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Weight, Density and Gravity 
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#1
Oct2404, 02:47 PM

P: 3

Hello,
I'm struggling to understand the relationship between SI units and Imperial units when it comes to weight, density and gravity. Using water as an example: I know that F = m g I also know that gravity is g = 9.81 m/s^2 or 32.174 ft/s^2 and that density of water is Pw = 1,000Kg/m^3 and that the weight of water is 62.43 pounds per cubic foot, or 62.43 lbf/ft^3. So with this knowledge what is the formula to get Weight of water (in SI units) == weight of water (in Imperial units) When starting form F = m g? Thanks! 


#2
Oct2604, 04:15 PM

P: 31

Pounds is a unit of force
Kilogram is a unit of mass Try this hyperlink: http://www.engineering.ucsb.edu/~me1...conversion.htm 


#3
Oct2704, 01:18 AM

P: 3

Ok, that's what I thought! So you would think that the SI water (water density * gravity) should equal the Imperial water (water weight * a conversion factor), right?
Well, let's see... First, the Imperial side of the equation: If [tex]1 m = 3.2808 ft[/tex] then [tex] 1m^3 = 35.31 ft^3[/tex] and if the weight of water is [tex] \frac{62.43 lb_{f}} {ft^3}}[/tex] then [tex]\frac{62.43 lb_{f}} {ft^3} \times \frac{35.31 ft^3} {m^3} = \frac{2,204.6 lb_{f}} {m^3}[/tex], right? Now for the SI side: If density of water is [tex] \frac{1,000Kg} {m^3}[/tex] and if density is another way of saying fluid mass, then the mass of water is also [tex]\frac{1,000Kg} {m^3}[/tex], right? And if [tex]1Kg = 2.2046 lb_{m}[/tex] then [tex] \frac{1,000Kg} {m^3}\times \frac{2.2046 lb_{m}}{1Kg} = \frac{2,204.6lb_{m}}{m^3}[/tex]. Wow, water = water, Right? Wrong! Even though (the Imperial water) [tex]\frac{2,204.6 lb_{f}} {m^3} = \frac{2,204.6lb_{m}}{m^3}[/tex] (the SI water) looks the same, they're not, look again! [tex] lb_{f} \neq lb_{m}[/tex], [tex] lb_{f}[/tex] is "pounds of force" whereas, [tex]lb_{m}[/tex] is "pounds of mass". We know that [tex]f=m \times g[/tex], thus, [tex] lb_{f} = lb_{m} \times g[/tex]! Conclusion As I see it, there are at lest three possible outcomes:
So, can someone help me out? What did I do wrong? Yes, I can... In writing this response, as carefully as I knew how, I discovered (just a moment ago) that I was wrong! Here's what I discovered... In (some) physics books, applications and web based conversion utilities they state that... [tex]1Kg = 2.2046 lb[/tex] However, it isn't clear that they are converting 1 unit of mass to 1 unit of weight. Therefore I think it should read: [tex]1Kg = 2.2046 lb\ (of\ weight)[/tex] or [tex]1Kg = 2.2046 lb_{f}[/tex] or better yet [tex]1Kg = 0.0685 lb\ (of\ mass)[/tex] I've spent some serious time and energy trying to figure out why it appeared that water did not equal water. I hope that sharing my frustrations and findings will help you as much as writing this has helped me. Thanks for reading. One final thought, explaining your problem (in writing or verbally) to someone will normally show you where you went wrong. kaboo 


#4
Oct2704, 02:10 AM

Emeritus
Sci Advisor
PF Gold
P: 5,197

Weight, Density and Gravity
Much of this makes no sense whatsoever:



#5
Oct3004, 10:20 PM

P: 3

I came to the physics forums to ask, what I thought, was a very straight forward question  obviously it wasn't.
Like most people, I've been raised to think in Imperial (British) system, namely feet, pounds and seconds (where a pound is a measurement of weight). I am trying to 'think' in SI. However, I can't tell if my answer makes sense because meters and grams don’t have any 'realworld' meaning to me yet. Therefore, I'm trying to figure out how to convert between SI and the old IM way of doing thing so I can see if my numbers and formulas 'looks' right. Also, I thought that the physics forums was to be a “safe” place to learn and to ask questions regarding physics, regardless if you are an expert on the subject or not. So, Cepheid, instead of “griping” about “how” I didn't setup the problem correctly or that I used thing incorrectly. Why don’t you first try answering the original question or seeking to understand what it is that I am trying to ask, and I am sorry if I didn't express things correctly. Let’s try this again. All I want to know is the force, mass and gravity (of water) in both SI and IM units, where the two sides of the equations are equal. Six values along with their proper units, that's all. If you want to show the formula on how they relate that would be a nice bonus. 


#6
Oct3104, 09:44 AM

Mentor
P: 41,315

To compare apples to apples, use the imperial unit for mass, the slug. 1 kg = 0.06852 slugs (approx). The weight of one slug can be found by w = mg > (1 slug) (32.174 ft/s^2) = 32.174 pounds.
In the imperial system, mass is properly measured in slugs. Sure, in common usage, it is also measured in pounds. To convert, use w = mg. The density of water (mass/volume) is 1000 kg/m^3. Let's convert: [tex]1000 {kg}/m^3 (\frac{0.0685 {slug}}{1 {kg}}) (\frac{1 m^3}{35.315 {ft}^3}) = 1.940{slugs}/{ft}^3[/tex]. If you want to get pounds per cubic foot, use w = mg to convert from slugs to pounds; you'll get 62.4 lbs/ft^3. Does this help? 


#7
Nov1304, 04:16 PM

P: 3

Thank you!



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