# Question about conversion to newtons

## Homework Statement

Why when I convert kg to newtons I simply multiply by g. But when I convert lbs I multiply by 4.48?? It makes no sense ! Shouldn't it be 32.2? Thanks, Kate

PeterO
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## Homework Statement

Why when I convert kg to newtons I simply multiply by g. But when I convert lbs I multiply by 4.48?? It makes no sense ! Shouldn't it be 32.2? Thanks, Kate

## The Attempt at a Solution

What are you converting the lbs to?

You said kg to N, but only said when I convert lbs?

kg are a unit of mass, Newtons of force, pounds of weight (force). Since the pound is already a force, multiplying by an acceleration doesn't result in a force.
The pound-mass is the mass of an object with 1 pound-force of weight, using the standard gravity as the acceleration of gravity. If you know that 1 lbm=2.2 kg, you can then get the value of 4.448 from $1lb_f=\frac{1}{2.2}kg*9.81\frac{m}{s^2}=4.448N$

On the other hand, if you wanted to go from pound-mass to pound-force, then you would use 32ft/s^2.

Last edited:
PhanthomJay
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The pound-mass concept is as bad or worse than the kilogram-force concept. Both should be deleted from all physics texts, or perhaps just referenced for historical purposes.

When a person with a mass of 70 kg in a country other than the USA or Myanmar steps on a bathroom scale, the scale most likely reads 70 Kg , and the lay person says "I weigh 70 kg". The technical person knows that this is wrong, and that the person weighs about 700 N. I seriously doubt that grandma knows what a Newton is, so she is content that she weighs 70 kg. A Physicist should not be content with such a concept.

When a person of the same mass steps on a scale in the US, the scale reads about 154 pounds. Grandma says "I weigh 154 pounds", and she is correct, as confirmed by the Physicist. Little does grandma know, or care, that her mass, as confirmed by the Physicist, is 154/32 or about 4.8 slugs. This is the proper unit of mass in the technical world in the USA.

One slug of mass weighs 32 pounds, on Planet Earth, per W = mg.
One Kg of mass weighs 9.8 N, on Planet Earth, per W =mg.
A net force of 1N will accelerate a mass of 1 kg at 1 m/s/s, anywhere, per Fnet = ma.
A net force of 1 pound will accelerate a mass of 1 slug at 1 ft/s/s, anywhere, per Fnet = ma.

Pounds and newtons are related by the conversion factor already noted.

Any attempt to use the pound-mass concept in physics will result in tearing your hair out.

Great explanation PhanthomJay. The only time 1 pound = 0.45 kg or 1 kg = 2.2 pounds is on planet Earth. Pounds are an English unit of Force and slugs are the English unit of mass. Newtons are the SI unit of Force and kilograms are the SI unit of mass. The acceleration due to gravity in English units is 32 feet/sec/sec. In the more civilized world, the acceleration due to gravity is 9.8 meters/sec/sec.
Since we all live on Earth, we (wrongly) allow this idea of converting pounds directly to kilograms to slide.

PeterO
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Great explanation PhanthomJay. The only time 1 pound = 0.45 kg or 1 kg = 2.2 pounds is on planet Earth. Pounds are an English unit of Force and slugs are the English unit of mass. Newtons are the SI unit of Force and kilograms are the SI unit of mass. The acceleration due to gravity in English units is 32 feet/sec/sec. In the more civilized world, the acceleration due to gravity is 9.8 meters/sec/sec.
Since we all live on Earth, we (wrongly) allow this idea of converting pounds directly to kilograms to slide.

I don't go along with your references here; had you said the US units rather than English units I would probably go along with you.

As for a "weighing 75 kg", as told by the bathroom scales, I believe the full description is really "weighs the same as a mass of 75 kg", and is just shortened , in common usage, to "weighs 75 kg" in much the same way as that well known city, whose veeery long name is shortened, in common usage, to Los Angeles.
lbs is also a unit of mass outside the US, with poundal the unit of force.
Mass kilogram (kg) - Force Newton (N)
Mass Pound (lb) - Force Poundal-(lbl)

Both those references come from the mks and fps system of units respectively

[metre-kilogram-second and foot-pound-second]

PhanthomJay
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Yikes the dreaded poundal! No one in the states , whether tech or non tech, uses it. It's tough enough having 2 systems of measure , let alone several. Let's say good bye to the poundal throughout the known world. I'd toss that one out before pound-mass.

PeterO
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Yikes the dreaded poundal! No one in the states , whether tech or non tech, uses it. It's tough enough having 2 systems of measure , let alone several. Let's say good bye to the poundal throughout the known world. I'd toss that one out before pound-mass.

Don't worry, no sooner did I learn there was a poundal and the country went metric, so it is now metres [note the spelling - re for the unit, er for a measuring device] and kilograms.
However - had never heard of the slug until I read it on here about 6 months ago.

Thanks a million! This REALLY clarified things for me! I truly appreciate your help! Kind regards, Kate
PS Indeed I was on the verge of tearing my hair out :)

PhanthomJay
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Indeed I was on the verge of tearing my hair out :)
We should both be thankful we still have hair

However - had never heard of the slug until I read it on here about 6 months ago.
No worry, even most americans, tech or non-tech, don't know what a slug is. Probably because we deal a lot with equilibrium and sum of forces = 0 , so it doesn't often matter. And when required to use mass, we just take the object's weight on earth and divide it by 32, and don't call it anything.