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Android Acceleration
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Educational Use
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Students prepare for the associated activity in which they investigate acceleration by collecting acceleration vs. time data using the accelerometer of a sliding Android device. Based on the experimental set-up for the activity, students form hypotheses about the acceleration of the device. Students will investigate how the force on the device changes according to Newton's Second Law. Different types of acceleration, including average, instantaneous and constant acceleration, are introduced. Acceleration and force is described mathematically and in terms of processes and applications.

Subject:
Applied Science
Engineering
Physical Science
Physics
Material Type:
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Brian Sandall
Scott Burns
Date Added:
09/18/2014
Basic Analysis: Introduction to Real Analysis
Conditional Remix & Share Permitted
CC BY-NC-SA
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This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.

Subject:
Mathematics
Material Type:
Textbook
Provider:
University of Illinois at Urbana-Champaign
Author:
Jiří Lebl
Date Added:
02/16/2011
Exploring Acceleration with an Android
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Educational Use
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Students conduct an experiment to study the acceleration of a mobile Android device. During the experiment, they run an application created with MIT's App Inventor that monitors linear acceleration in one-dimension. Students use an acceleration vs. time equation to construct an approximate velocity vs. time graph. Students will understand the relationship between the object's mass and acceleration and how that relates to the force applied to the object, which is Newton's second law of motion.

Subject:
Applied Science
Computer Science
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Brian Sandall
Scott Burns
Date Added:
09/18/2014
Mathematically Designing a Frictional Roller Coaster
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Educational Use
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Students apply high school-level differential calculus and physics to the design of two-dimensional roller coasters in which the friction force is considered, as explained in the associated lesson. In a challenge the mirrors real-world engineering, the designed roller coaster paths must be made from at least five differentiable functions that are put together such that the resulting piecewise curving path is differentiable at all points. Once designed mathematically, teams build and test small-sized prototype models of the exact designs using foam pipe wrap insulation as the roller coaster track channel with marbles as the ride carts.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Measurement and Data
Physical Science
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Miguel R. Ramirez
Date Added:
08/31/2017
A Tale of Friction
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Educational Use
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Roller coasters projects are frequently used in middle and high school physics classes to illustrate the principle of conservation of mechanical energy. Potential energy transforms to kinetic energy and vice versa, with gravity being the driving force during the entire process. Even though friction force is mentioned, it is rarely considered in the velocity calculations along the coasters’ paths. In this high school lesson, the friction force is considered in the process. Using basic calculus and the work-energy theorem for non-conservative forces, the friction along a curved path is quantified, and the cart’s velocity along this path is predicted. This activity and its associated lesson are designed for AP Calculus. Practice problems/answers, a PowerPoint® presentation and student notes are provided.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Measurement and Data
Physical Science
Physics
Material Type:
Lesson
Provider:
TeachEngineering
Provider Set:
Lessons
Author:
Miguel R. Ramirez
Date Added:
08/30/2017