QUBES - Resources

2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve

Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.

Keywords: kinematicscurve designhighway exittangential acceleration

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3-030-SecondOrderIntro-ModelingScenario

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...

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1-013-SleuthingWithDifferentialEquations-ModelingScenario

We present several situations in which differential equation models serve to aid in sleuthing and general investigations.

Keywords: projectile motionaccelerationNewton's Law of Coolingspeeding

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1-120-CircularRollerCoaster-ModelingScenario

Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction....

Keywords: population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts

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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...

Keywords: resistancegravityfalling bodyterminal velocitybuoyancy

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3-130-MatterOfSomeGravity-ModelingScenario

This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.

Keywords: gravityinverse problemacceleration

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2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations

Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.

Keywords: falling bodydimensional analysisdrag

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3-016-FallingCoffeeFilters-ModelingScenario

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.

Keywords: resistanceFree Body Diagramcoffee filterforcegraviityfalling object

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3-085-SimplePendulum-ModelingScenario

Thestudent is asked to derive and solve a differential equation that gives the position (angle

Keywords: Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error

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4-036-AltitudeDependentGravity-ModelingScenario

When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order...

Keywords: agravityprojectilelinearizationltitufealtitude

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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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3-042-CatapultLaunch-ModelingScenario

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...

Keywords: projectile motioncatapultuphilllaunch angle

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3-064-GearTrain-ModelingScenario

Students model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and...

Keywords: frictiongearspur geargear traintorquegear ratioangular accelerationangular velocitymoment of inertiadouble reduction gear

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1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom

The experiment consists of dropping a balloon from two different heights and recording the time it takes to hit the floor. The following experiment involves a balloon, a stopwatch, and a...

Keywords: differential equationsresistancegravityfree fallaccelerationballoon

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1-005-NavigatingNumericalMethods-TechniqueNarrative

This technique narrative is a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of...

Keywords: Euler's methodTaylor's Methodsearch and rescueCoaast Guardlost at sealongitudelatitudelimit definition

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Quantifying Uncertainty and Distinguishing Data Sets in Introductory Physics

Physics labs are moving increasingly to open-ended experiments where students develop experimental physics skills, rather than verify textbook physics concepts. This sequence of activities sets the...

Keywords: statisticsMeasurementlaboratoryuncertaintypendulumexperimental skills

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Science Behind the Lesson: It's a Bird! It's a Plane! It's Biomechanics!

Active flight is a specialized mode of movement found in insects, birds, and mammals. The anatomy, morphology, physiology, and ecology of flying taxa has changed over evolutionary time. Researchers...

Keywords: EvolutionecologybatphysiologyAnatomybiomechanicsbirdFlightinsect

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It's a bird! It's a plane! It's biomechanics!

Biomechanics is a discipline that draws from physics and engineering principles to understand the movement and structure of living organisms. It is highly interdisciplinary in nature and can be...

Keywords: EvolutionecologybatphysiologyAnatomybirdFlightforcesinsect

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2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve

3-030-SecondOrderIntro-ModelingScenario

1-013-SleuthingWithDifferentialEquations-ModelingScenario

1-120-CircularRollerCoaster-ModelingScenario

3-009-BallDropInWater-ModelingScenario

3-130-MatterOfSomeGravity-ModelingScenario

2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations

3-016-FallingCoffeeFilters-ModelingScenario

3-085-SimplePendulum-ModelingScenario

4-036-AltitudeDependentGravity-ModelingScenario

3-020-ChordPathTime-ModelingScenario

3-042-CatapultLaunch-ModelingScenario

3-064-GearTrain-ModelingScenario

1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom

1-005-NavigatingNumericalMethods-TechniqueNarrative

Quantifying Uncertainty and Distinguishing Data Sets in Introductory Physics

Science Behind the Lesson: It's a Bird! It's a Plane! It's Biomechanics!

It's a bird! It's a plane! It's biomechanics!

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