Dimensional analysis is really cool and handy when you get used to it. To me it is baciscally using the property of 1.
You can multiply any thing by one and not change its value....Like duh..
But when you tag numbers with units(dimensions) it opens up a bit for you.
Now stuff like 1 foot = 12 inches can be seen as
1 foot/12 inches = 1.
12 inches / 1 foot = 1.
but you have an extra bookkeeping duty to keep track of the units and the the numbers.
____________________________________
So then
you have .3 feet and you want to know how many inches.
0.3 foot * [ 12 inches / 1 foot ] = ??? inches
or
(0.3*12)/1 for numbers and (foot*inches)/foot for dimensions.
3.6 inches {...note foot/foot cancels out...}
Viola!
3.6 inches.
Simple case here, but it can be dragged out on and on and usually is.
__________________________________
You could have a problem with a set of numbers like
=(1000 * 50.2 *34)/ 24 * 43 * 500
=3.3
and a set of units like
=(Liters of Y * gms of X * moles of Y ) / (Liters of Y * gms of X * L of Y)
units cancel out and you are left with
=moles of Y / Liters of Y
= Molar Y
or
overall
3.3 Molar Y
They can even be longer and I will save your sufferring by not going any further with it.
------------------------------------------
But it boils down to bookkeeping your numbers and units....
Konwing what dimensions you have
Knowing what units you want to get to.
Using relationships that equal 1 with the dimensions you want to cancel or get to.
------------------------------------------
Do the same with your problem
You have ... 15.4 mL Bracelet.
You want .... ??? oz of Gold.
Relationships that equal 1 (note these are given here and only apply to this problem...Some constants and stufF can be applied to other problem,
but do not always make that assumption)
60.0% Gold by mass....so think of 60% as parts per hundred or
60 gms Gold / 100 gms Bracelet = 1
and
14.3 gm Bracelet / mL Bracelet = 1
Work the prob
15.4 mL Bracelet * (14.3 gm Bracelet / mL Bracelet) * (60 gms Gold / 100 gms Bracelet)
ml Bracelet cancels out
gm Bracelet cancels out
you are left with gms Gold and some numbers to multiply.
but you need to convert gms to ozs, so you need a conversion table for that and you should be home free.
I know this sounds complicated and maybe in the way I walked through it made it that way, but it really is a beatiful way to walk through problems
and you can use it in very many other disciplines as well. Learn it...it will make your life a whole lot easier down the road.
Terry
|