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Downloads
Views
Date
Relevance
Modeling Scenario
286
views
163
downloads
0
comments
3-009-BallDropInWater-ModelingScenario
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.
resistance
gravity
falling body
terminal velocity
buoyancy
Modeling Scenario
294
views
264
downloads
0
comments
3-013-WhiffleBallFall-ModelingScenario
We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.
Akaike Information Criterion
resistance
gravity
Free Body Diagram
force
falling object
Whiffle ball
Modeling Scenario
982
views
1535
downloads
0
comments
3-016-FallingCoffeeFilters-ModelingScenario
We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.
resistance
Free Body Diagram
coffee filter
force
graviity
falling object
Potential Scenario
131
views
47
downloads
0
comments
2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.
falling body
dimensional analysis
drag
Modeling Scenario
339
views
268
downloads
0
comments
3-017-StackedCoffeeFiltersFalling-ModelingScenario
Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.
data
resistance
falling body
coffee filter
stacked
Modeling Scenario
291
views
154
downloads
0
comments
3-015-StyrofoamBallFall-ModelingScenario
We are given data on a falling Styrofoam ball and we seek to model this motion.
football
resistance
gravity
falling body
sum of square errors
Newton's Second Law of Motion
sum of forces
styrofoam
Modeling Scenario
378
views
545
downloads
0
comments
3-019-ShuttleCockFalling-ModelingScenario
We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models.
resistance
gravity
Free Body Diagram
shuttlecock
fallingc object
Modeling Scenario
284
views
204
downloads
0
comments
3-044-DeepWell-ModelingScenario
We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.
gravity
projectile motion
falling body
speed of sound
Potential Scenario
98
views
46
downloads
0
comments
1994-T_Gruszka-A Balloon Experiment in the Classroom
The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick,
resistance
falling body
drag
balloon
Article or Presentation
234
views
59
downloads
0
comments
2011-Brian_Winkel-Cross_coursing_in_mathematics-physical_modeling_in_differential_equations_crossing_to_discrete_dynamical_systems
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course.
differential equations
mathematical model
difference equation
cross course
convert
Modeling Scenario
242
views
117
downloads
0
comments
3-041-UpDown-ModelingScenario
Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.
gravity
projectile motion
falling body
maximum heightf
timing
Modeling Scenario
328
views
149
downloads
0
comments
1-105-AnimalFall-ModelingScenario
This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.
animal
Netwon's Second Law of Motion
falling body
terminal velocity
air resistance
Newton
air friction
fall
Modeling Scenario
247
views
268
downloads
0
comments
1-055-WaterFallingInCone-ModelingScenario
We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.
Torricelli's Law
discharge coefficient
cone
contraction coefficient
Modeling Scenario
240
views
138
downloads
0
comments
3-027-BobbingDropping-ModelingScenario
We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
drug resistance
directed
buoyancy
free fall
static equilibrium
displacement
Modeling Scenario
239
views
184
downloads
0
comments
1-083-FallingMeteorites-ModelingScenario
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus...
falling object
drag
variable mass
factor ranking
meteor
meteorite
Modeling Scenario
273
views
134
downloads
0
comments
3-063-FallingBuildingIce-ModelingScenario
We model the fall of a piece of ice which is falling from a high building in New York City.
resistance
falling
gravity
ice
terminal velocity
skyscrapers
Modeling Scenario
253
views
179
downloads
0
comments
1-130-AspirinAbsorption-ModelingScenario
We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
pharmacokinetics
drug
aspirin
Modeling Scenario
292
views
106
downloads
0
comments
1-131-CaffeineElimination-ModelingScenario
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
caffeine
elimination
pharmacokinetics
drug
Potential Scenario
121
views
65
downloads
0
comments
1999-F_Brauer-What Goes Up Must Come Down
This paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces.
projectile
friction
falling time
rising time
maximum height
Modeling Scenario
268
views
253
downloads
0
comments
3-070-FallingInWater-ModelingScenario
We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and estimate appropriate parameters.
data
water
resistance
falling
buoyancy
mass
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