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Modeling Scenario

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3-103-PullBackCars-ModelingScenario

This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.

modeling dynamics hands-on toy pull-back car pullback

Modeling Scenario

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6-003-SchoolFluEpidemic-ModelingScenario

We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

infection epidemic SIR model flu peak school children

Modeling Scenario

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6-004-VillageEpidemic-ModelingScenario

Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they are to build a mathematical model.

SIR models epidemic susceptible infective removed Eyam English village

Modeling Scenario

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1-001-MM-DeathAndImmigration-ModelingScenario

We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!

simulation immigration death Spanish dats Winkel Brian Winkel

Modeling Scenario

478

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1-128-RocketFlight-ModelingScenario

We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...

resistance Flight Rocketry mass Newton's Second Law of Motion thrust Free Body Diagram apex rocket

Modeling Scenario

443

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1400

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comments

9-014-TurkeyCook-ModelingScenario

The goal of this project is to investigate several models for the cooking time for a turkey based on weight, test these models with data obtained from heating curves for turkeys of various weights, and develop a new model to fit this data.

sphere heat equation turkey Panofsky radial symmetry

Modeling Scenario

396

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585

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1-078-MonodGrowthModel-ModelingScenario

Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.

bacteria nutrient cycles growth Monod consumption

Modeling Scenario

850

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762

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1-015-Torricelli-ModelingScenario

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.

data Spanish tank column of water aperture Torricelli's Law Conservation of Energyt Solver water flow Excel Solver

Modeling Scenario

639

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634

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3-061-ChemEngApps-ModelingScenario

Students go through a chemical engineering problem: calculate concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation; then analyze the concentration as the radius of the catalyst...

Spanish porous medium catalyisis cyclohexene hydrogel dehydrogenation hyperbolic trig functions

Modeling Scenario

340

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113

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comments

1-031-CoolIt-ModelingScenario

We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...

Spanish Newton's Law of Cooling cooling

Modeling Scenario

935

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342

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1-030-EyeModel-ModelingScenario

We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina.

retinal surgery Akaike Information Criterion Spanish sum of square errors surgery retiona ophthalmology eye intraocular gas bubble

Modeling Scenario

848

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1033

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comments

1-070-FisheryHarvest-ModelingScenario

Students model with logistic growth, harvesting, and diffusion in analyzing ocean fisheries of the Atlantic cod. We help students build models, ever more complex, to capture physical realities. At each stage we ask students to reflect on the model.

logistic Diffusion management harvest fishery

Modeling Scenario

899

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485

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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

Modeling Scenario

181

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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

206

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3-104-BungeeJumping-ModelingScenario

In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.

design falling mass spring\ bungee elesticity recommendation consult