Mr. Rogers' AP Physics C: Mechanics (With IB Physics Topics) Objectives

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Vector Addition(2)
Projectile Motion(3)
Newton's Laws(4)
 

Chapter 3: Vector Addition

AP Physics C Newtonian Mechanics:

A. Kinematics (vectors, vector algebra, components of vectors) approx 6% cumulative 12%
    1.Motion in one dimension 
    2.Motion in two dimensions

Students measuring a fan's velocity profile  
 

Practice Test Study Guide

Objectives

Essential Question: Is 1+ 1 = 2 always true ?

Vector Addition Basics

  1. State the relationship between a force's direction to the resulting acceleration's direction.

  2. State the relationship of a velocity's direction to the resulting displacement's direction.

  3. Sketch 2 ways to graphically add vectors.

  • head-to-tail or heal to toe
  • parallelogram
  1. Define vector components.

  2. Given vector components find the resultant vector and its angle.

  3. 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.

 

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

  1. Erie Canal Problem
  2. 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.

Essential Question: What is the fastest way to swim across a raging river?

Using Vector Components

  1. State the relationship between the magnitudes of vector components.

  2. Solve problems involving adding or subtracting 2  vector components.

  • Swimmer problems--Running Bear
  • Airplane problems

Homefun:  problems 7, 17, 23, p.65 - 70; Serway

Metacognition Problem Solving Questions:
When adding two vector components (from different dimensions) :
  1. Is the resultant's magnitude less than the sum of the two magnitudes?
  2. 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.

 

Lesson 2
Key Concept: The x and y components are independent
Purpose: Solve vector problems involving components. 

 

Interactive Discussion: Objectives. Introduce the running bear problem .

In Class Problem Solving: Vector problems

  1. Add two components.

  2. Given a vector, convert it to components.

  3. Running Bear

Formative Assessment: Group and individual problem solving on white boards.

 

Essential Question: How can an airplane's speed be measured?

Special Vector Notation

  1. Use unit vectors (i, j, k).
  2. 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.

 

 
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

  1. Running Bear (continued)
  2. Airplane Problems - ground speed
  3. 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)
Title Analysis of Wind Tunnel Fan's Output
Purpose Measure the ACFM output of a wind tunnel's fan and compare it to the factory's specification.
Overview
  1. Divide the fan into annular rings with the same width (about 4-5 inches wide).
  2. Measure the air flow velocity in the annular rings at 4 positions--top, bottom, right side, left side--and average the measurements.
  3. 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.
  4. Sum up the volume flow rate for each ring. This gives an estimate of the total volume flow rate for the fan.
  5. Convert to the correct units.

Note: according to the factory, the fan's volume flow rate = 13,000 ACFM

Data, Calculations Calculate a % difference between the measured and factory specification of volume flow rate.
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?

Resources/Materials: Wind tunnel with fan, air velocity probe,
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