Density of soap

Laboratory 01 in SC 130 Physical Science focused on the linear relationship between volume and density for soap. Harmony beauty soap with a density greater than one gram per cubic centimeter was used along with Ivory soap with a density of less than one gram per cubic centimeter. The soap was carved into square chunks so the volume could be calculated from length × width × height.

Nayleen masses the Ivory soap

The class began with the Freeman Dyson quote:

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. ... the fact that nature talks mathematics, I find it miraculous. ... I spent my early days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too.

 Joyleen and Jeremy

At the start of the class I noted that if the density of the soap was less than one gram per cubic centimeter, the soap would float. If the density of the soap was more than one gram per cubic centimeter, then the soap would sink. The density would be determined from the slope of the graph later in the class period.

Merseny carves a chunk of soap

I also included a quote from William Gilbert on the need to perform experiments and when experimenting to "handle the bodies carefully, skilfully, and deftly, not heedlessly and bunglingly."

Massing the SafeGuard soap, a new addition summer 2011. Maimai massing.

This class also provides an opportunity to introduce the mass balance and measuring in centimeters. After gathering the data on the length, width, height, and mass of the soap, the class moved upstairs to the computer laboratory to plot the data and determine the slope of the best fit line.

Lavanaleen enters data gathered by Lewis and Jackleen into a laptop computer

The class does not presume prior knowledge of linear regressions, on the contrary the class teaches the concepts of slope and intercept through the science encountered in the class.

Raynard masses Harmony soap

Only after the students work out their slope data do I ask them to predict what their soap chunks will do when dropped into a beaker of water. Each makes a prediction. Then I drop the Harmony soap chunks into the water, followed by the Ivory soap chunks. As Dyson noted, the students made a mathematically based prediction and the soap knew what to do. 

 Kemble and Arthur working with Harmony soap

A chart of partial data from the three soaps

Data table, values rounded:

Volume (cm³)	Ivory mass (g)	Safeguard mass (g)	Harmony mass (g)
0	0	0	0
93	88
40	33
35	27
27	26
29		32
5		3
18		27
20			27
17			24
15			21
13			18