2007 AAPT Summer Meeting
Greensboro, NC
Easy
Cubic Meter
Brett
Carroll
Green River Community College
12401 SE 320^{th} St.
Auburn, WA 98092
2538339111 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 ¾Ó pipe are cut to
slightly less than 1 meter in length (to compensate for the thickness of the
corner fittings), and fitted into 3way pipe fittings.
For ease of use, it is helpful to assemble two
individual 1meter squares and join them permanently at the corners with pipe
cement. The final cubic meter can
then be assembled in the classroom (it wonÕt fit through most doors!) by
joining the two square meters together with four (almost) meterlong pieces of
pipe that are left uncemented for easy disassembly. Having the two squares preassembled greatly cuts down on
lastminute 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 1dimensional meter, the gluedtogether squares for a 2dimensional
square meter, and the fully assembled cube for a 3dimensional 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
handson examination of the concept of dimensional analysis, and the importance
of the use of proper units when solving physics problems.
Equipment and costs required
to construct apparatus:
Item 
Source 
Part
number 
Cost 
PVC
pipe 
LoweÕs
Hardware 

12.00 
Fittings 
LoweÕs
Hardware 

14.80 
Cement 
LoweÕs
Hardware 

0.50 
Total Cost 
27.30 