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How People Learn
Conclusion 1:
Henri Poincaré“We must, for example, use
language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.”
“Birds,” said the frog mysteriously. “Birds!” And he told the fish about the birds, who had wings, and two legs, and many many colors.
“Cows,” said the frog. “Cows! They have four legs, horns, eat grass and carry pink bags of milk.”
“And people,” said the frog. “Men, women, children!” And he talked and talked until it was dark in the pond.
Force / Motion Concept Map
Given some forces
1. F 2. m
1. Motion: r,v,a 2. F
Motion: r,v,a
Determine unknown forces
m
Vectors and component resolution
ENGINE
F = ma 1. Draw Picture. 2. Isolate Bodies. 3. Draw FBD. 4. Choose Axes. 5. Apply Fx = max Fy = may
6. Solve 7. Check
Special Cases 1. Constant v a = 0 v = r / t 2. Constant a a = v / t = F/m Example: ax=0, ay=-9.8m/s2 3. Motion in a circle ar = v2/r at = dv/dt
Models 1. Ropes massless and don't stretch. 2. Pulleys massless and frictionless. 3. Weight: Fg = mg 4. Equilibrium: F = 0 5. Friction: fs sn fk = kn f along common plane n common plane dimensionless materials parameter
v is slope of x vs t a is slope of v vs t
1. Motion: r,v,a 2. m
F and individual forces
INPUTS OUTPUTS
Constant Acceleration Kinematics
vxf = vxi + axt x = (vxi+vxf)t/2 x = vxit + axt
2/2 vxf
2 = vxi2 + 2axx
Conclusion 2: Expert vs. Novice Learners
Conclusion 3: Metacognition or reflection
1600to1900
ClassicalPhysics
Mechanics
Thermodynamics
Electromagnetism
1900to1940
ModernPhysics
RelativityLarge speeds (108 m/s).
Quantum MechanicsVery small scales (10-10 m).
1940topresent
CurrentPhysics
Particle Physics
Cosmology
Ch1-1 Physics and the Laws of Nature
How Physics Works
Model / Theory
Observation / Experiment
Length [L] meter Distance traveled by light in vacuum in 1 / 299792458 seconds
Mass [M] kilogram Mass of a platinum-iridium alloy kept in France at the International Bureau of Weights and Measures
Time [T] second 919263177 times the period of vibration of radiation from the Ce-133 atom
Ch1-2 Units of Length Mass and TimeStandards
Ch1-2 Standards of Length Mass and Time Standards
A Force acts on a mass resulting in motion.
M
L,T
Distance from the Earth to the nearest large galaxy (the Andromeda Galaxy, M31)
2 x 1022 m
Diameter of our galaxy (the Milky Way) 8 x 1020 m
Distance from the Earth to the nearest star (other than the Sun)
4 x 1016 m
One light year 9.46 x 1015 m
Average radius of Pluto’s orbit 6 x 1012 m
Distance from Earth to the Sun 1.5 x 1011 m
Radius of Earth 6.37 x 106 m
Length of football field 102 m
Height of a person 2 m
Diameter of a CD 0.12 m
Diameter of the aorta 0.018 m
Diameter of the period in a sentence 5 x 10–4 m
Diameter of a red blood cell 8 x 10–6 m
Diameter of the hydrogen atom 10–10 m
Diameter of a proton 2 x 10–15 m
Ch1-2 Standards of Length Mass and Time Typical Lengths
Galaxy (Milky Way) 4 x 1041 kg
Sun 2 x 1030 kg
Earth 5.97 x 1024 kg
Space Shuttle 2 x 106 kg
Elephant 5400 kg
Automobile 1200 kg
Human 70 kg
Baseball 0.15 kg
Honeybee 1.5 x 10–4 kg
Red blood cell 10–13 kg
Bacterium 10–15 kg
Hydrogen atom 1.67 x 10–27 kg
Electron 9.11 x 10–31 kg
Ch1-2 Standards of Length Mass and Time Typical Masses
Ch1-2 Standards of Length Mass and Time Typical Times
Age of the universe 5 x 1017 s
Age of the Earth 1.3 x 1017 s
Existence of human species 6 x 1013 s
Human lifetime 2 x 109 s
One year 3 x 107 s
One day 8.6 x 104 s
Time between heartbeats 0.8 s
Human reaction time 0.1 s
One cycle of a high-pitched sound wave 5 x 10–5 s
One cycle of an AM radio wave 10–6 s
One cycle of a visible light wave 2 x 10–15 s
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
10–1 deci d
10–2 centi c
10–3 milli m
10–6 micro
10–9 nano n
10–12 pico p
10–15 femto f
Power Prefix Abbreviation
Ch1-2 Standards of Length Mass and Time Common Prefixes
Concept Question 1.1
(2.44 x 10-5) / (2 x 103) =
a. 2.44 x 10-8
b. 2.44 x 10-2
c. 1.22 x 10-8
d. 1.22 x 102
e. 1.22 x 108
Distance [L]
Area [L2]
Volume [L3]
Velocity [L]/[T]
Acceleration [L]/[T2]
Energy [M][L2]/[T2]
Quantity Dimension
Ch1-2 Standards of Length Mass and Time Dimensions of Some Common Physical Quantities
Concept Question 1.2
Ch1-3 Dimensional Analysis
Given the following definitions with their dimensions:
v = velocity (L/T)
a = acceleration (L/T2)
t = time (T)
Which of the following equations could be correct as far as dimensions are concerned?
A. v = at2/2
B. v = a/2t
C. v = at
D. v = a2t/2
E. v = a/t2
How does v depend on a and x?
P1.5 (p. 14) Suppose v2 = 2axp
What is p?
Ch1-3 Dimensional Analysis
Concept Question 1.3
Which statement is correct regarding significant figures?
A. 1.355 + 1.2 = 2.555
B. 1.478 – 1.3 = 0.18
C. 1.513 / 1.5 = 1.009
D. 1.5 x 10-3 + 0.1 = 0.1015
E. 0.1513 x 1.5 = 0.23
Ch1-4 Significant Figures
Do P1.12 (p. 14)
P = 2l + 2 w
Ch1-4 Significant Figures
Round-off: If next digit is 5, then round up.
Scientific Notation: Covered previously.
Ch1-4 Significant Figures
Concept Question 1.4
How many seconds in a 50 minute class period?
A. 1000
B. 50
C. 3 x 10-3
D. 4500
E. 3 x 103
Ch1-5 Conversion of Units
Do P1.24 (p. 15)
Ch1-5 Conversion of Units
CT1.5 A. 500 B. 5,000 C. 50,000 D. 500,000
Ch1-6 Order-of-Magnitude Calculations
Shea Stadium holds about 55,000.
CT1.6 Donovan Bailey – Canada – 1996 Olympics
12345
Who is in 0.1 s of Donovan? A. 2,3,4,5 B. 2,3,4 C. 2,3 D. 2
Donavan is roughly 2 meters tall and that gives the scale. Since they covered 100 m in 10 seconds, each meter takes about 0.1 seconds. The answer is c because they are within roughly 1 meter (half Donovan’s height).
Estimate how many barbers in Chicago?
I started by assuming a typical person gets a haircut every two months. Next I assumed that a barber could give about 4 haircuts/hr or 20/day or 100/week or 400/month or 800/every two months. I rounded this off to about 500/every two months since there may be times when the barber doesn't have customers. So a barber could take care of about 500 customers and then they would all come back again. There are about 3 million people in Chicago proper and 8 million in the metropolitan area so I picked an average of 5 million to represent Chicago. That means about 5x106 / 500 or 104 or 10,000 barbers. This is just an estimate and may be off by a factor of 10 either way given all the questionable assumptions!
A Google search listed 1711 barbers around Chicago.
Ch1-7 Scalars and Vectors
• A scalar is a pure number. What are some examples?
• A vector has magnitude (value) and direction. What are some examples?
• The magnitude of a vector could be considered a scalar.
Ch1-8 Problem Solving
• Read the problem carefully.• Sketch the system.• Visualize the physical process.• Strategize.• Identify appropriate equations.• Solve the equations.• Check your answer.• Explore limits and special cases.
Ch1-8 Problem Solving
Do P1.39 (p. 16) N = number of beatsB = beats/second T = time
Mechanics
Study of forces and energy and motion.
• Force is an agent of change.• Energy is a measure of change.