Calculating Mass
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Check this link : http://www.grc.nasa.gov/WWW/K-12/airplane/mass.html
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Think about it in terms of the units and it makes much more sense, for example:
Density in kg/m3
Volume in m3
How do you turn kg/m3 into kg? Multiply by m3, thus to obtain volume in kg:
vol = density * volume
In calculations whatever you do to numbers you must also do to the units and vice-versa, so if you're ever stuck then look at the units involved and work it out from there.
HTH,
--rob
Density in kg/m3
Volume in m3
How do you turn kg/m3 into kg? Multiply by m3, thus to obtain volume in kg:
vol = density * volume
In calculations whatever you do to numbers you must also do to the units and vice-versa, so if you're ever stuck then look at the units involved and work it out from there.
HTH,
--rob
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robdesbois
Rob, I have applied that method all the way through highschool and it works really well. You only have to remember one additional thing: if there's any kind of circular motion involved, you usually have to add 2*pi. (When going from RPM and torque to power for instance.) I learned that the hard way...
I wonder if Einstein used this method too to derive E=Mc2?
Oh, and obviously this only works with number from the SI standards. With miles, feet, pounds, stone, inches, gallons, knots, horsepowers and so forth all bets are off!
I wonder if Einstein used this method too to derive E=Mc2?
Oh, and obviously this only works with number from the SI standards. With miles, feet, pounds, stone, inches, gallons, knots, horsepowers and so forth all bets are off!
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BackPacker,
Likewise - I didn't think of this method of 'remembering' formulae until a fantastic day in a Chemistry lesson when it struck me. Been using it ever since and it's brilliant.
Regarding only using SI units - that's not quite correct, you just have to be using the same units throughout, e.g.
P = pressure in PSI (pounds per square inch)
M = mass in pounds
A = area in square inches
then P = M / A
which reads as pressure equals mass per area, and 'per' just means divide
Likewise - I didn't think of this method of 'remembering' formulae until a fantastic day in a Chemistry lesson when it struck me. Been using it ever since and it's brilliant.
Regarding only using SI units - that's not quite correct, you just have to be using the same units throughout, e.g.
P = pressure in PSI (pounds per square inch)
M = mass in pounds
A = area in square inches
then P = M / A
which reads as pressure equals mass per area, and 'per' just means divide
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The problem is that outside the SI system you would not necessarily use the same base and derived units if you want to stick to standard speak. Torque in pound-feet, revolutions in RPM. Try to make that into horsepower... The beauty of SI is its consistency: five or so base units, and everything else is 1:1 derived from these units.
But I don't need to tell you this, I guess... :-)
"Air Force bla, descend 3.000 feet, QNH 1013" "Can we have that in inches please, sir?" "Sure, descend 36.000 inches, QNH 1013"
But I don't need to tell you this, I guess... :-)
"Air Force bla, descend 3.000 feet, QNH 1013" "Can we have that in inches please, sir?" "Sure, descend 36.000 inches, QNH 1013"
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Hey, thanks for that =)
I was stupidly dividing, i was doing Density / Mass to find volume.
I am having a stupid moment on re-arranging formulas.
You see i know Density = mass / volume and Volume = mass / density, but i have had a mental blank and cant figure out why Mass = density * volume, i dont get why i think its divide.
Shed some light please? I am sure its a stupid complication on my part, seem to have a mental blank on re-arranging formula as i have a few other forumulas for pressure to figure out, but dont get when its right to multiply and divide?
cheers
I was stupidly dividing, i was doing Density / Mass to find volume.
I am having a stupid moment on re-arranging formulas.
You see i know Density = mass / volume and Volume = mass / density, but i have had a mental blank and cant figure out why Mass = density * volume, i dont get why i think its divide.
Shed some light please? I am sure its a stupid complication on my part, seem to have a mental blank on re-arranging formula as i have a few other forumulas for pressure to figure out, but dont get when its right to multiply and divide?
cheers
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It's very basic math. Forget what the numbers stand for. If you have a formula like:
a = b / c
But you already have a and b, but want to know c, here's what you do.
In any formula, you can multiply both sides of the = sign with the same amount while retaining validity. Or divide each side by the same amount, or add or subtract the same amount. As long as you do the same thing consistently to both sides. And remember, a divided by a equals 1.
So I multiply both sides of the previous formula by c, to get:
a * c = b / c * c
which equals
a * c = b * c/c
which equals
a * c = b * 1
which equals
a * c = b
Then I divide both sides by a:
a * c / a = b / a
which equals
a/a * c = b / a
which equals
1 * c = b / a
which equals c = b / a
As I said, very basic math.
By the same token:
Density = mass / volume (a = b / c)
Density * volume = mass (a * c = b)
volume = mass / density (c = b / a)
a = b / c
But you already have a and b, but want to know c, here's what you do.
In any formula, you can multiply both sides of the = sign with the same amount while retaining validity. Or divide each side by the same amount, or add or subtract the same amount. As long as you do the same thing consistently to both sides. And remember, a divided by a equals 1.
So I multiply both sides of the previous formula by c, to get:
a * c = b / c * c
which equals
a * c = b * c/c
which equals
a * c = b * 1
which equals
a * c = b
Then I divide both sides by a:
a * c / a = b / a
which equals
a/a * c = b / a
which equals
1 * c = b / a
which equals c = b / a
As I said, very basic math.
By the same token:
Density = mass / volume (a = b / c)
Density * volume = mass (a * c = b)
volume = mass / density (c = b / a)
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Trivial to you and me perhaps, but apparently not for planecrazy.eu...
"You see i know Density = mass / volume and Volume = mass / density, but i have had a mental blank and cant figure out why Mass = density * volume, i dont get why i think its divide."
"You see i know Density = mass / volume and Volume = mass / density, but i have had a mental blank and cant figure out why Mass = density * volume, i dont get why i think its divide."
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Have you heard of a 'multiplication triangle'? Since there are quite a few formulae of the form X = Y/Z, there's a nifty trick if you haven't got the hang of rearranging.
The concept is usually taught using the distance, speed and time example. Draw a triangle:
/\
/ D\
/S|T\
To find a term, cover it and read the remaining items, e.g. distance D = ST = speed*time.
time T = D/S = distance / speed
Incidentally, to rearrange I find it helps to do the following: pick the term you want to be on its own. Remember that anything you do to one side of the equals sign you must do to the other. Refer to Backpacker's post for how this works.
@McAero - surely the temperature affects the density therefore doesn't need to be factored in at this point? Higher temp => lower density. Density in kg/m3 doesn't involve temperature so by definition must be equal to the mass in kg divided by volume in m3.
Oh btw Backpacker - nice quote, I like it
The concept is usually taught using the distance, speed and time example. Draw a triangle:
/\
/ D\
/S|T\
To find a term, cover it and read the remaining items, e.g. distance D = ST = speed*time.
time T = D/S = distance / speed
Incidentally, to rearrange I find it helps to do the following: pick the term you want to be on its own. Remember that anything you do to one side of the equals sign you must do to the other. Refer to Backpacker's post for how this works.
@McAero - surely the temperature affects the density therefore doesn't need to be factored in at this point? Higher temp => lower density. Density in kg/m3 doesn't involve temperature so by definition must be equal to the mass in kg divided by volume in m3.
Oh btw Backpacker - nice quote, I like it
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you can also use the 'pyramid' method for three quantities:
mass
______________
density * volume
If you want to know the equation for mass, cover it up mass (in your head or on paper) so the image of the equestion above becomes:
_______________
density * volume
so mass = density * volume.
Likewise if you want to know the equation for volume, cover 'volume' and the image of the equation will be:
mass
________
density
so volume = mass/density
You can use this method for any equation with 3 quantities
hope that helps
oh, just noticed it the same as robdesbois post
mass
______________
density * volume
If you want to know the equation for mass, cover it up mass (in your head or on paper) so the image of the equestion above becomes:
_______________
density * volume
so mass = density * volume.
Likewise if you want to know the equation for volume, cover 'volume' and the image of the equation will be:
mass
________
density
so volume = mass/density
You can use this method for any equation with 3 quantities
hope that helps
oh, just noticed it the same as robdesbois post
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Thanks guys for the help, its cleared it all up for me now =)
I have moved on to pressure and thermofluids, can work those equations now.
I do feel a little stupid asking, but i honestly forgot, no matter how basic stuff is, sometimes you do forget, especially when the last maths lesson you had was around 7 years ago.
Anyways, thanks to you all...
I have moved on to pressure and thermofluids, can work those equations now.
I do feel a little stupid asking, but i honestly forgot, no matter how basic stuff is, sometimes you do forget, especially when the last maths lesson you had was around 7 years ago.
Anyways, thanks to you all...
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McAero - surely the temperature affects the density therefore doesn't need to be factored in at this point? Higher temp => lower density. Density in kg/m3 doesn't involve temperature so by definition must be equal to the mass in kg divided by volume in m3.
