1.20 If A and B are vectors specified in magnitude-direction form, and C = A + B

Question

1.20 If A and B are vectors specified in magnitude-direction form, and C = A + B is to be found and to be expressed in magnitude-direction form. how is this done? That is, what is the procedure for adding vectors that are given in magnitude-direction form? 1.21 Suppose you solve a problem and your calculator's display reads 0.0000000036. Why not just write this down? Is there any advantage to using the scientific notation? 1.22 Since the British system of units is more familiar to most people in the United States, why is the international (SI) system of units used for scientific work in the United States? Is it possible to add three equal-length vectors and obtain a vector sum of zero? If so, sketch the arrangement of the three vectors. If not explain why not. 1.23

Explanation / Answer

1.22 There is a huge disconnect between the science that we do (SI units, commonly interchanged with the Metric System) and how we live our daily lives, (U.S. Customary Units, not Imperial Units).

U.S. scientists are used to converting units, an ideal scientifically literate society includes artists, public servants, business owners, and waitresses — people who don’t have to use the metric system on a regular basis — translating units is one more barrier to understanding the math and science that is used in research.

The only examples that come to my mind where the metric system is in common use in the United States are:

- Miles-per-hour Kilometers-per-hour speedometers in our vehicles

- A 750ml bottle of wine

- A 1-liter (1,000ml) Nalgene bottle

- The 100 meter dash

- 2 liter soda bottles

- 5k and 10k runs/races

- Most food nutrition labels (How many people actually read those?

Yet all science is done in the language of SI units. If the goal is for the non-scientific public to be able to engage regularly and enthusiastically with science, wouldn’t it make sense for scientists and non-scientists to speak the same language?

To really make SI units and the metric system commonplace in the United States requires more than a little effort on our part. Imagine how many local, state, and federal authorities would be required to change millions of road signs, food packaging, gas station signs and sports fields. And on top of that, does the general public want to make the switch?

Some selected history.

The reasons that hold us back from converting range from stubbornness to cost. In 1975, thanks to President Gerald Ford and Congress, the Metric Conversion Act was passed which would have led to the metric system being the preferred system of weights and measures in the United States. This act created the United States Metric Board, which was abolished in 1982, by President Reagan.

From The United States and the Metric System, NIST LC 1136: “The efforts of the Metric Board were largely ignored by the American public, and, in 1981, the Board reported to Congress that it lacked the clear Congressional mandate necessary to bring about national conversion. Due to this apparent ineffectiveness, and in an effort [by President Reagan] to reduce Federal spending, the Metric Board was disestablished in the fall of 1982.”

Some readers may be familiar with the “We the People” petition that the White House website hosts. As of this moment, over 35,000 people have digitally signed a petition to make the metric system the official system of weights and measures of the United States. Possibly another act from the federal government is needed to really get things moving again.

A more detailed history can be read here.

Solutions.

Thankfully, the metric system has been taught in schools and this should continue. From my experience, however, it was only as a way to solve given problems. Physics was taught in the metric system, as was chemistry. But when I got to my algebra class, and even in shop class, (a prime opportunity to “feel” what 50 centimeters was), we measured 20 inches (not the same, by the way). I would recommend that all rulers in school should all be inches and centimeters, though I must admit I attended a science teacher workshop and we were given 12 foot tape measurers to take back home.

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