Transcript Honors Physics

Honors Physics
A Physics Toolkit
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Honors Physics Chapter 1
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Turn in Contract/Signature
Lecture: A Physics Toolkit
Q&A
Website: http://www.mrlee.altervista.org
The Metric System
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Physics is based on measurement.
International System of Units (SI unit)
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Created by French scientists in 1795.
Two kinds of quantities:
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Fundamental (base)quantities: more intuitive
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Derived quantities: can be described using fundamental
quantities.
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length, time, mass …
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Speed = length / time
Volume = length3
Density = mass / volume = mass / length3
Units
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Unit: a measure of the quantity that is defined
to be exactly 1.0.
Fundamental (base) Unit: unit associated with
a fundamental quantity
Derived Unit: unit associated with a derived
quantity
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Combination of fundamental units
Units
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Standard Unit: a unit recognized and accepted
by all.
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Standard and non-standard are separate from
fundamental and derived.
Some SI standard base units
Quantity
Unit Name
Unit Symbol
Length
Time
Mass
Meter
Second
kilogram
m
s
kg
Prefixes Used With SI Units
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Prefix
nano
micro
Symbol
n

Fractions
 10-9
 10-6
milli
centi
kilo
m
c
k
 10-3
 10-2
 103
mega
giga
M
G
 106
 109
1 m  1 106 m
1mm  1  103 m
Conversion Factors
1 m = 100 cm
so
1m
 1 and 100cm  1
100cm
1m
Conversion factor:
1m
100cm
or
Which conversion factor to use?
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Depends on what we want to cancel.
100cm
1m
Example
2.1 km = ____ m
Given: 1 km = 1000 m
1km
2.1km  2.1km 
1000m
Not good, cannot cancel
1000m
 2100m  2.1103 m
2.1km  2.1km 
1km
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Practice
12 cm = ____ m
1m
12cm  12cm 
 0.12m
100cm
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Chain Conversion
1km  1000m
1m  100cm
1.1 cm = ___ km
1km
m

1.1cm  1.1cm 
 1.1  105 km
100cm 1000m
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Practice
1km  1000m
1m  100cm
7.1 km = ____ cm
1000m 100cm
7.1km  7.1km 

 7.1 105 cm
1km
1m
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Still simple? How about…
2 mile/hr = __ m/s
mile
mile
2
2

hr
hr
 1600m   1hr   0.89 m
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   3600 s 
s
 mile 
Chain Conversion
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1hr  3600s
1mile  1600m
When reading the scale,
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Estimate to 1/10th of the smallest division
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Draw mental 1/10 divisions
However, if smallest division is already too small,
just estimate to closest smallest division.
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1 cm
1.3 cm
but not 1.33 cm, why?
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Uncertainty of Measurement
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All measurements are subject to uncertainties.
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External influences: temperature, magnetic field
Parallax: the apparent shift in the position of an object when
viewed from different angles.
Uncertainties in measurement cannot be avoided,
although we can make it very small by using good
experimental skills and apparatus.
Uncertainties are not mistakes; mistakes can be
avoided.
Uncertainty = experimental error
Precision
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Precision: the degree of exactness to which a
measurement can be reproduced.
The precision of an instrument is limited by the smallest
division on the measurement scale.
Smaller uncertainty = more precise
Larger Uncertainty = less precise
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Uncertainty is one-tenth of the smallest division.
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Typical meter stick: Smallest division is 1 mm = 0.001 m,
uncertainty is 0.1 mm = 0.0001m.
A typical meterstick can give a measurement of 0.2345 m,
with an uncertainty of 0.0001 m.
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 
more precise
Accuracy
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
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more accurate
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Accuracy: how close the measurement is to the
accepted or true value
Accuracy  Precision
Accepted (true) value is 1.00 m. Measurement
#1 is 0.99 m, and Measurement #2 is 1.123 m.
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#1 is more accurate: closer to true value
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#2 is more precise: uncertainty of 0.001 m
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(compared to 0.01 m)
Significant Figures (Digits)
1. Nonzero digits are always significant.
2. The final zero is significant when there is a decimal
point.
3. Zeros between two other significant digits are always
significant.
4. Zeros used solely for spacing the decimal point are not
significant.
Example:
 1.002300  7 sig. fig’s
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0.004005600  7 sig. fig’s
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12300  3 sig. fig’s
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12300.  5 sig. fig’s
Practice:
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How many significant figures are there in
a)
b)
c)
d)
e)
f)
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123000
1.23000
0.001230
0.0120020
1.0
0.10
3
6
4
6
2
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Operation with measurements
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In general, no final result should be “more
precise” than the original data from which it
was derived.
Addition and subtraction with
measurements
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The sum or difference of two measurements is precise to
the same number of digits after the decimal point as the
one with the least number of digits after the decimal
point.
Example:
16.26 + 4.2 = 20.46 =20.5
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 Which number has the least digits after the DP?  4.2
 Precise to how many digits after the DP?
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 So the final answer should be rounded-off (up or
down) to how many digits after the DP?
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Practice:
1)
2)
3)
4)
1)
2)
3)
4)
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23.109 + 2.13 = ____
12.7 + 3.31 = ____
12.7 + 3.35 = ____
12. + 3.3= ____
23.109 + 2.13 = 25.239 = 25.24
12.7+3.31 = 16.01 = 16.0
12.7+3.35 = 16.05 = 16.1
12. + 3.3 = 15.3 = 15.
Must keep this 0.
Keep the decimal pt.
Multiplication and Division with
measurements
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The product or quotient has the same number of
significant digits as the measurement with the least
number of significant digits.
Example:
2.33  4.5 = 10.485 =10.
 Which number has the least number of sig. figs?  4.5
 How many sig figs does it have?
 So the final answer should be rounded-off (up
or down) to how many sig figs?
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2
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Practice:
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2.33/3.0 = ___
2.33 / 3.0 = 0.7766667 = 0.78
2 sig figs
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What about exact numbers?
Exact numbers have infinite number of sig. figs.
If 2 is an exact number, then 2.33 / 2 = __
2.33 / 2 = 1.165 = 1.17
Note:
 2.33 has the least number of sig. figs: 3
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Scientific Notation
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Whenever it becomes awkward to say a
number, use scientific notation.
M  10n
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1 <= |M| < 10
n: exponent (positive, zero, or negative integer)
Example:
 23000 = 2.3  104
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0.00032 = 3.2  10-4
4 times to the left
4 times to the right
Practice
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8.6 × 105
860000 = _________
1.02 × 10-5
0.0000102 = ________
3 × 107
30000000 = ________
0.0000003 = ________
3 × 10-7
Arithmetic Operations in Scientific Notation
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Adding and subtracting with like exponents
Adding and subtracting with unlike exponents
Adding and subtracting with unlike units
Multiplication using scientific notation
Division using scientific notation
Use calculator.
Skip to Slide 36
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Adding and subtracting with like exponents
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Add or subtract the values of M and keep the same n.
Example:
2  105 m + 3  105 m
= (2 + 3)  105 m
= 5  105 m
5.3  104 m – 2.1  104 m
= (5.3 – 2.1)  104 m
= 3.2  104 m
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Practice:
2
2
3  10 m  6  10 m  ___
2
2
3 10 m  6 10 m
  3  6  102 m
2
 9 10 m
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Adding and subtracting with unlike exponents
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2.
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First make the exponents the same.
Then add or subtract.
2.0  103 m + 5  102 m
= 2.0  103 m + 0.5  103 m
= (2.0 + 0.5)  103 m
= 2.5  103 m
Practice:
3  10 m  6.0  10 m  ___
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3 106 m  6.0  107 m
 0.3  10 m  6.0  10 m
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  0.3  6.0   107 m
 6.3 107 m
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 10 
3  106  3     106
 10 
3
  10  106   0.3  107
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Adding and subtracting with unlike units
1.
2.
3.
Convert to common unit
Make the components the same
Add or subtract
Example:
2.10 m + 3 cm
= 2.10 m + 0.03 m
= 2.13 m
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Multiplication using scientific notation
1.
2.
3.
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Multiply the values of M
Add the exponents
Units are multiplied
(3  104 kg)  (2  105 m)
= (3  2)  104+5 (kgm)
= 6  109 kg×m
Practice:
2 10 m 5 10 m  ___
3
5
3
5
35
2

10
m

5

10
m

2

5

10
mm

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
 

 10  108 m2
 1  109 m2
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Division using scientific notation
1.
2.
3.
Divide the values of M.
Subtract the exponent of the divisor from the
exponent of the dividend.
Divide the unit of the divisor from the unit of
the dividend.
6 106 m 6
6 ( 2) m
8m


10

2

10
s
3 102 s 3
s
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Displaying Data
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Table
Graph
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Independent variable: manipulated
Dependent variable: responding
Table
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Title or description
Variables (quantities)
Unit (either after variables or each value)
Table 1: Displacement and speed of cart at different times
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Time (s)
Displacement (m)
Speed
1.0
2.4
2.4 m/s
2.1
4.9
2.3 m/s
3.1
7.6
2.2 cm/s
Graph
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Title or description
Labels
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Units
Scales
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Independent variable on horizontal axis
Dependent variable on vertical axis
Horizontal and vertical can be different
Graph Example
Velocity of falling block at different time
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Velocity (m/s)
10
8
6
4
2
0
0
2
4
Time (s)
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6
8
Linear Relationship
y  mx  b
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y1
m: slope
m
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y
rise
run
y2  y1

x 2  x1
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b: y-intercept
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Direct Relationship:
b
x2
x1
y2
y  mx
x
Inverse Relationship
a
y
x
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Hyperbola
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5
4
3
2
1
0
0
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1
2
3
4
5