft Excel have the ability
to create graphs using x-y scatter plots. Within that program, the
data can be fitted with a “trendline” of best fit and the equation
can them be added to the graph. All of the previous graphs were
created using Excel.
Examples of non-scatter plot graphs in Excel
Bar Graph
Circle Graph
25
Seniors
20
Juniors
15
Sophomors
10
Freshmen
5
0
Seniors
Juniors
Sophomors
Freshmen