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Objectives |
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Essential Question:
Is 1+ 1 = 2 always true ? |
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Vector Addition Basics
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State the relationship between a force's direction to
the resulting acceleration's direction.
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State the relationship of a velocity's direction
to the resulting displacement's direction.
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Sketch 2 ways to graphically add vectors.
- head-to-tail or heal to toe
- parallelogram
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Define vector components.
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Given vector components find the resultant vector
and its angle.
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Given a vector find its components.
Homefun: Questions 1-10 p.64, Read
Chap. 3; Serway
Relevance: Vector addition makes it
possible to analyze complex motion in 3 dimensions. These motions
include everything from athletic activities to planetary motions.
Anyone who eventually wants to pilot an aircraft or sailboat needs to
have a basic understanding of vectors. |
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Activities |
- Lesson 1
- Key Concepts: 1)
certain types of vectors always go in the same direction. 2) Vectors
can be added graphically. 3) Vectors can be broken into components.
- Purpose: Add
vectors.
Interactive Discussion:
Objectives. Which types vectors always go the same direction?
How are two vectors added in one dimension?
Practice with components
In Class Problem Solving:
Vector Addition
- Erie Canal Problem
- Airplane Problems
Etch-a-sketch
Demo: Add vectors with the etch-a-sketch. Show
components and how they look when added together.
Interactive Discussion:
Objectives Find components and angles graphically. Derive
mathematical formulas for components. Find components
mathematically.
Resources/Materials: Protractors,
etch a sketch
Formative Assessment:
Group and individual problem solving on white boards. |
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Essential Question:
What is the fastest way to swim
across a raging river? |
Using Vector Components
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State the relationship between the magnitudes of
vector components.
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Solve problems involving adding or subtracting 2 vector
components.
- Swimmer problems--Running Bear
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Airplane problems
Homefun: problems 7, 17, 23, p.65
- 70; Serway
- Metacognition Problem Solving Questions:
- When adding two vector components (from different dimensions)
:
- Is
the resultant's
magnitude less than the
sum of the two magnitudes?
- Is the resultant's magnitude greater
than the smallest component?
The resultant is always less than the sum of
the components magnitudes but always greater than the smallest components
magnitude.
Relevance: Thinking in terms of
vector components helps simplify vector addition.
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- Lesson
2
- Key Concept: The
x and y components are independent
- Purpose: Solve vector
problems involving components.
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Interactive Discussion:
Objectives. Introduce the running bear problem . In Class Problem Solving:
Vector problems
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Add two components.
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Given a vector,
convert it to components.
- Running Bear
Formative
Assessment: Group and individual problem solving on white boards. |
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Essential Question:
How can an airplane's speed be
measured? |
Special Vector Notation
- Use unit vectors (i, j, k).
- Add
multiple vectors together using the three step component method.
Homefun: problems 47, 49, 53, 61, p.65
- 70; Serway
Relevance: Anyone who eventually
wants to pilot an aircraft or sailboat needs to have a basic understanding
of vectors. Summative
Assessment: Unit Exam objectives 1-10. |
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- Lesson 3
- Key Concept: Multiple vectors
at various angles can be added using components
- Purpose: Add multiple vectors.
Interactive Discussion:
Objectives. Discuss i, j, k unit vector notation and addition. Show three step method
In Class Problem Solving:
Vector problems
- Running Bear (continued)
- Airplane Problems - ground speed
- Three vector addition
Formative Assessment:
Group and individual problem solving on white boards. |
- Summative Assessment: Mini-Lab
Physics Investigation (Requires only Purpose,
data, and conclusion)
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Title |
Analysis of Wind Tunnel Fan's Output |
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Purpose |
Measure the ACFM output of a wind tunnel's fan and compare
it to the factory's specification. |
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Overview |
- Divide the fan into annular rings with the same width
(about 4-5 inches wide).
- Measure the air flow velocity in the annular rings at 4
positions--top, bottom, right side, left side--and average the
measurements.
- Multiply the average air flow velocity for each of the
rings by the area of the ring to obtain the volume flow rate
for each ring.
- Sum up the volume flow rate for each ring. This gives an
estimate of the total volume flow rate for the fan.
- Convert to the correct units.
Note: according to the factory, the fan's volume flow rate =
13,000 ACFM |
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Data,
Calculations |
Calculate a % difference between the measured and factory
specification of volume flow rate. |
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Questions,
Conclusions |
What would happen to the accuracy of the measured value if
it was calculated using many more rings. (Assume the velocity
measurements in any sized ring is perfect) Why is the velocity
in the outer ring higher than the inner rings? |
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Resources/Materials: |
Wind tunnel with fan, air velocity probe, |
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