Academic journal article The Science Teacher

Find Your Center: Using Stem Principles to Explore Center of Mass

Academic journal article The Science Teacher

Find Your Center: Using Stem Principles to Explore Center of Mass

Article excerpt

Mechanics is a branch of engineering and physics that deals with forces and motion, and its fundamental principles apply to all objects, whether a bouncing ball, flowing stream, bicycle, or the human body. The field of biomechanics applies mechanics concepts specifically to the bodies of humans (and other animals). Understanding biomechanics is important for such careers as biomedical engineering, physical therapy and athletic training, orthopedic surgery, and prosthetics. Biomechanics can also help teach core mechanics concepts through the lens of anatomy and medicine--subjects many students can relate to more readily than to more traditional examples from automotive and aerospace engineering.

In this lesson aligned with the Next Generation Science Standards (NGSS; see box, p. 50), students first learn about an object's balancing point, or center-of-mass (COM or CM). Students examine everyday objects to understand the unique features of COM and how to approximate and measure its location. Students then apply this knowledge to a real-world example of biomechanics: coaching a beginning diver to avoid hitting the diving board during flip dives.

Background

The center of mass has several interesting features:

* An object subjected to a force acting through its COM will translate (change position or location) but not spin.

* If you suspend or hold an object at its COM, it will balance perfectly. In this way, COM location is important to the stability of any object.

* The COM affects the motion of an object when it is thrown in the air or pushed (and not acted upon by any other outside forces). The object will spin about its COM, and the motion of the object can be modeled as translation of the COM combined with rotation about the COM.

* The center of mass may be located outside of, rather than directly on, an object. For example, the COM of a flying disc is in the hollow center of the disc, where there is no material. This is the natural balance point and point of rotation of the object.

There are three ways to locate the COM for any object:

1. Balance test with everyday objects. To balance a small object such as a pencil on the tip of your finger, you need to move it around until you find the balance point. This point is the COM of that object. In engineering, COM location is generally represented with a yellow-and-black-checked target, like those seen on a crash-test dummy.

2. Using geometry, symmetry, and mass distribution. A good example is a boomerang (Figure 1). Its two arms are symmetrical, so the COM lies somewhere along the line of symmetry. The overall geometry of the boomerang is similar to that of an isosceles triangle, and we can find the geometric center of a triangle by connecting the midpoint of each side to the opposite vertex. Along the line of symmetry, more of the boomerang mass lies above the geometric center of the triangle than below it; therefore, the COM will be located slightly above the geometric centroid of the triangle.

3. A balance board experiment (Figure 2). A balance board consists of two scales, scale #1 measuring weight [W.sub.1] and scale #2 measuring [W.sub.2], separated by a distance, L, upon which you place a rigid board. The scales are zeroed to subtract the weight of the board. The object for which you want to determine COM location is placed on the board, and the differences in the readings on the scales determines COM location according to the Balance Board Equation: d = [[[W.sub.2]]/[([W.sub.1] + [W.sub.2])]] L, where d is the distance from scale #1 to the COM.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Balance board setup for finding center of mass of an object.

The COM location of any object can be calculated from [W.sub.1] [W.sub.2], and L, as the distance d, where:

[ILLUSTRATION OMITTED]

There are two methods for deriving the Balance Board Equation, and full derivations using both methods are presented in supplemental online materials (see "On the web"). …

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