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Views
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Relevance
Modeling Scenario
469
views
280
downloads
0
comments
1-145-FastPitch-ModelingScenario
We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.
Measurement
resistance
air resistance
baseball
pitcher
fast
Modeling Scenario
1155
views
626
downloads
0
comments
3-065-UpDown-ModelingScenario
We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity
Newton's Second Law of Motion
velocity
motion
apex
Potential Scenario
215
views
46
downloads
0
comments
1980-Peastrel-Lynch-Armenti-Terminal velocity of a shuttlecock in vertical fall
We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable.
falling
terminal velocity
shuttlecock
vertical fall
Potential Scenario
191
views
44
downloads
0
comments
1994-Roland_Minton-A Progression of Projectiles-Examples from Sports
There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,
sports
resistance
projectile
baseball
drag
linear resistance
quadratic resistance
tennis
Modeling Scenario
358
views
352
downloads
0
comments
4-039-FallingDarts-ModelingScenario
we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined...
optimization
resistance
terminal velocity
muzzle velocity
drag coefficient
free fall
air drag
Article or Presentation
131
views
47
downloads
0
comments
1999-F_Brauer-What_Goes_Up_Must_Come_Down
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 that are nonlinear functions of velocity.
resistance
falling
projectile
vertical projectile
Modeling Scenario
343
views
278
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
Potential Scenario
130
views
34
downloads
0
comments
1999-Long-Weiss-The Velocity Dependence of Aerodynamic Drag A Primer for Mathematicians
This paper is exactly what it says it is, namely, a Primer for Mathematicians. There are ample models, data, attention to such issues as Reynolds’ numbers, and attention to aerodynamics issues.
drag force
aerodynamics
Article or Presentation
164
views
53
downloads
0
comments
1980-Peastrel-Lynch-Armenti-Terminal_velocity_of_a_shuttlecock_in_vertical_fall
This paper offers a set of data on a falling shuttlecock (the moving object in badminton) in air. How the authors collected the data is described fully and can be replicated easily by modern equipment.
parameter estimation
data collection
resistance
falling
terminal velocity
Newton's Second Law of Motion
shuttlecock
Modeling Scenario
295
views
155
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
366
views
215
downloads
1
comments
1-092-DashItAll-ModelingSenario
This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.
data
running
sprint
Hill-Keller
world record
Olympics
Potential Scenario
139
views
44
downloads
0
comments
2002-Chai-Optimal initial angle to fire a projectile
Assume a projectile is fired without air resistance and lands at a height y above its initial vertical position. What is the optimal initial angle of firing to maximize the horizontal distance traveled by the projectile?”
optimization
projectile motion
launch angle
Potential Scenario
143
views
51
downloads
0
comments
2014-Groetsch-Yost-Vertical Projection in a Resisting Medium - Revelations on Observations of Mersenne
This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
resistance
projectile
Modeling Scenario
276
views
255
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
Potential Scenario
153
views
75
downloads
0
comments
2017-David_Morin-Oscillations
So needless to say, an understanding of oscillations is required for an understanding of waves.
damping
frequency response
resonance
oscillation
beats
underdamping
harmonic oscillators
over damping
critical damping
Potential Scenario
161
views
68
downloads
0
comments
1972-R_C_Rothermel-A Mathematical Model for Predicting Fire Spread in Wildland Fuels
The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and demonstration of results to hypothetical fuel models.
prediction
forest fire
fire management
fire spread
fuel
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