Physics Lesson 3

Strategies of Studying Physics

Eleanor Roosevelt High School

Chin-Sung Lin

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

Physics Words

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

Physics Concepts

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

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

Know the Concepts behind the Formulas

Context of Physics Formulas

Engage in the “concept explaining process”

Any forms of teaching, explaining, or writing physics

Know the Concepts behind the Formulas

Teaching & Writing Process (Research Results)

Based on a student teaching research:

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

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

-

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)

Regents Test Score Prediction I(A Linear Function of Teaching Scores)

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

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)

Regents Test Score Prediction II(A Linear Function of Teaching Scores and Test Scores)

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

Dimensional Analysis

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)

• ………………………………

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

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)

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

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

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

Apply Dimensional Analysis

Dimensional Analysis

Unit Conversion – Use dimensional analysis to do unit conversion

Example: Find how many seconds per day

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 ______ = __________

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 ______ = __________

Problem Solving

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

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

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

Develop Problem Solving Skills

Example

Develop Problem Solving Skills

Example

Develop Problem Solving Skills

Example

Thinking through the Math

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

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

The End