Living Physics Portal: Dimensional analysis problems - Functional Dependence Table Problems

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Dimensional analysis problems - Functional Dependence Table Problems

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Part of Dimensional Analysis - Problems with Solutions

Part 2 of 5

Highlights: Homework problems using dimensional analysis throughout the curriculum

Abstract: DA plays a fundamental conceptual role as a way to help students learn to blend physical concepts with mathematical representations. This requires somewhat of a "phase transition" in student thinking - switching from thinking about variables as standing for numbers to ones standing for physical measurements. A good way to help them is to provide DA activities throughout the class. This section provides a set of 6 problems appropriate for homework or short in-class activities that combine DA with paying attention to physical functional dependence.

Resource Types: Homework, Exam problem, Restricted access

Remote Learning Ready: This resource has been designed or adapted for use in remote learning.

Commercially available in:

ExpertTA

Authors:

Edward Redish (he/him)

University of Maryland, College Park

NEXUS Physics

Living Physics Portal Team

TOPICS

Physics Topics:

Classical Mechanics > Statics of Rigid Bodies > Stresses

Electricity & Magnetism > Electrostatics > Coulomb's Law

Fluid Mechanics > Dynamics of Fluids > Hagen-Poiseuille Equation

Fluid Mechanics > Surface Tension > Capillary Action

Oscillations & Waves > Wave Motion > Transverse Pulses and Waves

Life Sciences Topics:

Botany > Fluid Transport

Human and Animal Physiology > Other Body Fluids

Math Topics:

Algebra

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Dimensional Analysis - Problems with Solutions > Dimensional analysis problems - Functional Dependence Table Problems

Dimensional analysis problems - Functional Dependence Table Problems

DA table - Capillary action.url

DA table - The electric dipole force.url

DA Table - Young's modulus.url

DA Table - The HP Equation.url

DA Table - Speed of deep water waves.url

DA table - Constructing the spring constant.url

DA Table - Capillary action.pdf

DA Table - Electric dipole force.pdf

DA Table - Young's modulus.pdf

DA Table - The H-P equation.pdf

DA Table - Speed of deep water waves.pdf

DA Table - Constructing the spring constant.pdf

DA table - Capillary action.url

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INSTRUCTOR GUIDE

IMPLEMENTATION

Equipment required: No equipment needed

Basic implementation tips & tricks: These problems as students to combine DA with an understanding of what the functional dependence of an equation tells them about the physics. These are appropriate for assigning for homework and for having students work in groups to solve. They also could be used on a quiz or exam.

How does this resource fit into the flow of your course? These problems contain topics that occur throughout the class.

PEDAGOGY

Pedagogical approach: Conceptually-oriented activities; Mathematically-focused activities

Skills / Competencies: Dimensional analysis; Multiple representations; Intuition building

What insights or realizations do you hope students gain from this resource? (1) That the symbols in our mathematical equations typically do not stand for numbers for for measurements - something in the physical world. (2) That even if they are not familiar with an equation, they can tell a lot about what it tells us (and its validity) by a DA. (3) That they can propose plausible equations in many situations just from DA.

Why is this resource useful to life sciences students? Life science students are often exposed to complex symbolic equations in more advanced classes. Knowing how to do DA can help. demystify new equations. In addition, both the biology research and pre-med communities have called for their students' educations to involve more quantification and use of mathematics. DA is an important first step in helping students "build the blend" of physical quantities and mathematical symbology. For pre-meds, DA is useful in dealing with equations in the MCAT.

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License: CC0 – Public Domain. No restrictions.

Last Edit Date: March 4, 2025