01-25-2005, 11:16 AM
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#107 (permalink)
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Junkie
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Quote:
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Originally Posted by supersix2
As a result, a pound and a kilogram are not actually the same thing. Infact this is the one thing that really annoys me about the english system.
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No, they are the same thing. You are just getting lbf and lb mixed up. The imperial system just uses two different units for mass.
http://en.wikipedia.org/wiki/Force#I...force_and_mass
Quote:
Imperial units of force and mass
The relationship F=m·a mentioned above may also be used with non-metric units. If those units do not form a consistent set of units, the more general form F=k·m·a must be used, where the constant k is a conversion factor dependent upon the units used.
For example, in imperial engineering units, F is in "pounds force" or "lbf", m is in "pounds mass" or "lb", and a is in feet per second squared. However, in this particular system, you need to use the more general form above, usually written F=m·a/gc with the constant normally used for this purpose gc = 32.174 lb·ft/(lbf·s2) equal to the reciprocal of the k above.
As with the kilogram, the pound is colloquially used as both a unit of mass and a unit of force. 1 lbf is the force required to accelerate 1 lb at 32.174 ft per second squared, since 32.174 ft per second squared is the standard acceleration due to terrestrial gravity.
Another imperial unit of mass is the slug, defined as 32.174 lb. It is the mass that accelerates by one foot per second squared when a force of one lbf is exerted on it.
When the acceleration of free fall is equal to that used to define pounds force (now usually 9.80665 m/s²), the magnitude of the mass in pounds equals the magnitude of the force due to gravity in pounds force. However, even at sea level on Earth, the actual acceleration of free fall is quite variable, over 0.53% more at the poles than at the equator. Thus, a mass of 1.0000 lb at sea level at the Equator exerts a force due to gravity of 0.9973 lbf, whereas a mass of 1.000 lb at sea level at the poles exerts a force due to gravity of 1.0026 lbf. The normal average sea level acceleration on Earth (World Gravity Formula 1980) is 9.79764 m/s², so on average at sea level on Earth, 1.0000 lb will exert a force of 0.9991 lbf.
The equivalence 1 lb = 0.453 592 37 kg is always true, anywhere in the universe. If you borrow the acceleration which is official for defining kilograms force to define pounds force as well, then the same relationship will hold between pounds-force and kilograms-force (an old non-SI unit which we still see used). If a different value is used to define pounds force, then the relationship to kilograms force will be slightly different—but in any case, that relationship is also a constant anywhere in the universe. What is not constant throughout the universe is the amount of force in terms of pounds-force (or any other force units) which 1 lb will exert due to gravity.
By analogy with the slug, there is a rarely used unit of mass called the "metric slug". This is the mass that accelerates at one metre per second squared when pushed by a force of one [Kilogram force|kgf]]. An item with a mass of 10 kg has a mass of 1.01972661 metric slugs (= 10 kg divided by 9.80665 kg per metric slug). This unit is also known by various other names such as the hyl, TME (from a German acronym), and mug (from metric slug).
Another unit of force called the poundal (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl.
In conclusion, we have the following conversions:
1 kgf (kilopond kp) = 9.80665 newtons
1 metric slug = 9.80665 kg
1 lbf = 32.174 poundals
1 slug = 32.174 lb
1 kgf = 2.2046 lbf
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Good luck in engineering school. Make sure you know your imperial units. Chances are pretty good that you will almost always use imperial and rarely use SI. That's how it is for me and most of the people I know. |
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