# Pound force to kg?

ok i understand how the conversions work and everything... 1 kg = 2.2 pounds... i was just thinking about this for a while and its kinda eating at me cuz i cant put it into good words.

why is it that when we measure something in the U.S. it is in pounds and we say that is the force it has from gravity not its mass but then if we measure something in kilograms it is mass... so they are different types of units but yet they can be converted into each other?

cristo
Staff Emeritus
There are two different "pounds"; one is a mass and one is a force. When you perform the conversion you are converting a mass in kg into a mass in lb. The pound force is a measure of force, and is different, but related, to the pound: see here.

stewartcs
ok i understand how the conversions work and everything... 1 kg = 2.2 pounds... i was just thinking about this for a while and its kinda eating at me cuz i cant put it into good words.

why is it that when we measure something in the U.S. it is in pounds and we say that is the force it has from gravity not its mass but then if we measure something in kilograms it is mass... so they are different types of units but yet they can be converted into each other?

Because kg and kgf are mistakenly taken to be equivalent, as are lbm and lbf. They are not equivalent. They are coincidentally equal to the same value at sea-level, i.e. 1 lbm = 1 lbf only under the same gravitational acceleration.

This is a major point of confusion in the US Customary System since the common form of lbf, which is meant to represent weight not mass, is written as lb instead of the appropriate lbf. Hence the confusion.

CS

ok so 1 kg is equal to 2.2 pound-mass and 1 newton is equal to .22 pound-force? I guess im just more familiar with pounds as force and slugs as mass... thanks for your input

ps... if i weigh something on a scale do i concider that to be pounds-force or mass?

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Although, obviously, scales are actually measuring the weight (the downward force on the scale) they are calibrated to display the mass (they are basically calibrated so that the amount is divided by 9.81 or whatever).

sweet... thanks for clearing up that confusion

D H
Staff Emeritus
ok so 1 kg is equal to 2.2 pound-mass and 1 newton is equal to .22 pound-force?
Correct.
I guess im just more familiar with pounds as force and slugs as mass
Force expressed in pounds-force and mass expressed in slugs lets you use Newton's second law in its canonical form, $F=ma$. With force and mass expressed in pounds-force and pounds-mass, one must use the more general form $F=kma$.

ps... if i weigh something on a scale do i concider that to be pounds-force or mass?
A balance scale require that the object to be "weighed" have some actual weight but measures the object's mass. Spring scales require require that the object to be "weighed" have some actual weight but measures the object's apparent weight.

On some books I saw the equation F = m·a/gc, what does the gc stand for ?

FredGarvin
$$g_c=32.1740 \frac{lb_m*ft}{lb_f*s^2}$$
It is the inverse of k in $\mathbf F=km\mathbf a$. Newton's second law says that force is proportional to the product of mass and acceleration: $\mathbf F \propto m\mathbf a$, or $\mathbf F=km\mathbf a$. SI units were designed so that the constant of proportionality is exactly one. The English pound force and pound mass (and pound sterling, for that matter) were defined a bit differently: The gravitational force exerted by the Earth on a mass of one pound (mass) at the surface of the Earth is one pound force (and in days of long ago, one pound mass of sterling silver was a pound (money)). Back to Newton's second law. An object dropped a short distance above the ground will accelerate at g=32.2 feet/second2. By Newton's second law, $a = F/(mk)$. Thus [itex]k= 1/g[/tex], the acceleration due to gravity if one uses English units.