1-090-EmptySphericalTank-ModelingScenario

23 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/873F-3471

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 cases.

1-093-SucroseReaction-ModelingScenario

23 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/EQ0G-4381

We offer data on the hydrolysis of sucrose in the presence of catalyst sucrase. We present students with several models and ask which model is best. We ask students to estimate parameters for the best model.

1-101-ClassMMDeathImmigration-ModelingScenario

22 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/5YN4-JG44

We offer students an opportunity to generate unique data for their team on a death and immigration model using m&m's and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters.

1-105-AnimalFall-ModelingScenario

22 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/WN9J-0B44

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.

1-122-SpreadPEV-ModelingScenario

22 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/BWDW-X026

We present data on world sales data of plug-in electric vehicles (PEVs) and request a model on the rate of change in sales over time, leading to prediction as to number of PEVs in the future.

1-140-LeakyBucket-ModelingScenario

22 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/B01H-KG54

We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.

3-001-SpringMassDataAnalysis-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/W79E-P417

We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.

3-002-ModelsMotivatingSecondOrder-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/9HJT-NG71

Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.

3-006-Buoyancy-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/AB4Y-VT18

We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body Diagram. We ask students to estimate the parameters.

3-009-BallDropInWater-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/AD5J-Y412

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.

3-013-WhiffleBallFall-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/NCPG-HQ07

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.

3-015-StyrofoamBallFall-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/Q4HP-SC29

We are given data on a falling Styrofoam ball and we seek to model this motion.

3-016-FallingCoffeeFilters-ModelingScenario

21 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/H1WK-M188

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.

3-017-StackedCoffeeFiltersFalling-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/SQ6S-J782

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.

3-019-ShuttleCockFalling-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/JD09-M668

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.

3-026-SpringInverseProblem-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/3XFZ-RZ66

We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

3-027-BobbingDropping-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/EZGZ-5T49

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.

3-029-FerrisWheelCatch-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/EQV9-YA59

We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.

3-030-SecondOrderIntro-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/Y8S9-C814

We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.

3-031-SpringCost-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/N71R-J453

We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and cost.

3-034-CarSuspension-ModelingScenario

27 May 2022 | Contributor(s): Therese Shelton, Brian Winkel | doi:10.25334/706H-1039

We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.

3-035-StadiumDesign-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/MTN0-RV51

For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?

3-040-FirstPassageTime-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/XNS7-ST57

We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.

3-041-UpDown-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/8XY8-C736

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.

3-042-CatapultLaunch-ModelingScenario

20 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/JRPS-5H67

We maximize the range of a projectile by backing up an incline in the opposite direction of the range to give some initial lift. Find the position on the hill from which to launch the projectile to give the best lift.