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Downloads
Views
Date
Relevance
Modeling Scenario
307
views
469
downloads
0
comments
6-070-BeerBubbles-ModelingScenario
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
molecular forensics
BEER
sphere
bubble
Newton' Second Law
Ideal Gas Law
drag force
Hadamard
Stokes
mole
Modeling Scenario
258
views
376
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
Modeling Scenario
189
views
81
downloads
0
comments
1-144-HeatCool-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
temperature
Newton's Law of Cooling
cooling
Modeling Scenario
297
views
206
downloads
0
comments
1-058-WaterClocks-ModelingScenario
We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out.
flow
Torricelli's Law
spigots
water clock
Modeling Scenario
247
views
181
downloads
0
comments
1-064-TorricelliBox-ModelingScenario
The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.
groundwater flow
column of water
Torricelli's Law
water displacement
submerged box
Modeling Scenario
257
views
262
downloads
0
comments
1-079-HomeHeating-ModelingScenario
This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
Optimal Control Theory
temperature
heat
furnace
Newton's Law of Cooling
home heating
specific heat
Modeling Scenario
277
views
200
downloads
0
comments
1-074-BottleWaterFlow-ModelingScenario
We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow.
b
water
Torricelli's Law
bottle
Modeling Scenario
1154
views
623
downloads
0
comments
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
Technique Narrative
424
views
206
downloads
0
comments
2-005-LinearizeItAll-TechniqueNarrative
Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
computation
error
Torricelli's Law
data fitting
linear approximation
Modeling Scenario
316
views
147
downloads
0
comments
1-014-DrainingContainers
Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?
containers
tank
flow
Torricelli's Law
draining
fixed volume
Modeling Scenario
294
views
321
downloads
0
comments
1-088-RoomTemperature-ModelingScenario
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
environment
climate
temperature
Newton's Law of Cooling
cooling
periodic function
Modeling Scenario
792
views
369
downloads
1
comments
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
335
views
149
downloads
0
comments
1-105-AnimalFall-ModelingScenario
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.
animal
Netwon's Second Law of Motion
falling body
terminal velocity
air resistance
Newton
air friction
fall
Article or Presentation
198
views
581
downloads
1
comments
2020-TeachingModule-ModelingFallingColumnOfWater
We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.
module
column of water
Torricelli's Law
Torricelli
Teaching Module
Modeling Scenario
377
views
441
downloads
0
comments
1-011A-Kinetics-ModelingScenario
We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.
kinetics
Law of Mass Action
fitting
order of reaction
chemical reaction
Modeling Scenario
262
views
162
downloads
0
comments
1-073-WaterExitBottle-ModelingScenario
We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container.
data
water
flow
Torricelli's Law
bottle
Modeling Scenario
266
views
385
downloads
0
comments
1-094-SteepingTea-ModelingScenario
We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration.
concentration
Surface Area
color
Newton's Law of Cooling
tea
sugar
Modeling Scenario
391
views
265
downloads
0
comments
5-076-LanchesterLaws-ModelingScenario
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
Lanchester's laws
sensitivity analysisanalysis
Modeling Scenario
201
views
268
downloads
0
comments
1-140-LeakyBucket-ModelingScenario
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.
flow
Torricelli's Law
leaky bucket
Modeling Scenario
204
views
211
downloads
0
comments
3-095-ShotInWater-ModelingScenario
This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.
projectile motion
terminal velocity
projectile
water resistance
reduction of order
friction
air resistance
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