Density of soap and speed of a ball

The fall term began with a laboratory that introduces measurement through the measurement of the density of soap.
Regina Moya measures her soap

I began the laboratory 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.

 Petery Peter measures her soap slab

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

Thus the laboratory echoes the quote. The students obtain the slope of the volume versus mass relationship, which is the density, to predict whether the soap will float or sink. The soap then knows what to do - if the students have measured carefully as admonished to do so by William Gilbert. Gilbert spoke on the need to perform experiments and when experimenting to "handle the bodies carefully, skilfully, and deftly, not heedlessly and bunglingly."

Macy records data

Sharisey records data, Ioakim measures the soap

In the second half of the laboratory the class moves to the computer laboratory to work on the laboratory report, determine the slope of the linear regression.

The laboratory always includes Ivory soap in the mix, which floats in water. This surprises some students who have never used Ivory soap. This allows me to repeat after Dyson, "You predicted the soap would float and the soap knew what to do." I also include sinking soaps. One complication this term: in the 8:00 class every group with Ivory had a slope greater than one. Measurement errors.

Laboratory two used a modification I first used this past summer. In the past the goal of ensuring that time was truly the independent variable and the distance was the dependent variable, the ball was rolled and the distance to the one, two, three, four, five, and six second mark was noted. This ensured the time was independent and made easier putting all of the data into a single graph. The common x-axis values meant all of distance values were in the same rows. At one time a ramp was used to try to replicate the ball speed.

Sharisey pitches a ball through an 800 cm stretch of sidewalk marked off every 200 cm with chalk marks

When the covered walkways went up, I moved the class from the gym parking lot to the covered walkway. This made the lab more functional on rainy days. I dispensed with the ramp as I found that pitchers could repitch the ball at a fairly constant rate. The use of a pitcher and preset times meant the laboratory only needed a single time who called out the seconds. Six students then jumped to the location of the ball at the nth second.

Ball on the roll, tape measure to the right

The complication was that the distance for the first second was always too big, yielding a large drop in speed from the first to the second second. Attempts to find ways to eliminate reaction time and reduce this error were futile, and the error was particularly problematic at high speeds.

Pitching a slow ball over a 400 cm stretch marked every 100 cm, Everashi bowling, Erika and Casan-Jenae timing

Last summer I rode a RipStik across preset distances and used the times to generate the data. Given that the class has multiple lap timing chronographs, this term I gave teams of two a chronograph and had them time the ball at each chalk mark crossing. The use of different distances accomodated a wider range of ball speeds, and the "first second" error all but disappeared. 

Meigan as catcher on the 400 cm stretch

Detail view of the 200 cm long lines and 100 cm short lines

Everashia proved to be a superb bowler 

For the fastest ball roll timing was done at 800 cm and 1600 cm only. 

To accommodate lack of a common set of x-axis values, the table used a diagonal layout. This is more complex than the original table layout which had only seven rows (zero to six seconds). 

The data was far more linear than any observed in the past. Note the addition of a stationary ball at 300 cm. The slowing of the ball seen over a six second span is not seen in these runs of under three seconds.

This format for the laboratory is not yet in the text book.


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