E=mc^2 using three unit systems

[ma1ic3]

If want to convert kilograms into energy, you times it by the speed of light squared in meters per second to get energy in joules. If you use grams or pounds, you use different units for both velocity and energy:

MKS: Joules = Kilograms * Meters Per Second ^2
CGS: Ergs = Grams * Centimeters Per Second ^ 2
FPS: Foot-pounds = Pounds * Feet Per Second ^2

I tried doing it with the MKS and CGS units and they both got the same answer, but the FPS one was far off. This is basically what Im doing:

180 pounds * 982080000 ^ 2 = 1.73606602752E+20 foot-pounds
82 kilograms * 299792458 ^ 2 = 7.36979246564191E+18 joules
82000 grams * 29979245800 ^ 2 = 7.36979246564191E+25 ergs

FOOT-POUNDS TO JOULES (wrong result)
1.73606602752E+20 * 1.355817948 = 2.35378947902468E+20 joules

ERGS TO JOULES (right result)
7.36979246564191E+25 * 0.0000001 = 7.36979246564191E+18 joules

It looks like 180 pounds times SOL^2 is too high of a number. And the conversation from foot-pounds to joules just makes it higher. What do I need to do to get pounds to work?

 

[Terry]

Use slugs.

 

[ponderingturtle]

It would seem to be the problem is in a error in using imperial units, while there is a lb as a mass unit some times, it might not quite work right to multiply it by the speed in feet per second of light squared. Or rather that the result will not be in the unit of foot pounds.

Look closer at your unit defintions and how they enter relate.

ed

Looking more I am sure that multiplying Lb(mass) by C^2 in feet per seconds will not result in an answer if foot pounds.

The definition of a foot pound is LB(force)xFeet(distance) similar to how jules is Newtons x Meters distance.

So a Lb(mass)x(32feet/second^2) is a pound force and multiplying it by feet will get an result in foot pounds. So there is a factor of the acceleration do to gravity that your answer is off by.

 

[Ziggurat]

Use slugs.

This is correct, but it helps to add a little bit of clarification. A pound is NOT a unit of mass. It is a unit of weight, or force, and is only related to mass by gravity (a non-universal constant). Which means that when you did your multiplication, you actually should NOT have ended up with units of energy (it should have been foot^2 * pounds/sec^2). IIRC, you divide by g to go from pounds to slugs. g is about 32 ft/sec^2, so if you divide your pound-based answer (with the real units you should have arrived at) by 32, you should get approximately the right answer, and by eye it looks like that should fix things. In other words, the weight of your object might be 180 pounts, but the mass is about 180/32 pound*sec^2/ft = 5.6 slugs.

 

[ponderingturtle]

This is correct, but it helps to add a little bit of clarification. A pound is NOT a unit of mass.

Lbs can be a unit of mass, but the kinetic energy of a object in foot pounds is not 1/2 lbs(mass)xvelocity(feet per second)^2. That would be a different unit of energy than the foot pound

 

[Ziggurat]

Lbs can be a unit of mass,

Properly they are never a unit of mass. They are used to REFER to mass, but always and only under the assumption of a specific g (which converts between mass and weight), usually that of earth. The mass is really (mass) pounds/g, so if you do 1/2 (mass) pounds/g * v^2, you will get the right answer, and the units will be in foot-pounds.

 

[ponderingturtle]

Properly they are never a unit of mass. They are used to REFER to mass, but always and only under the assumption of a specific g (which converts between mass and weight), usually that of earth. The mass is really (mass) pounds/g, so if you do 1/2 (mass) pounds/g * v^2, you will get the right answer, and the units will be in foot-pounds.

This depends alot on if you are an engeneer of a scientist. I don't see why you could not define a mass unit with the name pounds. The only reason I see why it is viewed as force is becuase you needed to weigh something. How fundamentaly different are say the two blocks that 150 years ago defined the lbs vs the kilogram?

The difference between weight and mass is important, but fully how much of the difference was commonly apritiated when the units where being defined?

 

[ma1ic3]

Ah... thanks. I knew about the whole mass/weight issue with the term "pounds", but I figured foot-pounds would actually have something to do with pounds...

Every website that gave info on it related pounds to kilograms and foot-pounds to joules too. Maybe I just need the conversion factors for different types of pounds, like I have for different types of calories and BUTS, such as international, thermochemical, nutritional, etc...

 

[ponderingturtle]

Ah... thanks. I knew about the whole mass/weight issue with the term "pounds", but I figured foot-pounds would actually have something to do with pounds...

It does, the problem is that is does not have the relationship you need to make it work. Foot pounds is the amount of work done by a force, and so it a measurement of energy. It is just not based on a lbs as a mass unit, but force unit. So the units don't work right with that kind of treatment

Every website that gave info on it related pounds to kilograms and foot-pounds to joules too. Maybe I just need the conversion factors for different types of pounds, like I have for different types of calories and BUTS, such as international, thermochemical, nutritional, etc...

They can the problem is that foot pounds are not based on a mass based pound, but useing the force based one. So they are newton meters in imperial units.

So the calculation works, the result is just in a different unit of measure than foot pounds.

 

[ponderingturtle]

You can see that it is off by a factor of 32 as 237.5/7.3697(the cited relationship in jules that the foot pounds calc is off by) and that is the 32 feet/second^2 that is in part of the foot pound calculation that was left out above.

 

[Beleth]

If want to convert kilograms into energy, you times it by the speed of light squared in meters per second to get energy in joules.

The word you are looking for is "multiply".

 

[Dave_46]

I think this thread illustrates exactly why I was glad to switch to the coherant SI units.

Dave

 

[ponderingturtle]

I think this thread illustrates exactly why I was glad to switch to the coherant SI units.

Dave

This isn't really a problem with the units, it is a problem with not understanding how they are defined. You can get that with any unit system.

 

[Lucky]

I think this thread illustrates exactly why I was glad to switch to the coherant SI units.

Dave

Pardon me, but how old are you? I'm a fairly ancient Brit with a degree in Physics, and I've never had to so much as sniff a foot-pound in my life. We started going metric in the 19th century, and it really gets up my nose (just thought I'd mention) when Americans refer to their ludicrous FPS 'system' as British, or English. OK, I know (or perhaps hope) that American scientists and engineers have abandoned it now, but they were at least 50 years behind us.

This isn't really a problem with the units, it is a problem with not understanding how they are defined. You can get that with any unit system.

I don't agree; it's obvious that any system, or standard, can be well- or ill-suited to its purpose. I can immediately think of two reasons why FPS is inferior to SI:

1) The individual systems for mass and length units are not suited to science and engineering, as they depend on arbitrary (historical) conversions from small to large (e.g. inches:feet:yards). Any metric system, which uses only powers of 10, is plainly superior.

2) FPS treats weight (force), not mass, as a fundamental dimension. That's stupid, because physics recognises mass as fundamental, and is a relic of the days when the distinction wasn't clearly understood. To make matters worse, in order to keep the colloquial equivalence between 'pound' as weight and 'pound' as mass, the system doesn't include a simple derived unit for mass. Instead it's force/g.

FPS perpetuated the confusion between 'pound' as mass and 'pound' as force. I'm told by scientists and engineers even more ancient than me that you were supposed to qualify the term as 'pounds-mass' or 'pounds-weight' (or 'poundals', but let's not even go there). It seems sensible to me (and, I guess, to any logical thinker) that the unqualified 'pound' should mean mass rather than force, as this (a) is more fundamental, and (b) corresponds better to colloquial usage over the centuries (i.e. amount of substance). Unfortunately FPS takes the opposite view, which has caused serious confusion.

Anyway, the simple answer to ma1ic3's question is that there's a missing constant for mass that's required in FPS mechanics calculations.

 

[Art Vandelay]

Ah... thanks. I knew about the whole mass/weight issue with the term "pounds", but I figured foot-pounds would actually have something to do with pounds...

If you look at it from a dimensional analysis standpoint, it's obvious that there's a problem. You have foot-pounds on the LHS, but you have pounds-foot-foot/second-second on the RHS. The latter can be rewritten as (foot-pounds)-(foot/second-second). Now it's clear that you're off by foot/second-second, which are units of g. Of course, if you're in Planck units, then c is 1.

 

[Dilb]

FPS perpetuated the confusion between 'pound' as mass and 'pound' as force. I'm told by scientists and engineers even more ancient than me that you were supposed to qualify the term as 'pounds-mass' or 'pounds-weight' (or 'poundals', but let's not even go there).

In my Canadian engineering program, we do problems with feet, pounds, and one of my favourite units, the British Thermal Unit per pound-mass degree Rankine. Quantities are given in pounds-force (lbf) or pounds-mass (lbm) where appropriate, although it usually isn't too much of a problem since basic physics is taught in metric, so we didn't have to use F=ma, _{forget the factor of g, then swear at the dead people who developed the system because everyone got that problem wrong on the assignment}. It just adds that final touch to thermodynamics and fluid mechanics that prevents anyone from ever understanding it.

 

[ma1ic3]

Anyway, the simple answer to ma1ic3's question is that there's a missing constant for mass that's required in FPS mechanics calculations.

I always assumed it was energy-mass-velocity, like in MKS. If mass is force/g, then force can't be mass * acceleration like it is in SI right?

 

[Lucky]

I always assumed it was energy-mass-velocity, like in MKS. If mass is force/g, then force can't be mass * acceleration like it is in SI right?

I don't think I explained myself very well.

You would expect that in a scientific/engineering system of units the force required to accelerate 1 <primary mass unit> by 1 <primary length unit> per <primary time unit>² would be 1 <primary force unit>. Unfortunately that is not the case in FPS; instead, 1 <primary force unit> is the force required to accelerate 1 <primary mass unit> by g, the acceleration due to gravity (and the same word is used for the primary force unit and the primary mass unit). That's because the system was devised by imbeciles.

So, either the primary force unit should be smaller by a factor equal to the numerical value of g in the system, or the primary mass unit should be bigger by this factor. There have been attempts to make the system more logical by replacing one or other of the 'pounds' by a unit that's consistent with the other (by my definition above): the poundal for force or the slug for mass, but obviously the whole thing should just have been scrapped. Anyway, if you are doing a calculation that starts with a mass (in primary units) and produces a force (in primary units) you have to divide by the numerical value of g.

It just adds that final touch to thermodynamics and fluid mechanics that prevents anyone from ever understanding it.

I have the greatest admiration for our predecessors who actually managed to do science and engineering in these units. It seems hopelessly difficult (like being able to think in French).

 

[epepke]

Note that the same problems happen when people use kilograms as a unit of weight, i.e. force. That's why you have to use the Newton meter rather than the kilogram meter as a unit of energy.

 

[Lucky]

Note that the same problems happen when people use kilograms as a unit of weight, i.e. force. That's why you have to use the Newton meter rather than the kilogram meter as a unit of energy.

I'd forgotten about the Kilogram-force, which is every bit as stupid as the pound-force (as it's not part of SI I've never had to use it). Why is it so difficult for the scientists/engineers who invent these systems to understand that units should not include arbitrary conversion constants such as the standard value of the earth's gravitational field at its surface? Seems a simple enough concept to me.