Course: Statics (or Physics or Math)

Topic: Center of gravity, center of mass, volumetric centroid, area centroid, composite body theory

Type: in-class example problem with EML context and practice in an un-familiar context (homework problem)

Components:
Primary Example with physical model
Introduction engaging 3Cs
EML Context for abstract concept
Homework Problem with EML context

Time:
Primary Example: 30-40min.
Introduction: 30-40min.
EML Context: ~5min.
Homework Problem: 30-60min.

Materials:3D printed model(s) (Primary Example)
toy balance bird (Introduction)

As an instructor, this card can help you...
1. Replace a textbook-based example problem (Primary Example)
2. Introduce centroid concepts and connect to equivalent systems topics with a very simple model (Introduction)
3. Incorporate quick, fun, and non-technical EML context for centroids (EML Context)
4. Replace a textbook homework problem. (Homework Problem)
5. Engage all 3C's with examples that engage opportunity (identify), design (analyze, validate), and impact (communicate)

Overview

Though often presented as an additional math concept in many Statics courses, centroids should be connected directly to the concept of equivalent systems. A 3D printed composite body model illustrates and connects the math intensive concept of area centroid to the real world. The concept of equivalent load systems informs the derivation of area centroids, and a 3D printed prismatic model illustrates the connection between area centroid and center of gravity encouraging students to develop curiosity about the common mathematical expressions shared by various physical phenomenon. A construction engineering lifting scenario provides meaningful EML context.

Method

This ASEE PEER paper contains the complete details for the concepts and demos in the card. The high level outline looks something like this:

1. Introduce the concept of centroids with the Introduction slides and board notes connecting the concept to equivalent system concepts using a toy balance bird.

2. Introduce EML Context:

A law office is renovating their downtown Charleston office overlooking the harbor to include a custom shark tank (featuring a dry shark cage). The very large pre-fabricated tank has arrived on site. As the construction contractor, the time has come to lift the tank into place. To further complicate things, the sharks have arrived on the same day and have already been placed and the tank filled. What information and constraints are required to safely lift the tank and keep it level as it is installed in the building? What calculations will protect your construction company's profits from shark bites of both the biological and legal variety? Can you use the skills learned in statics to make those calculations? Can you validate your calculations with your mental model? Can you experimentally validate your calculations with a scaled model?

3. Calculate the area centroid for the footprint of the tank (Primary Example). Have students work in groups responsible for one of each of the composite shapes.

4. Balance the 3D printed model (Primary Example, *.stl file in the file section) on a pencil/knife point illustrating that the area centroid is the same as the gravity centroid.

Explore Further

Use the provided homework problem to let students apply and test their skills in a (slightly more) realistic engineering application.