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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...

    Keywords: dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver

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    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,

    Keywords: resistancefalling bodydragballoon

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    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.

    Keywords: differential equationsmathematical modeldifference equationcross courseconvert

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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...

    Keywords: designfallingmassspring\bungeeelesticityrecommendationconsult

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    1-063-ThreeHoleColumnOfWater-ModelingScenario
    We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

    Keywords: fallingcolumn of waterTorricelli's Lawmultiple spigotsspigots

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    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...

    Keywords: VolumesphereTorricelli's Lawtimingspherical tankfluidempty

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    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...

    Keywords: gravityprojectile motionfalling bodymaximum heightftiming

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    2017-Russell+Herman-A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers
    This is a self-published text book with excellent coverage and solid mathematics and theory to support applications.

    Keywords: textbookengineeringapplications

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    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...

    Keywords: Torricelli's Lawdischarge coefficientconecontraction coefficient

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    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.

    Keywords: bacteriafalling objectNewton's Law of Coolingdrugcoolingdrag

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    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...

    Keywords: drug resistancedirectedbuoyancyfree fallstatic equilibriumdisplacement

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    3-020-ChordPathTime-ModelingScenario
    Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is...

    Keywords: Unit CirclepathfallinggravitychordNetwon's Second Law of Motion

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    2017-CW_Groetsch-Hammer and Feather - Some Calculus of Mass and Fall Time
    Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a falcon feather on the surface of the moon to...

    Keywords: gravityfree falllinear resistancequadratic resistancehammerfeatherMoon resistanceGalileo

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    1-057-FiguringFluidFlow-ModelingScenario
    We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which...

    Keywords: dischargetankTorricelli's LawConservation of Energyfluid flowheightliquid

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    1-116-TropicalStormWindspeeds-ModelingScenario
    We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential...

    Keywords: hurricanedecaytropical stormcyclones

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    3-045-RampBounce-ModelingScenario
    Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile...

    Keywords: projectile motioninclined rampcoefficient of restitutionoptimal anglebounce

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    Disease Spread Simulation with M&M's and Information on the wider SIMIODE community
    This is a Student Version of a Modeling Scenario from the community, SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations at www.simiode.org

    Keywords: resourcesdifferential equationsmodelingsimulationmoduledataepidemicsdiseasecommunityapplied mathematicsResources @ SIMIODEretinal surgeryinsect colonyLSDm&mparameter estimationin-class activityproject

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    Online Adaptation of the Cell Engineer/Detective Lesson
    One of the most fundamental themes of biology is the relationship between structure and function, which is particularly evident when it comes to cells; however, the traditional cartoon depictions...

    Keywords: cell functionCell StructureOrganelles

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    Teaching the Biological Relevance of Chemical Kinetics Using Cold-Blooded Animal Biology
    This lesson plan was created to support non-chemistry major students in making connections between chemical kinetics and biological systems. Chemical kinetics is often viewed by students as an...

    Keywords: kineticsMetabolismEctothermPoikilotherm

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    How to Design a Classroom Activity that Integrates 3D Print Models with Active Learning
    Student exploration of relevant physical models can deepen knowledge of course material. In this guide we describe a method by which instructors can integrate 3D printing technology with an...

    Keywords: active learning3D print modelsclassroom jigsaw

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