physics lesson 3 strategies of studying physics eleanor roosevelt high school chin-sung lin
TRANSCRIPT
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Physics Lesson 3
Strategies of Studying Physics
Eleanor Roosevelt High School
Chin-Sung Lin
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Strategies of Studying Physics
Use physics words with precision
Know the concepts behind the formulas
Apply dimensional analysis
Develop problem solving skills
Think through the math
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Physics Words
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Use Physics Words with Precision
Definition of Physics Words
Physics words have precise definitions May be different from their regular English meanings Engage in “physics talk”
Distance Displacement
Speed Velocity
Force
Work
Energy
Momentum
Impulse
Acceleration Gravity Normal
Power
Field
Potential
Current
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Physics Concepts
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Know the Concepts behind the Formulas
Context of Physics Formulas
Physics formulas has conditions attached to them
Fnet = ma W = Fd
Net force Any force
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Know the Concepts behind the Formulas
Context of Physics Formulas
Concepts and principles form the basis of formulas
ETA = ETB
PEA + KEA = PEB + KEB
Conservation of Energy
mghA + ½ mvA2 = mghB + ½ mvB
2
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Know the Concepts behind the Formulas
Context of Physics Formulas
Engage in the “concept explaining process”
Any forms of teaching, explaining, or writing physics
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Know the Concepts behind the Formulas
Teaching & Writing Process (Research Results)
Based on a student teaching research:
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Assume:
ti is the teaching score of ith student
ri is the Regents score of ith student
pi is the predicted Regents score of ith student based on ti
where i = 1, 2, 3, ……12
Know the Concepts behind the Formulas
Data Comparison - Definition
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Define an objective function M: the root-mean-square (rms) value of the
difference between ri and pi
12
M = (ri - pi)2 /12 I = 1
Know the Concepts behind the Formulas
Data Comparison - Objective Function
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-
Results
pi = f(ti) = 1.9 ti - 100 or p = f(t) = 1.9 t - 100
M = 15.4 for all studentsM = 3.5 excluding 3 exceptions
Know the Concepts behind the Formulas
Regents Scores Prediction (A Linear Function of Teaching Scores)
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Regents Test Score Prediction I(A Linear Function of Teaching Scores)
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Assume:
s1i - ave. test score of 1st mp for ith student
s2i - ave. test score of 2nd mp for ith student
di - difference btw s2i & s1i for ith student
where i = 1, 2, 3, ……12
di = s2i - s1i
Know the Concepts behind the Formulas
Data Comparison - Definition
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Results
pi = f(ti, di) = 1.615 ti + 0.3 di - 74.5 or
p = f(t, d) = 1.615 t + 0.3 d - 74.5
M = 13.3 for all studentsM = 1.9 excluding 3 exceptions
Know the Concepts behind the Formulas
Regents Scores Prediction –
(A Linear Function of Teaching Scores and Test Scores)
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Regents Test Score Prediction II(A Linear Function of Teaching Scores and Test Scores)
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Know the Concepts behind the Formulas
Teaching & Writing Process (Research Results)
Based on a student teaching research:
• Teaching scores is a strong predictor for the Regents test
• The trend of the average test score serves as a modifier
• The impact of teaching scores is five times stronger than the trend of the average test scores
• Teaching (including writing) represents understanding
• Teaching (including writing) could strongly improve understanding
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Dimensional Analysis
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Apply Dimensional Analysis
Derived Units
Know the symbols/definitions of derived units
• Velocity (v): m/s
• Acceleration (a): m/s2
• Force (F): kg m/s2 (N, newton)
• Work (W): kg m2/s2, N m (J, joule)
• Power (P): kg m2/s3, N m/s (W, watt)
• ………………………………
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Apply Dimensional Analysis
Dimensional Analysis
Every equation must be balanced dimensionally
Units on both sides of the equation must be identical
d = v t + ½ a t2
m = (m/s) s + (m/s2) s2
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Apply Dimensional Analysis
Dimensional Analysis
Example:
If v is velocity, m is mass, a is acceleration, and a = Δv/t and F = ma, find the unit of force (F)
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Apply Dimensional Analysis
Dimensional Analysis
Example:
If v is velocity, m is mass, a is acceleration, and a = Δv/t and F = ma, find the unit of force (F)
Unit of F = kg m/s/s = kg m/s2
F = m a = m Δv / t
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Apply Dimensional Analysis
Dimensional Analysis
Example:
If gravitation force (Fg) can be described by the following formula, find the dimension of G
Fg = G m1 m2 / d2
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Apply Dimensional Analysis
Dimensional Analysis
Example:
If gravitation force (Fg) can be described by the following formula, find the dimension of G
kg m/s2 = [G] kg kg / m2
[G] = m3 / kg s2
Fg = G m1 m2 / d2
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Apply Dimensional Analysis
Dimensional Analysis
Unit Conversion – Use dimensional analysis to do unit conversion
Example: Find how many seconds per day
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Apply Dimensional Analysis
Dimensional Analysis
Unit Conversion – Use dimensional analysis to do unit conversion
Example: Find how many seconds per day
? sec 24 hrs 60 min 60 sec 86400 sec 1 day 1 day 1 hr 1 min 1 day_____ = ______ x _____ x ______ = __________
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Apply Dimensional Analysis
Dimensional Analysis
Unit Conversion – Use dimensional analysis to do unit conversion
Example: Find how many seconds per day
? sec 24 hrs 60 min 60 sec 86400 sec 1 day 1 day 1 hr 1 min 1 day_____ = ______ x _____ x ______ = __________
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Problem Solving
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Develop Problem Solving Skills
Physics Problem Solving
Encompass many physics concepts, principles, formulas, and mathematical disciplines
Problem solving skills:
• Analyze problems
• Associating physics concepts/principles/formulas
• Apply mathematical skills
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Develop Problem Solving Skills
Physics Problem Solving Steps
Make a sketch
Classify the description
Identify and list all the known & the unknown
Associate with physics concepts, definitions, relationships, formulas, and principles
Form & solve mathematical models
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Develop Problem Solving Skills
Example
A block is placed on an incline plane with angle . The coefficient of friction between the block and the incline plane is . The acceleration due to gravity is g. Find the acceleration of the block a in terms of g, and
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Develop Problem Solving Skills
Example
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Develop Problem Solving Skills
Example
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Develop Problem Solving Skills
Example
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Thinking through the Math
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Thinking through the Math
Mathematical Models
Math can describe complex physics phenomena and capture the relationship among physics quantities in an elegant and concise way
Fnet = ma W = Fd
V = IR Q = It
p = mv P = w/t
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Thinking through the Math
Mathematical Models
You have to analyze physics problems and reduce them into mathematical forms. On the other hand, you can apply physics laws in mathematic forms (formulas) to solve physics problems
Math is a powerful tool for understanding those physics phenomena that go against or beyond our common sense
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The End