PHYS 20 LESSONS: INTRO Lesson 1: Intro to CH Physics Measurement.
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Transcript of PHYS 20 LESSONS: INTRO Lesson 1: Intro to CH Physics Measurement.
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PHYS 20 LESSONS:
INTRO
Lesson 1: Intro to CH Physics
Measurement
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A. EXPRESSING ERROR IN SCIENCE
Error is unavoidable in science.
There are 3 major sources of error:
Systematic Errors
Random Errors
Blunders
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Systematic Errors
These are errors from identifiable causes.
They can be improved (reduced).
There are a variety of systematic errors possible ...
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1. Instrument Error
There might be error in the measuring instrument itself.
e.g. Calibration error
0
1
2
This scale has a reading of 0.3 kg, even though there is nothing on it yet. As a result, all measurements will be 0.3 kg too high.
To reduce this error, you need to adjust this scale to a zero reading before you make a measurement.
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2. Observation Error
The student / scientist may be observing the measurement
in a way that introduces error.
e.g.
Parallax Error (reading from an angle)
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Consider measuring the length of an object with a thick ruler:
10 20 30
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10 20 30
From one side, the reading may seem to be 14.0 mm
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10 20 30
From the other side, the reading may seem to be 17.0 mm.
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10 20 30
To reduce parallax error, try to look directly
above the ruler.
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Other Forms of Systematic Error
3. Environmental Error
e.g. A strong wind affects the object's motion
4. Theoretical Error
e.g. You assume there is no friction, but it is significant.
5. Analysis Error
e.g. Rounding error - the more calculations you do withmeasurements, the greater the error
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Random Errors
Errors that are unavoidable.
Some readings are too high, while others are too low.
e.g. Reaction times using a stopwatch
To improve this error, calculate the average.
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Blunders
These are outright mistakes.
e.g.
t (s) d (cm)
0
1
2
3
4
5
3.7
4.6
5.8
1.7
7.5
8.7
This value clearly does not fit the pattern. It is a blunder.
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When blunders are discovered, they are ignored (removed).
t (s) d (cm)
0
1
2
3
4
5
3.7
4.6
5.8
1.7
7.5
8.7
The blunder is ignored when you do the analysis.
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ACTIVITY
Timing a tennis ball (with and without technology)
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A1. Measurements
When you are taking a reading from a measurement device,
how many digits should you record?
The more digits, the more precise (i.e. the better) the device.
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Rule for measurement
You can have only one uncertain digit in a measurement
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Rule for measurement
You can have only one uncertain digit in a measurement
The last digit of a recorded measurement is assumed to be uncertain.
e.g.
4 3 7 . 4 kg
Uncertain digit (could be a 3 or 5)
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e.g. Consider the following measurement:
What would the measurement be?
30 mm10 20
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Measurement: 1 8 mm
The object is longer than 18 mm, but less than 19 mm.
Thus, the first two digits will definitely be 18
Since these are certain, we are still allowed more digits.
30 mm10 201819
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Measurement: 1 8 . 3 mm
Since the length is about 3/10 between 18 and 19,
the next digit is likely a 3.
However, we are not certain about this digit.
30 mm10 201819
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Measurement: 1 8 . 3 mm
This digit could also have been a 2 or a 4
It is impossible to know for sure with this ruler.
Thus, this is our one uncertain digit. We stop here.
30 mm10 201819
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A2. Significant Digits
Significant digits are the digits that are the direct result
of reading the measuring instrument.
Not all digits in a measurement are significant.
It is important to know the conventions for significant digits,
since it is a key skill when doing arithmetic with measured quantities.
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Rule for Measured Quantities
Locate the first nonzero digit from the left
(i.e. the leftmost digit)
This digit, and all digits to the right, are significant
Use this rule for any quantity that is the result of
measurement (i.e. a number with units)
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e.g.
Consider the quantity 28 000 kg
How many significant digits are there?
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2 8 0 0 0 kg
Find the first nonzero digit from the left
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2 8 0 0 0 kg
This digit, and all digits to the right, are significant.
Thus, this quantity has 5 significant digits.
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e.g.
Consider the quantity 0.00720 m
How many significant digits are there?
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0 . 0 0 7 2 0 m
Find the first nonzero digit from the left
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0 . 0 0 7 2 0 m
This digit, and all digits to the right, are significant.
Thus, this quantity has 3 significant digits.
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Rule for Definitions and Counting Numbers
Not all quantities used in science are the result of
measurement. Any quantities based on counting or
definition are considered to be perfect numbers.
Thus, counting numbers and definitions have an infinite
number of significant digits. No uncertainty exists.
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e.g.
Definition: 1 mm = 1 10-3 m Perfect numbers
Counting: 7 tennis balls Infinite significant
digits ()
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A3. Scientific Notation
Definition:
A number is in scientific notation when it is a number
between 1 and 10, multiplied by a power of 10
e.g. 4.85 103 m/s
A number between Multiplied by a power
1 and 10 of 10
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Why use scientific notation?
There are two reasons why this notation is very useful:
1. For very big or small numbers
2. A clear number of significant digits
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1. For big or small numbers
When numbers get really large or really small, there are
many zeros in the number. This makes them difficult to read.
Scientific notation makes them much easier to handle.
e.g.
The radius of a hydrogen atom
is 0.000 000 000 0529 m
Much easier if we express it as
5.29 1011 m
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2. Clear number of significant digits
What if your calculator showed the number 142 000 , but
the answer was supposed to have only 3 significant digits?
You can't simply remove the last 3 digits, since it would
become 142 (clearly not the same number).
But you can't leave the number as 142 000, since this
would have 6 significant digits.
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What if your calculator showed the number 142 000 , but
the answer was supposed to have only 3 significant digits?
So, we put it into scientific notation:
142 000 (3 sig digs) = 1.42 105
This clearly has 3 significant digits
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Method:
To change a number into scientific notation:
Move the decimal to the right of the first nonzero digit
Multiply the resulting number by the appropriate
power of 10
Each time you moved the decimal to the left,
increase the exponent by 1
Each time you moved the decimal to the right,
decrease the exponent by 1
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Key things to remember:
1. Positive exponents for big numbers (greater than 1)
Negative exponents for small numbers (less than 1)
2. If you need to round:
When the next digit is 5 or greater, then round up
Otherwise, don't round up.
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e.g Convert 84170 (3 sig digs) to scientific notation
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8 4 1 7 0 . (3 sig digs)
The decimal is placed at the end of the number
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8 4 1 7 0 (3 sig digs)
The decimal is moved 4 digits to the left
(placed after the 1st nonzero digit)
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8 4 1 7 0 . (3 sig digs)
= 8 . 4 1 7 0 10 4
A number between Moved 4 digits
1 and 10 to the left
(big number = positive exponent)
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8 4 1 7 0 (3 sig digs)
= 8 . 4 1 7 0 10 4
Only 3 sig digs
are allowed
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8 4 1 7 0 (3 sig digs)
= 8 . 4 1 7 0 10 4
Since the next digit is 5 or greater,
you will round up
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8 4 1 7 0 (3 sig digs)
= 8 . 4 1 7 0 10 4
= 8 . 4 2 10 4
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e.g. Convert 0.000 000 056 1 (2 sig digs) to scientific notation
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0 . 0 0 0 0 0 0 0 5 6 1 (2 sig digs)
The decimal is moved 8 digits to the right
(right after the 1st nonzero digit)
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0 . 0 0 0 0 0 0 0 5 6 1 (2 sig digs)
= 5 . 6 1 10 8
A number between Moved 8 digits
1 and 10 to the right
(small number = negative exponent)
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0 . 0 0 0 0 0 0 0 5 6 1 (2 sig digs)
= 5 . 6 1 10 8
Only 2 sig digs
are allowed
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0 . 0 0 0 0 0 0 0 5 6 1 (2 sig digs)
= 5 . 6 1 10 8
Since the next digit is less than 5,
you do not round up
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0 . 0 0 0 0 0 0 0 5 6 1 (2 sig digs)
= 5 . 6 1 10 8
= 5 . 6 10 8
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Normal Sci Eng
Note: Scientific Notation using a TI-83
1. Change to Scientific Notation
Enter: Mode
Sci
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4.73 E 62. To enter the number 4.73 106 :
Enter: 4.73 EE 6
2nd Comma