Dimensional Analysis
How far away is the
beach from where you live? If you're American, you'd probably answer in miles. But if you're
from almost every other country in the world, you'd probably answer in kilometers.
So while
Susie from America might say that she lives 2 miles from the beach, Kiara from Australia might
say that she lives 3.2 kilometers away from the beach. 2 miles and 3.2 kilometers are both the
same distance, but they're just represented in different units.
Since people use different
units, it's critical that we're able to convert between units so we can accurately convey
measurements to one another. In science, there is a standardized system of units, known
as SI units. While kilometers are the standard unit for distance, miles are a customary unit
because within American culture, people are accustomed to using them.
So how do we convert
from one unit to another? First, we need to know what the conversion factor is. We can look this up
online or in a textbook!
Let's do an example!
If I travel 241 kilometers to get to the beach, how
far is that in miles?:
The conversion factor tells us that 1 km = 0.6214 miles. We can write this
conversion factor as:
0.6214 miles divided by 1 kilometer
Then we multiply the distance
in kilometers by the conversion factor:
So, 241 kilometers times 0.6214 miles over 1 kilometer
equals 150 miles. The kilometers in the numerator cancel out with the kilometers in the denominator,
leaving us with the distance in miles.
We can write the general formula for converting units
as:
Initial units times desired units over initial units equals desired units.
Okay, now let's try
a challenge problem!
We re driving to the beach at 60 miles/hour. What is that in kilometers per
second?
So first, let s get our conversion factors. We know that 1 km = 0.6214 miles.
And that one hour = 60 minutes. And that one minute equals 60 seconds.
I like to work out
my dimensional analysis problems on train tracks like this because it's easy to follow which units
cancel out. You want all the unwanted units to cancel out until you're only left with the units
that you desire. So 60 miles per hour becomes kilometers per miles then kilometers per minute
and finally kilometers per second! You multiply across the top and then divide by all the numbers
in the bottom row to obtain your final answer with the desired units!
In this case our final answer
is 0.027 kilometers per second.
Converting units can be tricky but is extremely important
and like everything else, becomes easier with practice. And maybe after solving all
of your dimensional analysis problems, you can travel however many centimeters or kilometers
or inches it will take you to get to the beach!