Apparatus Competition

2007 AAPT Summer Meeting

Greensboro, NC

 

Easy Cubic Meter

 

Brett Carroll

Green River Community College

12401 SE 320th St.

Auburn, WA 98092

 

253-833-9111  x4322

bcarroll@greenriver.edu

 

Abstract

            The cubic meter is a frequently used unit in introductory physics, but surprisingly few students have ever actually seen one.  Misconceptions about the size of common objects such as the human body in cubic meters are common, with many students estimating their body volume at up to 1 cubic meter, while the actual average is closer to 0.15 cubic meters.

The Easy Cubic Meter is an inexpensive and easily constructed teaching tool that allows students to get a feel for the size of both the square and the cubic meter.  For a bit of fun, let them experiment to see how many bodies will actually fit inside!

Construction of Apparatus: 

The cubic meter apparatus is simply constructed from PVC pipe and fittings that are available at any hardware store.  Pieces of ¾” pipe are cut to slightly less than 1 meter in length (to compensate for the thickness of the corner fittings), and fitted into 3-way pipe fittings.

For ease of use, it is helpful to assemble two individual 1-meter squares and join them permanently at the corners with pipe cement.  The final cubic meter can then be assembled in the classroom (it won’t fit through most doors!) by joining the two square meters together with four (almost) meter-long pieces of pipe that are left uncemented for easy disassembly.  Having the two squares pre-assembled greatly cuts down on last-minute assembly time, missing parts, and assembly confusion.

The various pieces can then be used to demonstrate the meter unit in three variations – the unattached pipes for a linear 1-dimensional meter, the glued-together squares for a 2-dimensional square meter, and the fully assembled cube for a 3-dimensional cubic meter.

Use of Apparatus: 

The cubic meter apparatus is easily put together in front of the students out of a unit they are already familiar with. 

The unattached pipes are first shown in comparison with a standard meter stick to show the basic unit, then one of the unattached pipes can be held to each side of an assembled square meter to show the derivation of that unit and its relative size.  If you desire, a square foot piece of cardboard can be used for comparison to standard Imperial units.

At this point it is vital to point out to the students that the square meter unit is the area outlined by the four pipes, not the combined length of the pipes.  That can lead to a useful discussion of the perimeter of the square as a separate measurement, and one that is of a different type entirely from the square meter that the pipes outline.

The same is true of the cubic meter that the finished cube encloses, and the volume unit that is required for its measurement can be compared and contrasted with the units of length and area for the smaller parts that make up the cube. 

These concepts can be used for a thorough hands-on examination of the concept of dimensional analysis, and the importance of the use of proper units when solving physics problems.

    

 

Parts List

 

Equipment and costs required to construct apparatus:

Item

Source

Part number

Cost

PVC pipe

Lowe’s Hardware

 

12.00

Fittings

Lowe’s Hardware

 

14.80

Cement

Lowe’s Hardware

 

0.50

Total Cost

27.30