FHSST Physics/Units/How Units Can Help You
How Units Can Help You
We conclude each section of this book with a discussion of the units most relevant to that particular section. It is important to try to understand what the units mean. That is why thinking about the examples and explanations of the units is essential.
If we are careful with our units then the numbers we get in our calculations can be checked in a 'sanity test'.
What is a 'sanity test'?
This isn't a special or secret test. All we do is stop, take a deep breath, and look at our answer. Sure we always look at our answers—or do we? This time we mean stop and really look—does our answer make sense?
Imagine you were calculating the number of people in a classroom. If the answer you got was 1 000 000 people you would know it was wrong—that's just an insane number of people to have in a classroom. That's all a sanity check is—is your answer insane or not? But what units were we using? We were using people as our unit. This helped us to make sense of the answer. If we had used some other unit (or no unit) the number would have lacked meaning and a sanity test would have been much harder (or even impossible).
It is useful to have an idea of some numbers before we start. For example, let's consider masses. An average person has mass 70 kg, while the heaviest person in medical history had a mass of 635 kg. If you ever have to calculate a person's mass and you get 7000 kg, this should fail your sanity check—your answer is insane and you must have made a mistake somewhere. In the same way an answer of 0.00001 kg should fail your sanity test.
The only problem with a sanity check is that you must know what typical values for things are. In the example of people in a classroom you need to know that there are usually 20-50 people in a classroom. Only then do you know that your answer of 1 000 000 must be wrong. Here is a table of typical values of various things (big and small, fast and slow, light and heavy—you get the idea):
(NOTE TO SELF: Add to this table as we go along with examples from each section)
Note that you do not have to memorize this table. However, read it so that you can refer to it when you do a calculation.