Center of Mass Design Challenge

Description

In an introductory Kinematics course, undergraduate engineering students are taught how to find the center of mass of 2D and 3D objects. This is a core concept that appears throughout the engineering curriculum and has importance in real world applications. The COM design challenge aims to foster an intuitive, physical understanding of the concept center of mass. The students will be presented with nine composite shapes. It was important that the shape designs included a range of geometric shapes, allowed for multiple configurations for stacking, and differed in the type of center of mass calculations required.

Engineering Topic Covered

Descriptions of the concept “center of mass” are obtained from the textbook Vector Mechanics for Engineers: Statics, which is used in the UCSD class MAE30A: Kinematics:

Section 5.11 Composite Bodies:

If a body can be divided into several common shapes, its center of gravity G can be determined by expressing that the moment about O (origin) of its total weight is equal to the sum of the moments about O of the weights of the various component parts. We obtain the following equations defining the coordinates X,Y, and Z of the center of gravity G:

If the body is made of a homogeneous material, its center of gravity coincides with the centroid of its volume, and we obtain:

Learning Objective

Students will develop an intuitive, physical understanding of the concept “center of mass” as well as how to “counterbalance” mass through use of physical shapes and the act of attempting to stack a vertical tower of shapes.
Students will improve their ability to calculate the center of mass of various geometric shapes.

Procedure

1 ) Calculate the center of mass of the following shapes. Note: shapes have uniform densities and all dimensions are in inches

2) Design a vertical tower of all nine shapes. Your goal is to maximize the height while keeping the tower of shapes stable. Consider the center of mass of each shape and the changing center of mass of the tower as it grows!

3) Build your designed stack using the physical shapes. If your design turns out to be not feasible, build another tower that attempts to reach the tallest height possible while remaining stable. (Tip: You can stabilize an unstable stack as you build by adding shapes as counterweights).

4) The winning team will be the team that builds the tallest tower of shapes that also will remain stable. If there is a tie, the winning team will be the team whose final tower matched the original design.

Results from Testing:

For the Center of Mass Design Challenge, our team built eleven different stacks of all nine shapes as examples to prove that student teams will be able to create designs that differ from each other. The figures of the stacks will not be included on this website to ensure that our team's stack designs will not be copied by future student teams. The goal of each student team in the Center of Mass Design Challenge is to produce the tallest stack out of all the teams. Thus during testing it was important to see a range in the heights of the tested stacks. The heights of each of the eleven tested stacks varied from around 18.25 inches to 28.25 inches. It is possible that student teams could create stacks that fall outside this range.

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