Storyboard Example: Outline
Drag Forces Content
Simple outline for entire Drag Forces module
The Drag Forces module content is divided into the categories for the Content navigation from the Side Navigation Bar-- each numbered point is intended to be a link from the Side Navigation Bar. The outline here is just a sketch--a good place to start. Each numbered point, however, should develop into a more detailed explanation of the content and activities to be included in a final storyboard, much like the Schematic Storyboard Example for the Drag Forces Module's "Experiment Analysis" section.
Objectives
In this module, students will study the drag force exerted by a fluid on a solid object in motion relative to the fluid. There will be a number of problems and interactive exercises to link everyday experiences, fluid mechanics and mathematics. In particular, students will:
study the motion of a body falling in a vacuum;
study the motion of a body falling in a fluid;
do a quantitative analysis of how the additional drag exerted by a parachute enables a skydiver to land safely.
Falling in a Vacuum
Force Balance
velocity as a function of time--Newton's second law; gravity as force, equations and derivations; falling bob experiment
Velocity and Acceleration
velocity as a function of distance--rewrite equations using chain rule.
Falling in a Fluid
Force Balance
velocity as a function of time; introduce concept of drag force; equations--include derivations and solutions
Velocity and Acceleration
velocity as a function of distance including drag coefficient
Summary of Force Balance and Velocity and Acceleration
Summarize essential equations and concepts for a body falling from rest in a vacuum and a body falling from rest in a fluid.
Describe a common skydive-- use this example in other sections of module
Skydiver applet
Skydiver video
Homework problems from chapter 9.4 in text, based on applet and graphs
Comparison of Falling in a Vacuum and Falling in a Fluid
Two cases: when k/m<<1 and when k/m>>1.
Links to Taylor Series
Discussion question: why is the velocity of skydiver greater in vacuum?
Practice problems from chapter 9.5 in text.
Terminal Velocity
Discuss quantitative vs. qualitative differences in falling in a vacuum and falling in a fluid.
equation and derivation for terminal velocity
discussion question: relationship of terminal velocity of skydiver example
practice problems pertaining to skydiver example: calculate terminal velocity under different conditions.
Save a Skydiver!
using a parachute to reduce terminal velocity
set up equations to mathematically represent a common skydive example
discussion question: properties of a parachute that make it effective
practice problems using skydiver applet and graphs
Experiment Analysis
explanation of falling bob experiment--include mathematical vs. experimental observations.
generalize velocity vs. time data to any object
video and explanation of the steel bob experiment
Experiment analysis--graph of results: strange result, explain. mathematical representation of results (eqn. mdv/dt = mg), analysis of why drag forces are negligible in this experiment. Include links to solution and derivation for the equations.
Discussion questions: Is the first analysis a strange result? Why? Under what circumstances are eqns. 9.1 and 9.2 identical?
Homework problems from chapter 9.6
Dynamic Similarity
comparison of real world examples--bob experiment and skydiver-- and translation into universal equation
include derivation and explanation.
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