0.8 Phy1050: units and dimensional analysis  (Page 2/11)

Listings

• Listing 1 . Convert from paces to miles.
• Listing 2 . Free fall exercise.
• Listing 3 . A plotting exercise.

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

General background information

As a young engineering student many years ago, I was told that when evaluating mathematical expressions, I should always embed the units in theexpression, manipulate them algebraically, and confirm that the units that survive until the end of the evaluation are correct relative to the problemspecifications.

Three good reasons

There are at least three good reasons for following this procedure:

• It shows what the units of the result are. A common mistake is to get the correct numerical result of a calculation but to write it with the wrong units.
• It shows where unit conversions must be performed. If units that should have canceled do not cancel, we need to go back and perform the necessary conversions. Forexample, when a speed in miles per hour is being calculated and the result comes out with units of miles per second, we should convert seconds to hours.
• It helps to locate mistakes. If a velocity (meters per second) is being calculated and the units come out as seconds per meter, we know to look for an error.

Formatting mathematical expressions

A significant disadvantage

This is an area where blind students may be at a significant disadvantage relative to sighted students due mainly to the fact that blind students usingscreen readers and Braille displays can only see one line of text at a time. It is much easier (for me anyway) to correctly manipulate the units when theexpression is written on two or more lines.

Multiple-line format

What I mean by this is that a sighted student would typically write a fraction as a horizontal line with the numerator above the line and thedenominator below the line using superscripts to indicate exponents. The product of two fractions would typically be written in the same format with a multiplication indicator joining the twofractions.

Single-line format

A blind student constrained to seeing only one line of text at a time would probably need to write and evaluate the product of the two fractions using aformat something like that shown in Figure 1 .

With enough time and practice, I might become almost as proficient in evaluating expressions as shown in Figure 1 as in evaluating expressions in a multiple-line format, but I'm afraid that I would need a lot oftime and a lot of practice to achieve that proficiency.

We must work with what we are given

However, we must work with what we are given so the mathematical expressions in this module (and most of the other modules as well) will all be in a single-line format. The good news isthat the single-line format can usually be easily translated into a format that is suitable for evaluation using JavaScript.