PHY131-H1S |
Math Hints |
Prof. Jason Harlow |
Introduction
to Physics I |
|
Physics Department, |
The language of science is
math. Doing the calculations involved in
physical situations familiarizes you with the concepts, develops your intuition
and allows you to discover things yourself. Here are a couple of hints which
you might find useful as the course progresses.
Units
Imagine your instructor
asks you for the height of the CN Tower. The answer,"the height of the CN
Tower is about 500" does not make sense. A correct statement is: "The height
of the CN Tower is about 500 metres." In this case, you need to
specify the unit of distance. Another unit of distance is the kilometre,
or 1000 metres. So the statement could
also be correctly worded: "The height of the CN Tower is about half a
kilometre." Both are perfectly acceptable answers. Almost every number has units. When we mark your problem sets and tests, we will deduct points if we see
numerical final answers with units missing.
Calculators
Arithmetic
can be a fun game, but I think it's much better to just type the numbers into a
calculator and concentrate on the physics and math. Don't you agree? That being said, you shouldn't just blindly
trust everything your calculator tells you. It's easy to make a typing mistake and it's good to double-check things.
You should always think about your numerical answers when you write them down
and ask yourself, "Does this make sense?"
If you don't already have one, please buy a pocket calculator for this course. It doesn't have to be fancy or expensive, but it should have an "EE" or "EXP" button on it at least.
Google's Calculator
Feature
If
you don't have a calculator handy, but you have the internet, you can use
Google instead. (Although this won't help you on a test...) Go to www.google.com. In the window,
type the expression followed by an = sign, then click
Search. For example, if you search on
"1+1=", it will respond with "2". For
multiplication, use the * sign, for divide use /. You may use parentheses, such as
"7*(6-2)/2=", which should give 14. You
can also use well known constants, such as "pi", which is 3.14159265 and "c",
which is the speed of light.
Scientific Notation
Sometimes, in this course, we
will deal with very large and very small numbers. It is very tedious to
write down numbers such as 100000000000 and 0.00000000000008, and also hard to
type them into your calculator. So in this course we will sometimes use a
short-form called "scientific notation" which uses powers of ten (e.g. 1011
and 8×10−14). For
example, 187,000,000 in scientific notation is 1.87×108. Here are
some powers of ten facts which may help you:
1000 |
= |
103 |
= |
10×10×10 |
100 |
= |
102 |
= |
10×10 |
10 |
= |
101 |
= |
10 |
1 |
= |
100 |
|
|
0.1 |
= |
10−1 |
= |
|
0.01 |
= |
10−2 |
= |
× |
0.001 |
= |
10−3 |
= |
×× |
Remember that raising a
number to a power just means multiplying that number
by itself the number of times in the exponent. For example, 24=2×2×2×2=16.
A BIG HINT about typing numbers
in scientific notation into your calculator: The or key on your calculator stands for "times ten
to the power..." So, for example, to type 6.1×109, you would type . To type a negative power of ten,
such as 3.4×10−4, on most inexpensive calculators you would type . For scientific notation on Google, use "e" to stand for "times ten to the power". For example, 3.4×10−4 is 3.4e-4.
Practice exercises: Use your calculator or Google to
solve:
x = 1+1.5×10−4
y = 2.2×1015/(1.1×1012)
z = (9×10−25) × (5×10−34)
(Answers: x=1.00015,
y=2000, z=4.5×10−58, if you got them all right, then you are
an expert on scientific notation!!)