Transcript Physics - Teacher Pages

Physics
Topic #1
MEASUREMENT & MATHEMATICS
Scientific Method
• Problem to Investigate
• Observations
• Hypothesis
• Test Hypothesis
• Theory
• Test Theory
• Scientific Law  Mathematical proof
Measurement & Uncertainty
• Uncertainty:
• No measurement is absolutely precise
• Estimated Uncertainty:
• Width of a board is 8.8cm +/- 0.1cm
• 0.1cm represents the estimated uncertainty in the
measurement
• Actual width  between 8.7-8.9cm
Measurement & Uncertainty
• Percent Uncertainty:
• Ratio of the uncertainty to the measured value, x 100
• Example:
• Measurement = 8.8 cm
• Uncertainty = 0.1 cm
• Percent Uncertainty =
Is the diamond yours?
A friend asks to borrow your precious diamond for
a day to show her family. You are a bit worried, so
you carefully have your diamond weighed on a
scale which reads 8.17 grams. The scale’s accuracy
is claimed to be +/- 0.05 grams. The next day you
weigh the returned diamond again, getting 8.09
grams. Is this your diamond?
Scale Readings
- Measurements do not necessarily give the “true” value of
the mass
- Each measurement could have a high or low by up to 0.05g
- Actual mass of your diamond  between 8.12g and 8.22g
Reasoning: (8.17g – 0.05g = 8.12g)
(8.17g + 0.05g= 8.22g)
* Actual mass your diamond
- Between 8.12g and 8.22g
* Actual mass of the returned diamond
- 8.09g +/- 0.05g  Between 8.04g and 8.14g
** These two ranges overlap  not a strong
reason to doubt that the returned diamond is
yours, at least based on the scale readings
Accuracy, Precision, and
Percent Error
ACCURACY-
PRECISION-
How close a
measurement
comes to the TRUE
value
How close a SERIES of
measurements are to ONE
ANOTHER
PERCENT (%) ERROR- Absolute value of the
theoretical minus the experimental, divided by the
theoretical, multiplied by 100
Theoretical - Experimental / Theoretical x 100
Metric System
• Expanded & updated version of the metric system:
Systeme International d’Unites
Fundamental SI Units
Physical Quantity
Name
Abbreviation
Length
meter
m
Mass
kilogram
kg
Time
second
s
Temperature
Kelvin
K
Electric current
ampere
A
Amt of Substance
mole
mol
Luminous Intensity
candela
cd
Metric System
kilo
k
103 = 1000
hecto
h
102 = 100
deka
da
101 = 10
meter, liter,
gram (Base)
deci
m, l, g
100 = 1
d
10-1 = 0.1
centi
c
10-2 = 0.01
milli
m
10-3 = 0.001
SI Prefixes
Little Guys
Big Guys
-12
nano
p 10
-9
n 10
micro
µ
pico
milli
centi
m
c
10
-6
10
-3
10
-2
kilo
k
mega
M
giga
G
tera
T
10
3
10
6
10
9
10
12
Reference
Table
Scientific Notation
• Alternative way to express very large or very small
numbers
• Number is expressed as the product of a number
between 1 and 10 and the appropriate power of 10.
Large Number: 238,000. =2.38 x 105
Decimal placed between 1st and 2nd digit
Small Number : 0.00043 = 4.3 x 10-4
Scientific Notation
Express the following numbers in Scientific Notation
1. 3,570
2. 0.0055
3. 98,784 x 104
4. 45
Scientific Notation
• “Scientific Notation” or “Powers of Ten”
• Allows the number of significant figures to be clearly
expressed
• Example:
• 56, 800  5.68 x 104
• 0.0034  3.4 x 10-3
• 6.78 x 104  Number is known to an accuracy of 3
significant figures
• 6.780 x 104  Number is known to an accuracy of 4
significant figures
Scientific Notation
• Multiplying Numbers in Scientific Notation
• Multiply leading values
• Add exponents
• Adjust final answer, so leading value is between 1
and 10
• Dividing Numbers in Scientific Notation
• Divide leading values
• Subtract exponents
• Adjust final answer, so leading value is between 1
and 10
Scientific Notation
• Adding & Subtracting Numbers in Scientific
Notation
• Adjust so exponents match
• Then, add or subtract leading values only
• Adjust final answer, so leading value is between 1
and 10
Significant Figures
• All of the important/necessary or reliably known numbers
• GUIDELINES
• Non-zero digits  always significant
• Zeros at the beginning of a number  Not significant
(Decimal point holders)
• 0.0578 m
3 Significant Figures
(5, 7, 8)
• Zeros within the number  Significant
• 108.7 m
4 Significant Figures
(1, 0, 8, 7)
• Zeros at the end of a number, after a decimal point 
Significant
• 8709.0 m
5 Significant Figures
(8, 7, 0, 9, 0)
Significant Figures
• Non-zero integers
• Always counted as significant figures
** How many significant figures are there in 3,456?
4 Significant Figures
Significant Figures
ZEROS
* Leading Zeros
- Never significant
0.0486
0.003


3 Significant Figures
1 Significant Figure
Significant Figures
ZEROS
* Captive zeros
- Always significant
16.07  4 Significant Figures
10.98  4 Significant Figures
70.8  3 Significant Figures
Significant Figures
ZEROS
* Trailing Zeros
- Significant only if the number
contains a decimal point
9.300  4 Significant Figures
1.5000  5 Significant Figures
Converting Units
• Physics problems require the use of the correct units
• Conversion factors
• Allow you to change from one unit of measurement to
another
• Ex: 1 foot = 12 inches
• Converting units
• Choose the appropriate conversion factor
• Multiply by the conversion factor as a fraction
• Make sure units cancel!
Derived Units
Units for length, mass, and time (as
well as a few others), are regarded as
base SI units
These units are used in combination to
define additional units for other
important physical quantities, such as
force and energy  Derived Units
Derived Units
website
• Units that are created based on formulas and
equations
– Volume
– V = length·width·height = m·m·m = m3
– Area
– A = length·width = m·m = m2
– Force
•
F = mass·acceleration = kg·m·s-2 = Newton, N
– Work
•
W = Force·distance = N·m = Joule, J
– Pressure
•
P = Force/Area = N·m-2 = Pascal, Pa
Dimensional Analysis
• Useful tool utilized to check the dimensional
consistency of any equation to check whether
calculations make sense
• Length is represented by L
• Mass is represented by M
• Time is represented by T
• For an equation to be valid, the left dimension must
equal the right dimension
Trigonometry
• Pythagorean Theorem
• Used to find the length of any side of a right triangle
when you know the lengths of the other two sides
• Right triangle  Triangle with a 90° angle
• c2 = a 2 + b 2
• c = Length of the hypotenuse
• a, b, = Lengths of the legs
Trigonometric Functions
• sin θ = opposite/hypotenuse
• cos θ = adjacent/hypotenuse
• tan θ = opposite/adjacent
Trigonometric Functions
• If you know the ratio of lengths of 2 sides of a right
triangle, you can use inverse functions to determine
the angles of that triangle
• θ = arcsin (opposite/hypotenuse)
• θ = arccos (adjacent/hypotenuse)
• θ = arctan (opposite/adjacent)
• Often written: sin−1, cos−1, tan−1