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Downloads
Views
Date
Relevance
Modeling Scenario
234
views
240
downloads
0
comments
1-090-EmptySphericalTank-ModelingScenario
We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...
Volume
sphere
Torricelli's Law
timing
spherical tank
fluid
empty
Modeling Scenario
260
views
158
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
258
views
173
downloads
0
comments
3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy
mass-spring system
kinetic energy
potential energy
total energy
Modeling Scenario
218
views
184
downloads
0
comments
5-014-TwoSpringMass-ModelingScenario
We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.
mass
spring mass damper
springs
Modeling Scenario
223
views
126
downloads
0
comments
6-030-SaltAndTorricelli-ModelingScenario
We build on a model for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water.
whole picture
tank
mixing
flow
column of water
salt mixing
graduated cylinder
aperture
Torricelli's Law
Modeling Scenario
238
views
357
downloads
0
comments
3-080-PendulumModeling-ModelingScenario
We lead students through building model for several pendulum configurations in motion and ask students to compare results.
pendulum
period
linearization
Article or Presentation
141
views
42
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
205
views
326
downloads
0
comments
5-090-SolidParticleErosion-ModelingScenario
By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.
classical mechanics
solid mechanics
Newton's Laws of Motion
rigid body
plasticity
pitting
ductile surface
Modeling Scenario
632
views
182
downloads
0
comments
5-026-Evictions-ModelingScenario
In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .
carrying capacity
compartment
eviction
homeowner
SIS model
homelessness
Potential Scenario
234
views
35
downloads
0
comments
2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
predator-prey
harvesting
Pontryagin’s maximum principle
bioeconomic
bionomic equilibrium
biotechnical productivity
catch-rate function
optimal equilibrium
Potential Scenario
127
views
73
downloads
0
comments
2003-Fay-Graham-Coupled spring equations
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
mass
oscillation
spring\
coupled springs
periodic
fporcing
Modeling Scenario
366
views
248
downloads
0
comments
1-029-ConeToCubeFlow-ModelingScenario
An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...
water
flow
Torricelli's Law
cone
cube
Modeling Scenario
316
views
399
downloads
0
comments
1-028-SouthernSweetIcedTea-ModelingScenario
We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea. We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.
data
Newton's Law of Cooling
tea
sweet tea
Modeling Scenario
411
views
521
downloads
0
comments
1-011-Kinetics-ModelingScenario
We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.
kinetics
chemistry
Law of Mass Action
chemical kinetics
order of reaction
chemical reaction
Modeling Scenario
231
views
230
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
245
views
184
downloads
0
comments
1-059-ContainerShapeFallingWater-ModelingScenario
We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.
containers
Torricelli's Law
shape
discharge coefficient
Modeling Scenario
395
views
297
downloads
0
comments
1-061-PotatoCooling-ModelingScenario
We model the cooling of a baked potato and compare it to student-collected data.
least sum of square errors
Newton's Law of Cooling
cooling
potato
Modeling Scenario
265
views
151
downloads
0
comments
1-071-NewtonWatson-ModelingScenario
Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis
temperature
death
Newton's Law of Cooling
time of death
Sherlock Holmes
Modeling Scenario
286
views
132
downloads
0
comments
1-115-ModelingWithFirstOrderODEs-ModelingScenario
Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.
bacteria
falling object
Newton's Law of Cooling
drug
cooling
drag
Modeling Scenario
242
views
141
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
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